Age dependent vitality loss in Calluna heather plants OR 3.2: LMM
Dipl.-Biol. Jenny Schellenberg
2021-02-10
This documentation contains the LMM modeling procedure for the article mentioned above. For more method details, see the methdos section of the article.
In this documentation, dataroot refers to subdatasets with _RA, for datastem subdatasets, ending _AAA was used.
- p_a_r = life history, with p = PS, r = PR, a = PL, referring to the terms used in the article maintext.
- man = Heavy managements, categories: F = burning, M = mowing, S = sod cutting/plaggen, none = no heavy management applied in the past 5 years.
- grazing = grazing regime, no = not grazed, sheep trad = year-round traditional shepherding, sheep trad+ = year-round intensively used areas in traditionally shepherded sites, deer = year-round browsing by free-ranging deer (roar deer, red deer, fallow deer), sheep fenced = temporary intensive grazing of sheep in a fenced area, horses and cattle = year-round extensive horse and cattle grazing in fenced areas
setup
setwd("C:/Users/Jenny/Dropbox/Diss/Auswertung/vitality_I")
load("C:/Users/Jenny/Dropbox/Diss/Auswertung/vitality_I/vitality_I.RData")library(vegan)
library(lme4)
library(lmerTest)
library(sjstats)
library(multcomp)
library(merTools)
library(r2glmm)
library(car)Models
Inflorescence density (flowers/cm inflorescence length)
Infl dens: plant age
dataset <- vita_all[complete.cases(vita_all$infl_dens) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_infl_dens_RA <- dataset
shapiro.test(dataset$infl_dens) # not normally distributed, but looks ok##
## Shapiro-Wilk normality test
##
## data: dataset$infl_dens
## W = 0.96502, p-value = 3.277e-05hist(dataset$infl_dens)
pairwise.wilcox.test(dataset$infl_dens, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$infl_dens and dataset$man
##
## F Ma none
## Ma 1 - -
## none 1 1 -
## S 1 1 1
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$infl_dens, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$infl_dens and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m4 <- lmer(infl_dens ~ RA + (1|area), data = dataset)
m4g <- lmer(infl_dens ~ RA + p_a_r + (1|area), data = dataset)
m4gi <- lmer(infl_dens ~ RA * p_a_r + (1|area), data = dataset)
m6 <- lmer(infl_dens ~ poly(RA,2) + (1|area), data = dataset)
m6g <- lmer(infl_dens ~ poly(RA,2) + p_a_r + (1|area), data = dataset)
m6gi <- lmer(infl_dens ~ poly(RA,2) * p_a_r + (1|area), data = dataset)
anova(m4, m4g, m4gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m4: infl_dens ~ RA + (1 | area)
## m6: infl_dens ~ poly(RA, 2) + (1 | area)
## m4g: infl_dens ~ RA + p_a_r + (1 | area)
## m6g: infl_dens ~ poly(RA, 2) + p_a_r + (1 | area)
## m4gi: infl_dens ~ RA * p_a_r + (1 | area)
## m6gi: infl_dens ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 4 1150.4 1164.0 -571.22 1142.4
## m6 5 1151.8 1168.7 -570.89 1141.8 0.6567 1 0.41771
## m4g 6 1148.2 1168.5 -568.10 1136.2 5.5777 1 0.01819 *
## m6g 7 1150.1 1173.8 -568.05 1136.1 0.0902 1 0.76392
## m4gi 8 1148.2 1175.3 -566.10 1132.2 3.9038 1 0.04818 *
## m6gi 11 1152.4 1189.6 -565.20 1130.4 1.8096 3 0.61285
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m4g, m4gi)## Data: dataset
## Models:
## m4g: infl_dens ~ RA + p_a_r + (1 | area)
## m4gi: infl_dens ~ RA * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4g 6 1148.2 1168.5 -568.1 1136.2
## m4gi 8 1148.2 1175.3 -566.1 1132.2 3.994 2 0.1357# m4g or m4gi, both are similar in AIC and deviance
summary(m4g)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: infl_dens ~ RA + p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 1140.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.53870 -0.48898 0.01757 0.56224 2.55932
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.00 0.000
## Residual 10.94 3.308
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.712010 0.736625 214.000000 10.469 <2e-16 ***
## RA 0.032641 0.045709 214.000000 0.714 0.4759
## p_a_rp -1.142952 0.588635 214.000000 -1.942 0.0535 .
## p_a_rr 0.003478 0.724877 214.000000 0.005 0.9962
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.729
## p_a_rp -0.705 0.162
## p_a_rr -0.606 0.177 0.625
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularm7 <- lmer(infl_dens ~ p_a_r + (1|area), data = dataset)
anova(m4g, m7)## Data: dataset
## Models:
## m7: infl_dens ~ p_a_r + (1 | area)
## m4g: infl_dens ~ RA + p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m7 5 1146.7 1163.6 -568.36 1136.7
## m4g 6 1148.2 1168.5 -568.10 1136.2 0.5189 1 0.4713# it is not significantly better when including age!- visual pretests show that there are no differences in management and only weak in area
- no influence of age detected.
# model_infl_dens_RA <- m7
model <- model_infl_dens_RA
plot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 2.4777 0.08633 .
## 215
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.027 0.4311
## 199boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ dataset$man)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 1.567 0.1984
## 214boxplot(residuals(model) ~ dataset$man)
leveneTest(residuals(model) ~ dataset$grazing)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 5 0.68 0.6391
## 212boxplot(residuals(model) ~ dataset$grazing)
no heteroscedasticity, deviations from normality acceptable due to binary predictor
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: infl_dens ~ p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 1136.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.45016 -0.48464 0.00311 0.54961 2.48665
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.00 0.000
## Residual 10.92 3.304
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 8.09535 0.50386 215.00000 16.067 <2e-16 ***
## p_a_rp -1.21126 0.58015 215.00000 -2.088 0.038 *
## p_a_rr -0.08837 0.71256 215.00000 -0.124 0.901
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p_a_rp
## p_a_rp -0.868
## p_a_rr -0.707 0.614
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.046 0.142 0.006
## 2 p_a_rp 0.031 0.111 0.001
## 3 p_a_rr 0.000 0.037 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## p_a_r 71.095 35.547 2 215 3.2563 0.04044 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = infl_dens ~ p_a_r + (1 | area), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -1.21126 0.58015 -2.088 0.0907 .
## r - a == 0 -0.08837 0.71256 -0.124 0.9914
## r - p == 0 1.12289 0.58015 1.936 0.1266
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)infl dens: stem age
dataset <- vita_all[complete.cases(vita_all$infl_dens) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_infl_dens_AAA <- dataset
shapiro.test(dataset$infl_dens)##
## Shapiro-Wilk normality test
##
## data: dataset$infl_dens
## W = 0.95588, p-value = 2.833e-10hist(dataset$infl_dens)
pairwise.wilcox.test(dataset$infl_dens, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$infl_dens and dataset$man
##
## F Ma none
## Ma 1 - -
## none 1 1 -
## S 1 1 1
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$infl_dens, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$infl_dens and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m8 <- lmer(infl_dens ~ AAA + (1|area), data = dataset)
m8g <- lmer(infl_dens ~ AAA + p_a_r + (1|area), data = dataset)
m8gi <- lmer(infl_dens ~ AAA * p_a_r + (1|area), data = dataset)
m10 <- lmer(infl_dens ~ poly(AAA,2) + (1|area), data = dataset)
m10g <- lmer(infl_dens ~ poly(AAA,2) + p_a_r + (1|area), data = dataset)
m10gi <- lmer(infl_dens ~ poly(AAA,2) * p_a_r + (1|area), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: infl_dens ~ AAA + (1 | area)
## m10: infl_dens ~ poly(AAA, 2) + (1 | area)
## m8g: infl_dens ~ AAA + p_a_r + (1 | area)
## m10g: infl_dens ~ poly(AAA, 2) + p_a_r + (1 | area)
## m8gi: infl_dens ~ AAA * p_a_r + (1 | area)
## m10gi: infl_dens ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 4 2294.3 2310.7 -1143.2 2286.3
## m10 5 2291.8 2312.3 -1140.9 2281.8 4.5444 1 0.033026 *
## m8g 6 2279.1 2303.7 -1133.5 2267.1 14.7003 1 0.000126 ***
## m10g 7 2278.7 2307.4 -1132.4 2264.7 2.3766 1 0.123168
## m8gi 8 2276.4 2309.2 -1130.2 2260.4 4.3459 1 0.037098 *
## m10gi 11 2273.6 2318.7 -1125.8 2251.6 8.7568 3 0.032706 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m8gi, m10gi)## Data: dataset
## Models:
## m8gi: infl_dens ~ AAA * p_a_r + (1 | area)
## m10gi: infl_dens ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8gi 8 2276.4 2309.2 -1130.2 2260.4
## m10gi 11 2273.6 2318.7 -1125.8 2251.6 8.7568 3 0.03271 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m10gi# model_infl_dens_AAA <- m10gi
model <- model_infl_dens_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: infl_dens ~ poly(AAA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2219.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5475 -0.5902 0.0109 0.5777 3.2240
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.002262 0.04756
## Residual 9.413495 3.06814
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.5124 0.2460 21.8349 30.539 < 2e-16 ***
## poly(AAA, 2)1 3.3116 5.5707 433.7765 0.594 0.55250
## poly(AAA, 2)2 -2.6266 5.4130 407.0989 -0.485 0.62777
## p_a_rp -0.9596 0.3208 435.5391 -2.992 0.00293 **
## p_a_rr 1.3718 0.8766 435.5786 1.565 0.11835
## poly(AAA, 2)1:p_a_rp 18.2834 6.8163 431.1011 2.682 0.00759 **
## poly(AAA, 2)2:p_a_rp -7.6953 6.7742 413.5179 -1.136 0.25663
## poly(AAA, 2)1:p_a_rr 28.3390 27.3390 428.9972 1.037 0.30052
## poly(AAA, 2)2:p_a_rr 29.7873 19.8812 433.0076 1.498 0.13479
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.005
## ply(AAA,2)2 0.216 0.132
## p_a_rp -0.764 -0.003 -0.166
## p_a_rr -0.279 -0.001 -0.061 0.214
## ply(AAA,2)1:p__rp -0.004 -0.817 -0.108 -0.026 0.001
## ply(AAA,2)2:p__rp -0.172 -0.105 -0.799 0.075 0.049 0.047
## ply(AAA,2)1:p__rr -0.001 -0.204 -0.027 0.001 0.812 0.167
## ply(AAA,2)2:p__rr -0.058 -0.036 -0.272 0.045 0.671 0.029
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.022
## ply(AAA,2)2:p__rr 0.218 0.744plot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 8.3807 0.0002677 ***
## 442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Warning in leveneTest.default(y = y, group = group, ...): group coerced to
## factor.## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.4664 0.09779 .
## 426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$area)
heteroscedasticity detected in p_a_r, but boxplot shows it is acceptable. deviance from normality is acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: infl_dens ~ poly(AAA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2219.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.5475 -0.5902 0.0109 0.5777 3.2240
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.002262 0.04756
## Residual 9.413495 3.06814
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 7.5124 0.2460 21.8349 30.539 < 2e-16 ***
## poly(AAA, 2)1 3.3116 5.5707 433.7765 0.594 0.55250
## poly(AAA, 2)2 -2.6266 5.4130 407.0989 -0.485 0.62777
## p_a_rp -0.9596 0.3208 435.5391 -2.992 0.00293 **
## p_a_rr 1.3718 0.8766 435.5786 1.565 0.11835
## poly(AAA, 2)1:p_a_rp 18.2834 6.8163 431.1011 2.682 0.00759 **
## poly(AAA, 2)2:p_a_rp -7.6953 6.7742 413.5179 -1.136 0.25663
## poly(AAA, 2)1:p_a_rr 28.3390 27.3390 428.9972 1.037 0.30052
## poly(AAA, 2)2:p_a_rr 29.7873 19.8812 433.0076 1.498 0.13479
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.005
## ply(AAA,2)2 0.216 0.132
## p_a_rp -0.764 -0.003 -0.166
## p_a_rr -0.279 -0.001 -0.061 0.214
## ply(AAA,2)1:p__rp -0.004 -0.817 -0.108 -0.026 0.001
## ply(AAA,2)2:p__rp -0.172 -0.105 -0.799 0.075 0.049 0.047
## ply(AAA,2)1:p__rr -0.001 -0.204 -0.027 0.001 0.812 0.167
## ply(AAA,2)2:p__rr -0.058 -0.036 -0.272 0.045 0.671 0.029
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.022
## ply(AAA,2)2:p__rr 0.218 0.744r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.103 0.173 0.068
## 4 p_a_rp 0.020 0.053 0.002
## 6 poly(AAA, 2)1:p_a_rp 0.016 0.047 0.001
## 5 p_a_rr 0.005 0.027 0.000
## 9 poly(AAA, 2)2:p_a_rr 0.005 0.026 0.000
## 7 poly(AAA, 2)2:p_a_rp 0.003 0.021 0.000
## 8 poly(AAA, 2)1:p_a_rr 0.002 0.020 0.000
## 2 poly(AAA, 2)1 0.001 0.015 0.000
## 3 poly(AAA, 2)2 0.001 0.014 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 51.034 25.517 2 432.79 2.7107 0.0676188 .
## p_a_r 132.260 66.130 2 435.67 7.0250 0.0009936 ***
## poly(AAA, 2):p_a_r 122.674 30.668 4 429.14 3.2579 0.0119415 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = infl_dens ~ poly(AAA, 2) * p_a_r + (1 | area),
## data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.9596 0.3208 -2.992 0.00676 **
## r - a == 0 1.3718 0.8766 1.565 0.24303
## r - p == 0 2.3314 0.8665 2.691 0.01698 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.002262 /(0.002262 +9.413495 )## [1] 0.0002402356proportion blooming long shoots
proportion blooming long shoots - plant age
dataset <- vita_all[complete.cases(vita_all$prop_blooming) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_prop_bloom_RA <- dataset
shapiro.test(dataset$prop_blooming) # not normally distributed##
## Shapiro-Wilk normality test
##
## data: dataset$prop_blooming
## W = 0.92544, p-value = 4.717e-09hist(dataset$prop_blooming)
hist(sqrt(dataset$prop_blooming))
pairwise.wilcox.test(dataset$prop_blooming, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_blooming and dataset$man
##
## F Ma none
## Ma 0.14 - -
## none 0.11 1.00 -
## S 1.00 0.16 0.11
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_blooming, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_blooming and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.00 - - - -
## no 1.00 0.25 - - -
## sheep fenced 1.00 1.00 1.00 - -
## sheep trad 1.00 0.51 1.00 1.00 -
## sheep trad+ 1.00 0.51 1.00 1.00 1.00
##
## P value adjustment method: holm# no sign
m4 <- lmer(prop_blooming ~ RA + (1|area), data = dataset)
m4g <- lmer(prop_blooming ~ RA + p_a_r + (1|area), data = dataset)
m4gi <- lmer(prop_blooming ~ RA * p_a_r + (1|area), data = dataset)
m6 <- lmer(prop_blooming ~ poly(RA,2) + (1|area), data = dataset)
m6g <- lmer(prop_blooming ~ poly(RA,2) + p_a_r + (1|area), data = dataset)
m6gi <- lmer(prop_blooming ~ poly(RA,2) * p_a_r + (1|area), data = dataset)
anova(m4, m4g, m4gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m4: prop_blooming ~ RA + (1 | area)
## m6: prop_blooming ~ poly(RA, 2) + (1 | area)
## m4g: prop_blooming ~ RA + p_a_r + (1 | area)
## m6g: prop_blooming ~ poly(RA, 2) + p_a_r + (1 | area)
## m4gi: prop_blooming ~ RA * p_a_r + (1 | area)
## m6gi: prop_blooming ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 4 2068.0 2081.5 -1030.0 2060.0
## m6 5 2067.3 2084.2 -1028.6 2057.3 2.7236 1 0.0988758 .
## m4g 6 2055.8 2076.1 -1021.9 2043.8 13.4548 1 0.0002444 ***
## m6g 7 2057.1 2080.8 -1021.5 2043.1 0.7080 1 0.4000945
## m4gi 8 2058.5 2085.6 -1021.3 2042.5 0.5789 1 0.4467535
## m6gi 11 2063.9 2101.1 -1020.9 2041.9 0.6577 3 0.8830956
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# including growth phase makes model much better
anova(m4g, m6g) # m4g is simpler## Data: dataset
## Models:
## m4g: prop_blooming ~ RA + p_a_r + (1 | area)
## m6g: prop_blooming ~ poly(RA, 2) + p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4g 6 2055.8 2076.1 -1021.9 2043.8
## m6g 7 2057.1 2080.8 -1021.5 2043.1 0.708 1 0.4001# model_prop_bloom_RA <- m4g
# model diagnostics
model <- model_prop_bloom_RA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_blooming ~ RA + p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2031.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2581 -0.6678 0.1431 0.7904 1.8487
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.0 0.00
## Residual 703.4 26.52
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 72.1165 5.9063 214.0000 12.210 < 2e-16 ***
## RA -1.4456 0.3665 214.0000 -3.944 0.000108 ***
## p_a_rp -11.5737 4.7197 214.0000 -2.452 0.014999 *
## p_a_rr 5.7695 5.8121 214.0000 0.993 0.321996
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.729
## p_a_rp -0.705 0.162
## p_a_rr -0.606 0.177 0.625
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 2.4295 0.0905 .
## 215
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.847 0.6432
## 199boxplot(residuals(model) ~ dataset$area)
patterning in residuals and deviance from normality ok, no heteroscedasticity.
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_blooming ~ RA + p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2031.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2581 -0.6678 0.1431 0.7904 1.8487
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.0 0.00
## Residual 703.4 26.52
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 72.1165 5.9063 214.0000 12.210 < 2e-16 ***
## RA -1.4456 0.3665 214.0000 -3.944 0.000108 ***
## p_a_rp -11.5737 4.7197 214.0000 -2.452 0.014999 *
## p_a_rr 5.7695 5.8121 214.0000 0.993 0.321996
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.729
## p_a_rp -0.705 0.162
## p_a_rr -0.606 0.177 0.625
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.190 0.320 0.099
## 2 RA 0.103 0.212 0.028
## 3 p_a_rp 0.042 0.129 0.002
## 4 p_a_rr 0.007 0.062 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## RA 10943 10943.4 1 214 15.5576 0.0001085 ***
## p_a_r 11596 5798.1 2 214 8.2429 0.0003559 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = prop_blooming ~ RA + p_a_r + (1 | area), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -11.574 4.720 -2.452 0.037 *
## r - a == 0 5.769 5.812 0.993 0.577
## r - p == 0 17.343 4.664 3.718 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)Fit: lmer(formula = prop_blooming ~ RA + p_a_r + (1 | area), data = dataset)
Linear Hypotheses: Estimate Std. Error z value Pr(>|z|)
p - a == 0 -11.574 4.720 -2.452 0.0369 *
r - a == 0 5.769 5.812 0.993 0.5773
r - p == 0 17.343 4.664 3.718 <0.001 *** — Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Adjusted p values reported – single-step method)
proportion blooming long shoots - stem age
dataset <- vita_all[complete.cases(vita_all$prop_blooming) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_prop_bloom_AAA <- dataset
shapiro.test(dataset$prop_blooming)##
## Shapiro-Wilk normality test
##
## data: dataset$prop_blooming
## W = 0.92961, p-value = 1.274e-13hist(dataset$prop_blooming)
hist(sqrt(dataset$prop_blooming))
hist(asin(sqrt(dataset$prop_blooming/100)*2/pi))
pairwise.wilcox.test(dataset$prop_blooming, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_blooming and dataset$man
##
## F Ma none
## Ma 0.367 - -
## none 0.090 1.000 -
## S 1.000 0.367 0.098
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_blooming, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_blooming and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m8 <- lmer(prop_blooming ~ AAA + (1|area), data = dataset)
m8g <- lmer(prop_blooming ~ AAA + p_a_r + (1|area), data = dataset)
m8gi <- lmer(prop_blooming ~ AAA * p_a_r + (1|area), data = dataset)
m10 <- lmer(prop_blooming ~ poly(AAA,2) + (1|area), data = dataset)
m10g <- lmer(prop_blooming ~ poly(AAA,2) + p_a_r + (1|area), data = dataset)
m10gi <- lmer(prop_blooming ~ poly(AAA,2) * p_a_r + (1|area), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: prop_blooming ~ AAA + (1 | area)
## m10: prop_blooming ~ poly(AAA, 2) + (1 | area)
## m8g: prop_blooming ~ AAA + p_a_r + (1 | area)
## m10g: prop_blooming ~ poly(AAA, 2) + p_a_r + (1 | area)
## m8gi: prop_blooming ~ AAA * p_a_r + (1 | area)
## m10gi: prop_blooming ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 4 4222.1 4238.4 -2107.0 4214.1
## m10 5 4193.4 4213.9 -2091.7 4183.4 30.632 1 3.119e-08 ***
## m8g 6 4170.4 4195.0 -2079.2 4158.4 25.052 1 5.580e-07 ***
## m10g 7 4150.0 4178.7 -2068.0 4136.0 22.332 1 2.293e-06 ***
## m8gi 8 4174.3 4207.1 -2079.2 4158.3 0.000 1 1
## m10gi 11 4156.7 4201.8 -2067.3 4134.7 23.618 3 3.002e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m10g, m10gi) # m10g## Data: dataset
## Models:
## m10g: prop_blooming ~ poly(AAA, 2) + p_a_r + (1 | area)
## m10gi: prop_blooming ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m10g 7 4150.0 4178.7 -2068.0 4136.0
## m10gi 11 4156.7 4201.8 -2067.3 4134.7 1.337 4 0.8551# model_prop_bloom_AAA <- m10g
# model diagnostics
model <- model_prop_bloom_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_blooming ~ poly(AAA, 2) + p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 4108.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3682 -0.8381 0.1572 0.7165 2.2351
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 28.29 5.319
## Residual 626.93 25.039
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 54.926 2.441 67.734 22.506 < 2e-16 ***
## poly(AAA, 2)1 132.592 25.787 438.631 5.142 4.11e-07 ***
## poly(AAA, 2)2 -122.714 25.759 439.593 -4.764 2.58e-06 ***
## p_a_rp -14.390 2.633 438.755 -5.466 7.74e-08 ***
## p_a_rr 8.634 4.078 439.944 2.117 0.0348 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 -0.027
## ply(AAA,2)2 0.105 0.012
## p_a_rp -0.633 -0.035 -0.177
## p_a_rr -0.399 0.158 -0.047 0.365plot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 10.446 3.692e-05 ***
## 442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.8273 0.6681
## 426boxplot(residuals(model) ~ dataset$area)
heteroscedasticity in p_a_r, but acceptable. deviance from normality acceptable, too.
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: prop_blooming ~ poly(AAA, 2) + p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 4108.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.3682 -0.8381 0.1572 0.7165 2.2351
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 28.29 5.319
## Residual 626.93 25.039
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 54.926 2.441 67.734 22.506 < 2e-16 ***
## poly(AAA, 2)1 132.592 25.787 438.631 5.142 4.11e-07 ***
## poly(AAA, 2)2 -122.714 25.759 439.593 -4.764 2.58e-06 ***
## p_a_rp -14.390 2.633 438.755 -5.466 7.74e-08 ***
## p_a_rr 8.634 4.078 439.944 2.117 0.0348 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 -0.027
## ply(AAA,2)2 0.105 0.012
## p_a_rp -0.633 -0.035 -0.177
## p_a_rr -0.399 0.158 -0.047 0.365r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.185 0.254 0.131
## 4 p_a_rp 0.062 0.111 0.026
## 2 poly(AAA, 2)1 0.055 0.102 0.022
## 3 poly(AAA, 2)2 0.048 0.093 0.017
## 5 p_a_rr 0.010 0.036 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 31177 15589 2 439.18 24.865 5.890e-11 ***
## p_a_r 30984 15492 2 439.27 24.711 6.764e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = prop_blooming ~ poly(AAA, 2) + p_a_r + (1 | area),
## data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -14.390 2.633 -5.466 <0.001 ***
## r - a == 0 8.634 4.078 2.117 0.0834 .
## r - p == 0 23.024 3.964 5.809 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)28.29 /(28.29 + 626.93 )## [1] 0.04317634nr flowers/plant
nr of flowers/ - plant age
dataset <- vita_all[complete.cases(vita_all$blossom_per_plant) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_nr_flowers_RA <- dataset
shapiro.test(dataset$blossom_per_plant)##
## Shapiro-Wilk normality test
##
## data: dataset$blossom_per_plant
## W = 0.46131, p-value < 2.2e-16hist(dataset$blossom_per_plant)
hist(sqrt(dataset$blossom_per_plant))
pairwise.wilcox.test(dataset$blossom_per_plant, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$blossom_per_plant and dataset$man
##
## F Ma none
## Ma 0.76 - -
## none 1.00 1.00 -
## S 1.00 0.66 1.00
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$blossom_per_plant, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$blossom_per_plant and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m4 <- lmer(sqrt(blossom_per_plant) ~ RA + (1|area), data = dataset)
m4g <- lmer(sqrt(blossom_per_plant) ~ RA + p_a_r + (1|area), data = dataset)
m4gi <- lmer(sqrt(blossom_per_plant) ~ RA * p_a_r + (1|area), data = dataset)
m6 <- lmer(sqrt(blossom_per_plant) ~ poly(RA,2) + (1|area), data = dataset)
m6g <- lmer(sqrt(blossom_per_plant) ~ poly(RA,2) + p_a_r + (1|area), data = dataset)
m6gi <- lmer(sqrt(blossom_per_plant) ~ poly(RA,2) * p_a_r + (1|area), data = dataset)
anova(m4, m4g, m4gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m4: sqrt(blossom_per_plant) ~ RA + (1 | area)
## m6: sqrt(blossom_per_plant) ~ poly(RA, 2) + (1 | area)
## m4g: sqrt(blossom_per_plant) ~ RA + p_a_r + (1 | area)
## m6g: sqrt(blossom_per_plant) ~ poly(RA, 2) + p_a_r + (1 | area)
## m4gi: sqrt(blossom_per_plant) ~ RA * p_a_r + (1 | area)
## m6gi: sqrt(blossom_per_plant) ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 4 2228.2 2241.7 -1110.1 2220.2
## m6 5 2222.8 2239.7 -1106.4 2212.8 7.3991 1 0.006526 **
## m4g 6 2228.9 2249.2 -1108.5 2216.9 0.0000 1 1.000000
## m6g 7 2224.9 2248.6 -1105.5 2210.9 5.9436 1 0.014771 *
## m4gi 8 2224.4 2251.4 -1104.2 2208.4 2.5927 1 0.107355
## m6gi 11 2226.4 2263.7 -1102.2 2204.4 3.9186 3 0.270387
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m6, m6g, m4gi) # m6 is best## Data: dataset
## Models:
## m6: sqrt(blossom_per_plant) ~ poly(RA, 2) + (1 | area)
## m6g: sqrt(blossom_per_plant) ~ poly(RA, 2) + p_a_r + (1 | area)
## m4gi: sqrt(blossom_per_plant) ~ RA * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m6 5 2222.8 2239.7 -1106.4 2212.8
## m6g 7 2224.9 2248.6 -1105.5 2210.9 1.8478 2 0.3970
## m4gi 8 2224.4 2251.4 -1104.2 2208.4 2.5927 1 0.1074# model_blossoms_RA <- m6
model <- model_blossoms_RA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(blossom_per_plant) ~ poly(RA, 2) + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2190.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.5643 -0.6357 -0.1668 0.4555 5.7230
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 30.53 5.525
## Residual 1496.32 38.682
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 40.911 3.164 4.965 12.929 5.17e-05 ***
## poly(RA, 2)1 187.021 40.114 106.409 4.662 9.12e-06 ***
## poly(RA, 2)2 -106.612 39.265 205.343 -2.715 0.00719 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(RA,2)1
## poly(RA,2)1 -0.087
## poly(RA,2)2 0.021 -0.011plot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.3962 0.9875
## 199boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 23 1.8501 0.0135 *
## 194
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1plot(residuals(model) ~ dataset$RA)
heteroscedasticity detected in RA… obvious in residuals plot, keep in mind for predicition validity
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(blossom_per_plant) ~ poly(RA, 2) + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 2190.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.5643 -0.6357 -0.1668 0.4555 5.7230
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 30.53 5.525
## Residual 1496.32 38.682
## Number of obs: 218, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 40.911 3.164 4.965 12.929 5.17e-05 ***
## poly(RA, 2)1 187.021 40.114 106.409 4.662 9.12e-06 ***
## poly(RA, 2)2 -106.612 39.265 205.343 -2.715 0.00719 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(RA,2)1
## poly(RA,2)1 -0.087
## poly(RA,2)2 0.021 -0.011r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.183 0.307 0.088
## 2 poly(RA, 2)1 0.144 0.261 0.055
## 3 poly(RA, 2)2 0.052 0.144 0.004anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(RA, 2) 43161 21580 2 138.5 14.422 2.043e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 130.53 /(30.53 +1496.32 )## [1] 0.01999542nr flowers/ plant - stem age
dataset <- vita_all[complete.cases(vita_all$blossom_per_plant) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_nr_flowers_AAA <- dataset
shapiro.test(dataset$blossom_per_plant)##
## Shapiro-Wilk normality test
##
## data: dataset$blossom_per_plant
## W = 0.50751, p-value < 2.2e-16hist(dataset$blossom_per_plant)
hist(sqrt(dataset$blossom_per_plant))
pairwise.wilcox.test(dataset$blossom_per_plant, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$blossom_per_plant and dataset$man
##
## F Ma none
## Ma 1 - -
## none 1 1 -
## S 1 1 1
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$blossom_per_plant, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$blossom_per_plant and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m8 <- lmer(sqrt(blossom_per_plant) ~ AAA + (1|area), data = dataset)
m8g <- lmer(sqrt(blossom_per_plant) ~ AAA + p_a_r + (1|area), data = dataset)
m8gi <- lmer(sqrt(blossom_per_plant) ~ AAA * p_a_r + (1|area), data = dataset)
m10 <- lmer(sqrt(blossom_per_plant) ~ poly(AAA,2) + (1|area), data = dataset)
m10g <- lmer(sqrt(blossom_per_plant) ~ poly(AAA,2) + p_a_r + (1|area), data = dataset)
m10gi <- lmer(sqrt(blossom_per_plant) ~ poly(AAA,2) * p_a_r + (1|area), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: sqrt(blossom_per_plant) ~ AAA + (1 | area)
## m10: sqrt(blossom_per_plant) ~ poly(AAA, 2) + (1 | area)
## m8g: sqrt(blossom_per_plant) ~ AAA + p_a_r + (1 | area)
## m10g: sqrt(blossom_per_plant) ~ poly(AAA, 2) + p_a_r + (1 | area)
## m8gi: sqrt(blossom_per_plant) ~ AAA * p_a_r + (1 | area)
## m10gi: sqrt(blossom_per_plant) ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 4 4523.7 4540.1 -2257.8 4515.7
## m10 5 4506.7 4527.2 -2248.3 4496.7 19.008 1 1.302e-05 ***
## m8g 6 4510.1 4534.7 -2249.1 4498.1 0.000 1 1.0000000
## m10g 7 4497.0 4525.7 -2241.5 4483.0 15.087 1 0.0001026 ***
## m8gi 8 4497.3 4530.0 -2240.6 4481.3 1.755 1 0.1852491
## m10gi 11 4488.8 4533.8 -2233.4 4466.8 14.480 3 0.0023194 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m10g, m10gi, m8gi) # m10gi is best## Data: dataset
## Models:
## m10g: sqrt(blossom_per_plant) ~ poly(AAA, 2) + p_a_r + (1 | area)
## m8gi: sqrt(blossom_per_plant) ~ AAA * p_a_r + (1 | area)
## m10gi: sqrt(blossom_per_plant) ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m10g 7 4497.0 4525.7 -2241.5 4483.0
## m8gi 8 4497.3 4530.0 -2240.6 4481.3 1.755 1 0.185249
## m10gi 11 4488.8 4533.8 -2233.4 4466.8 14.480 3 0.002319 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# model_blossoms_AAA <- m10gi
# model diagnostics
model <- model_blossoms_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(blossom_per_plant) ~ poly(AAA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 4388.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2813 -0.5460 -0.1989 0.3685 5.9734
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 36.92 6.076
## Residual 1341.32 36.624
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 50.271 3.390 43.477 14.829 < 2e-16 ***
## poly(AAA, 2)1 407.182 67.097 435.587 6.069 2.81e-09 ***
## poly(AAA, 2)2 -175.073 65.470 435.581 -2.674 0.007775 **
## p_a_rp -9.141 3.856 434.810 -2.371 0.018189 *
## p_a_rr 40.022 10.516 429.595 3.806 0.000162 ***
## poly(AAA, 2)1:p_a_rp 114.566 82.138 435.624 1.395 0.163789
## poly(AAA, 2)2:p_a_rp 55.294 81.793 435.938 0.676 0.499386
## poly(AAA, 2)1:p_a_rr 1187.935 327.289 426.119 3.630 0.000318 ***
## poly(AAA, 2)2:p_a_rr 433.313 239.236 433.828 1.811 0.070796 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.014
## ply(AAA,2)2 0.176 0.128
## p_a_rp -0.671 -0.002 -0.166
## p_a_rr -0.238 -0.006 -0.068 0.215
## ply(AAA,2)1:p__rp -0.024 -0.818 -0.103 -0.026 0.004
## ply(AAA,2)2:p__rp -0.138 -0.101 -0.801 0.077 0.055 0.043
## ply(AAA,2)1:p__rr 0.001 -0.203 -0.031 0.001 0.811 0.165
## ply(AAA,2)2:p__rr -0.029 -0.031 -0.277 0.041 0.667 0.022
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.027
## ply(AAA,2)2:p__rr 0.226 0.742plot(model)
qqnorm(residuals(model))
qqline(residuals(model), lwd=2, col="red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 1.0445 0.3527
## 442boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.1643 0.2876
## 426boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 2.1007 0.0054 **
## 426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1heteroscedasticity concerning AAA… keep im mind that may bias the predictions
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(blossom_per_plant) ~ poly(AAA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 4388.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.2813 -0.5460 -0.1989 0.3685 5.9734
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 36.92 6.076
## Residual 1341.32 36.624
## Number of obs: 445, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 50.271 3.390 43.477 14.829 < 2e-16 ***
## poly(AAA, 2)1 407.182 67.097 435.587 6.069 2.81e-09 ***
## poly(AAA, 2)2 -175.073 65.470 435.581 -2.674 0.007775 **
## p_a_rp -9.141 3.856 434.810 -2.371 0.018189 *
## p_a_rr 40.022 10.516 429.595 3.806 0.000162 ***
## poly(AAA, 2)1:p_a_rp 114.566 82.138 435.624 1.395 0.163789
## poly(AAA, 2)2:p_a_rp 55.294 81.793 435.938 0.676 0.499386
## poly(AAA, 2)1:p_a_rr 1187.935 327.289 426.119 3.630 0.000318 ***
## poly(AAA, 2)2:p_a_rr 433.313 239.236 433.828 1.811 0.070796 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.014
## ply(AAA,2)2 0.176 0.128
## p_a_rp -0.671 -0.002 -0.166
## p_a_rr -0.238 -0.006 -0.068 0.215
## ply(AAA,2)1:p__rp -0.024 -0.818 -0.103 -0.026 0.004
## ply(AAA,2)2:p__rp -0.138 -0.101 -0.801 0.077 0.055 0.043
## ply(AAA,2)1:p__rr 0.001 -0.203 -0.031 0.001 0.811 0.165
## ply(AAA,2)2:p__rr -0.029 -0.031 -0.277 0.041 0.667 0.022
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.027
## ply(AAA,2)2:p__rr 0.226 0.742r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.333 0.405 0.276
## 2 poly(AAA, 2)1 0.076 0.128 0.036
## 5 p_a_rr 0.031 0.070 0.007
## 8 poly(AAA, 2)1:p_a_rr 0.028 0.066 0.006
## 3 poly(AAA, 2)2 0.016 0.047 0.001
## 4 p_a_rp 0.012 0.041 0.000
## 9 poly(AAA, 2)2:p_a_rr 0.007 0.031 0.000
## 6 poly(AAA, 2)1:p_a_rp 0.004 0.025 0.000
## 7 poly(AAA, 2)2:p_a_rp 0.001 0.016 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 164964 82482 2 432.56 61.4933 < 2.2e-16 ***
## p_a_r 33734 16867 2 432.01 12.5748 4.919e-06 ***
## poly(AAA, 2):p_a_r 21787 5447 4 433.36 4.0608 0.003042 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(blossom_per_plant) ~ poly(AAA, 2) * p_a_r +
## (1 | area), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -9.141 3.856 -2.371 0.0422 *
## r - a == 0 40.022 10.516 3.806 <0.001 ***
## r - p == 0 49.163 10.393 4.730 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)36.92 /(36.92 +1341.32)## [1] 0.02678779length of inflorescence [cm]
length of inflorescence [cm] - plant age
dataset <- vita_all[complete.cases(vita_all$l_infl) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_l_infl_RA <- dataset
shapiro.test(dataset$l_infl)##
## Shapiro-Wilk normality test
##
## data: dataset$l_infl
## W = 0.89918, p-value = 6.052e-11hist(dataset$l_infl)
shapiro.test(sqrt(dataset$l_infl)) ##
## Shapiro-Wilk normality test
##
## data: sqrt(dataset$l_infl)
## W = 0.96573, p-value = 4.004e-05hist(sqrt(dataset$l_infl))
pairwise.wilcox.test(dataset$l_infl, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$l_infl and dataset$man
##
## F Ma none
## Ma 0.0060 - -
## none 0.0049 0.5103 -
## S 0.4708 0.5103 0.5103
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$l_infl, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$l_infl and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.000 - - - -
## no 0.343 0.915 - - -
## sheep fenced 1.000 1.000 0.083 - -
## sheep trad 1.000 1.000 0.083 1.000 -
## sheep trad+ 1.000 1.000 1.000 1.000 1.000
##
## P value adjustment method: holm# man is sign
m8 <- lmer(sqrt(l_infl) ~ RA + (1|area) + (1|man), data = dataset)
m8g <- lmer(sqrt(l_infl) ~ RA + p_a_r + (1|area) + (1|man), data = dataset)
m8gi <- lmer(sqrt(l_infl) ~ RA * p_a_r + (1|area)+ (1|man), data = dataset)
m10 <- lmer(sqrt(l_infl) ~ poly(RA,2) + (1|area)+ (1|man), data = dataset)
m10g <- lmer(sqrt(l_infl) ~ poly(RA,2) + p_a_r + (1|area)+ (1|man), data = dataset)
m10gi <- lmer(sqrt(l_infl) ~ poly(RA,2) * p_a_r + (1|area) + (1|man), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: sqrt(l_infl) ~ RA + (1 | area) + (1 | man)
## m10: sqrt(l_infl) ~ poly(RA, 2) + (1 | area) + (1 | man)
## m8g: sqrt(l_infl) ~ RA + p_a_r + (1 | area) + (1 | man)
## m10g: sqrt(l_infl) ~ poly(RA, 2) + p_a_r + (1 | area) + (1 | man)
## m8gi: sqrt(l_infl) ~ RA * p_a_r + (1 | area) + (1 | man)
## m10gi: sqrt(l_infl) ~ poly(RA, 2) * p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 5 504.10 521.03 -247.05 494.10
## m10 6 505.90 526.21 -246.95 493.90 0.2064 1 0.649576
## m8g 7 499.43 523.13 -242.72 485.43 8.4639 1 0.003623 **
## m10g 8 501.39 528.46 -242.69 485.39 0.0480 1 0.826577
## m8gi 9 500.94 531.40 -241.47 482.94 2.4512 1 0.117434
## m10gi 12 505.17 545.79 -240.59 481.17 1.7622 3 0.623185
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m8g, m8gi) # m8g## Data: dataset
## Models:
## m8g: sqrt(l_infl) ~ RA + p_a_r + (1 | area) + (1 | man)
## m8gi: sqrt(l_infl) ~ RA * p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8g 7 499.43 523.13 -242.72 485.43
## m8gi 9 500.94 531.40 -241.47 482.94 2.4992 2 0.2866# model_l_infl_RA <- m8g
# model diagnostics
model <- model_l_infl_RA
summary(model) ## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(l_infl) ~ RA + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 500.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.57902 -0.65126 0.09763 0.67535 2.77262
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.03411 0.1847
## man (Intercept) 0.00000 0.0000
## Residual 0.53058 0.7284
## Number of obs: 218, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.95646 0.17972 131.55432 10.886 < 2e-16 ***
## RA -0.03132 0.01077 193.53659 -2.908 0.00406 **
## p_a_rp -0.17929 0.13302 213.86147 -1.348 0.17912
## p_a_rr 0.19782 0.16213 213.14154 1.220 0.22376
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.736
## p_a_rp -0.633 0.147
## p_a_rr -0.532 0.147 0.622
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.6065 0.5462
## 215boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.9661 0.5005
## 199boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ dataset$man)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 0.3653 0.7781
## 214boxplot(residuals(model) ~ dataset$man)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 23 0.8618 0.6494
## 194ok
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(l_infl) ~ RA + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 500.7
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.57902 -0.65126 0.09763 0.67535 2.77262
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.03411 0.1847
## man (Intercept) 0.00000 0.0000
## Residual 0.53058 0.7284
## Number of obs: 218, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.95646 0.17972 131.55432 10.886 < 2e-16 ***
## RA -0.03132 0.01077 193.53659 -2.908 0.00406 **
## p_a_rp -0.17929 0.13302 213.86147 -1.348 0.17912
## p_a_rr 0.19782 0.16213 213.14154 1.220 0.22376
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.736
## p_a_rp -0.633 0.147
## p_a_rr -0.532 0.147 0.622
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.079 0.166 0.031
## 2 RA 0.041 0.106 0.005
## 3 p_a_rp 0.008 0.049 0.000
## 4 p_a_rr 0.007 0.045 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## RA 4.4878 4.4878 1 193.54 8.4583 0.004059 **
## p_a_r 4.6254 2.3127 2 213.85 4.3589 0.013949 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(l_infl) ~ RA + p_a_r + (1 | area) + (1 |
## man), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.1793 0.1330 -1.348 0.365
## r - a == 0 0.1978 0.1621 1.220 0.437
## r - p == 0 0.3771 0.1310 2.878 0.011 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.03411 /(0.03411 +0.53058 ) # area## [1] 0.06040482length of inflorescence [cm] - stem age
dataset <- vita_all[complete.cases(vita_all$l_infl) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_l_infl_AAA <- dataset
hist(dataset$l_infl)
hist(sqrt(dataset$l_infl))
pairwise.wilcox.test(dataset$l_infl, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$l_infl and dataset$man
##
## F Ma none
## Ma 0.00634 - -
## none 0.00038 0.81961 -
## S 0.51912 0.81961 0.81961
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$l_infl, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$l_infl and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.000 - - - -
## no 0.199 1.000 - - -
## sheep fenced 1.000 1.000 0.055 - -
## sheep trad 1.000 1.000 0.455 0.455 -
## sheep trad+ 1.000 1.000 1.000 1.000 1.000
##
## P value adjustment method: holm# man is sign
m8 <- lmer(sqrt(l_infl) ~ AAA + (1|area) + (1|man), data = dataset)
m8g <- lmer(sqrt(l_infl) ~ AAA + p_a_r + (1|area) + (1|man), data = dataset)
m8gi <- lmer(sqrt(l_infl) ~ AAA * p_a_r + (1|area)+ (1|man), data = dataset)
m10 <- lmer(sqrt(l_infl) ~ poly(AAA,2) + (1|area)+ (1|man), data = dataset)
m10g <- lmer(sqrt(l_infl) ~ poly(AAA,2) + p_a_r + (1|area)+ (1|man), data = dataset)
m10gi <- lmer(sqrt(l_infl) ~ poly(AAA,2) * p_a_r + (1|area) + (1|man), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: sqrt(l_infl) ~ AAA + (1 | area) + (1 | man)
## m10: sqrt(l_infl) ~ poly(AAA, 2) + (1 | area) + (1 | man)
## m8g: sqrt(l_infl) ~ AAA + p_a_r + (1 | area) + (1 | man)
## m10g: sqrt(l_infl) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## m8gi: sqrt(l_infl) ~ AAA * p_a_r + (1 | area) + (1 | man)
## m10gi: sqrt(l_infl) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 5 1016.37 1036.9 -503.19 1006.37
## m10 6 1002.02 1026.6 -495.01 990.02 16.348 1 5.271e-05 ***
## m8g 7 988.51 1017.2 -487.26 974.51 15.513 1 8.195e-05 ***
## m10g 8 977.36 1010.1 -480.68 961.36 13.150 1 0.0002876 ***
## m8gi 9 989.41 1026.3 -485.71 971.41 0.000 1 1.0000000
## m10gi 12 976.83 1026.0 -476.41 952.83 18.587 3 0.0003328 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m10g, m10gi)## Data: dataset
## Models:
## m10g: sqrt(l_infl) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## m10gi: sqrt(l_infl) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m10g 8 977.36 1010.1 -480.68 961.36
## m10gi 12 976.83 1026.0 -476.41 952.83 8.5348 4 0.07384 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m10g# model_l_infl_AAA <- m10g
# model diagnostics
model <- model_l_infl_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(l_infl) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 968.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2446 -0.6114 0.0056 0.6525 3.1324
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.049179 0.22176
## man (Intercept) 0.004773 0.06909
## Residual 0.489103 0.69936
## Number of obs: 445, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.60296 0.08972 10.02946 17.866 6.20e-09 ***
## poly(AAA, 2)1 3.96342 0.72950 417.34003 5.433 9.43e-08 ***
## poly(AAA, 2)2 -2.62359 0.72471 436.70679 -3.620 0.000329 ***
## p_a_rp -0.23490 0.07411 435.20037 -3.170 0.001634 **
## p_a_rr 0.36350 0.11626 362.30793 3.127 0.001911 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 0.008
## ply(AAA,2)2 0.094 0.017
## p_a_rp -0.471 -0.024 -0.173
## p_a_rr -0.340 0.131 -0.057 0.350plot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 3.025 0.04956 *
## 442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.0873 0.3622
## 426boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ dataset$man)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 3.7709 0.01078 *
## 441
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$man)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.9022 0.01433 *
## 426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1heteroscedasticity detetcted in p_a_r, man and AAA, but it looks acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(l_infl) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 968.4
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2446 -0.6114 0.0056 0.6525 3.1324
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.049179 0.22176
## man (Intercept) 0.004773 0.06909
## Residual 0.489103 0.69936
## Number of obs: 445, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.60296 0.08972 10.02946 17.866 6.20e-09 ***
## poly(AAA, 2)1 3.96342 0.72950 417.34003 5.433 9.43e-08 ***
## poly(AAA, 2)2 -2.62359 0.72471 436.70679 -3.620 0.000329 ***
## p_a_rp -0.23490 0.07411 435.20037 -3.170 0.001634 **
## p_a_rr 0.36350 0.11626 362.30793 3.127 0.001911 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 0.008
## ply(AAA,2)2 0.094 0.017
## p_a_rp -0.471 -0.024 -0.173
## p_a_rr -0.340 0.131 -0.057 0.350r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.136 0.202 0.088
## 2 poly(AAA, 2)1 0.061 0.110 0.026
## 3 poly(AAA, 2)2 0.028 0.065 0.006
## 5 p_a_rr 0.022 0.056 0.003
## 4 p_a_rp 0.022 0.056 0.003anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 21.189 10.5942 2 425.63 21.660 1.100e-09 ***
## p_a_r 14.921 7.4606 2 386.21 15.254 4.208e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(l_infl) ~ poly(AAA, 2) + p_a_r + (1 | area) +
## (1 | man), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.23490 0.07411 -3.170 0.00410 **
## r - a == 0 0.36350 0.11626 3.127 0.00483 **
## r - p == 0 0.59839 0.11390 5.254 < 0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.049179 /(0.049179 +0.004773 +0.489103 ) # area## [1] 0.090559890.004773 /(0.049179 +0.004773 +0.489103 ) ## [1] 0.008789165proportion bare long shoot tips [%]
proportion bare long shoot tips [%] - plant age
dataset <- vita_all[complete.cases(vita_all$prop_bare) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_bare_RA <- dataset
shapiro.test(dataset$prop_bare)##
## Shapiro-Wilk normality test
##
## data: dataset$prop_bare
## W = 0.53164, p-value < 2.2e-16hist(dataset$prop_bare)
hist(sqrt(dataset$prop_bare))
pairwise.wilcox.test(dataset$prop_bare, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_bare and dataset$man
##
## F Ma none
## Ma 0.13 - -
## none 0.16 0.79 -
## S 0.22 1.00 1.00
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_bare, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_bare and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# no sign
m4 <- lmer(sqrt(prop_bare) ~ RA + (1|area), data = dataset)
m4g <- lmer(sqrt(prop_bare) ~ RA + p_a_r + (1|area), data = dataset)
m4gi <- lmer(sqrt(prop_bare) ~ RA * p_a_r + (1|area), data = dataset)
m6 <- lmer(sqrt(prop_bare) ~ poly(RA,2) + (1|area), data = dataset)
m6g <- lmer(sqrt(prop_bare) ~ poly(RA,2) + p_a_r + (1|area), data = dataset)
m6gi <- lmer(sqrt(prop_bare) ~ poly(RA,2) * p_a_r + (1|area), data = dataset)
anova(m4, m4g, m4gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m4: sqrt(prop_bare) ~ RA + (1 | area)
## m6: sqrt(prop_bare) ~ poly(RA, 2) + (1 | area)
## m4g: sqrt(prop_bare) ~ RA + p_a_r + (1 | area)
## m6g: sqrt(prop_bare) ~ poly(RA, 2) + p_a_r + (1 | area)
## m4gi: sqrt(prop_bare) ~ RA * p_a_r + (1 | area)
## m6gi: sqrt(prop_bare) ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 4 973.99 987.42 -482.99 965.99
## m6 5 975.81 992.59 -482.90 965.81 0.1836 1 0.6682783
## m4g 6 945.27 965.41 -466.64 933.27 32.5335 1 1.172e-08 ***
## m6g 7 946.46 969.96 -466.23 932.46 0.8084 1 0.3686025
## m4gi 8 933.46 960.31 -458.73 917.46 15.0079 1 0.0001071 ***
## m6gi 11 938.28 975.20 -458.14 916.28 1.1765 3 0.7586402
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m4gi is best#model_prop_bare_RA <- m4gi
# model diagnostics
model <- model_prop_bare_RA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(prop_bare) ~ RA * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 930.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8867 -0.5496 -0.1372 0.4354 3.3415
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.01605 0.1267
## Residual 4.55153 2.1334
## Number of obs: 212, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.03533 0.90568 188.03867 -0.039 0.968925
## RA 0.12704 0.07184 202.14167 1.768 0.078508 .
## p_a_rp -1.39723 0.98141 205.94116 -1.424 0.156048
## p_a_rr -1.27510 1.29684 205.36757 -0.983 0.326648
## RA:p_a_rp 0.29699 0.07977 205.87391 3.723 0.000254 ***
## RA:p_a_rr 0.09285 0.12114 205.49512 0.766 0.444290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp p_a_rr RA:p__rp
## RA -0.932
## p_a_rp -0.918 0.857
## p_a_rr -0.694 0.648 0.641
## RA:p_a_rp 0.837 -0.899 -0.920 -0.585
## RA:p_a_rr 0.550 -0.591 -0.509 -0.926 0.533plot(model)
qqnorm(residuals(model))
qqline(residuals(model), col = "red")
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 9.0425 0.0001712 ***
## 209
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.822 0.673
## 193boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 23 3.5011 9.768e-07 ***
## 188
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1variance heterogeneity detected in p_a_r and concerning RA … but acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(prop_bare) ~ RA * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 930.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.8867 -0.5496 -0.1372 0.4354 3.3415
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.01605 0.1267
## Residual 4.55153 2.1334
## Number of obs: 212, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) -0.03533 0.90568 188.03867 -0.039 0.968925
## RA 0.12704 0.07184 202.14167 1.768 0.078508 .
## p_a_rp -1.39723 0.98141 205.94116 -1.424 0.156048
## p_a_rr -1.27510 1.29684 205.36757 -0.983 0.326648
## RA:p_a_rp 0.29699 0.07977 205.87391 3.723 0.000254 ***
## RA:p_a_rr 0.09285 0.12114 205.49512 0.766 0.444290
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp p_a_rr RA:p__rp
## RA -0.932
## p_a_rp -0.918 0.857
## p_a_rr -0.694 0.648 0.641
## RA:p_a_rp 0.837 -0.899 -0.920 -0.585
## RA:p_a_rr 0.550 -0.591 -0.509 -0.926 0.533r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.582 0.673 0.494
## 5 RA:p_a_rp 0.094 0.201 0.022
## 2 RA 0.023 0.097 0.000
## 3 p_a_rp 0.015 0.081 0.000
## 4 p_a_rr 0.007 0.062 0.000
## 6 RA:p_a_rr 0.004 0.054 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## RA 168.976 168.976 1 168.50 37.1250 7.298e-09 ***
## p_a_r 9.264 4.632 2 205.73 1.0177 0.3632545
## RA:p_a_r 72.528 36.264 2 205.28 7.9674 0.0004651 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(prop_bare) ~ RA * p_a_r + (1 | area), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -1.3972 0.9814 -1.424 0.321
## r - a == 0 -1.2751 1.2968 -0.983 0.580
## r - p == 0 0.1221 1.0063 0.121 0.992
## (Adjusted p values reported -- single-step method)0.01605 /(0.01605 + 4.55153 ) # area## [1] 0.003513896proportion bare long shoot tips [%] - stem age
dataset <- vita_all[complete.cases(vita_all$prop_bare) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_bare_AAA <- dataset
hist(dataset$prop_bare)
hist(sqrt(dataset$prop_bare))
pairwise.wilcox.test(dataset$prop_bare, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_bare and dataset$man
##
## F Ma none
## Ma 0.0026 - -
## none 0.0013 0.2721 -
## S 0.2466 0.2048 0.2721
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_bare, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_bare and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# man sign
m4 <- lmer(sqrt(prop_bare) ~ AAA + (1|area) + (1|man), data = dataset)
m4g <- lmer(sqrt(prop_bare) ~ AAA + p_a_r + (1|area) + (1|man), data = dataset)
m4gi <- lmer(sqrt(prop_bare) ~ AAA * p_a_r + (1|area)+ (1|man), data = dataset)
m6 <- lmer(sqrt(prop_bare) ~ poly(AAA,2) + (1|area)+ (1|man), data = dataset)
m6g <- lmer(sqrt(prop_bare) ~ poly(AAA,2) + p_a_r + (1|area)+ (1|man), data = dataset)
m6gi <- lmer(sqrt(prop_bare) ~ poly(AAA,2) * p_a_r + (1|area) + (1|man), data = dataset)
anova(m4, m4g, m4gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m4: sqrt(prop_bare) ~ AAA + (1 | area) + (1 | man)
## m6: sqrt(prop_bare) ~ poly(AAA, 2) + (1 | area) + (1 | man)
## m4g: sqrt(prop_bare) ~ AAA + p_a_r + (1 | area) + (1 | man)
## m6g: sqrt(prop_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## m4gi: sqrt(prop_bare) ~ AAA * p_a_r + (1 | area) + (1 | man)
## m6gi: sqrt(prop_bare) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 5 2086.6 2106.9 -1038.3 2076.6
## m6 6 2082.2 2106.6 -1035.1 2070.2 6.3677 1 0.01162 *
## m4g 7 2046.7 2075.1 -1016.3 2032.7 37.5694 1 8.822e-10 ***
## m6g 8 2045.9 2078.4 -1015.0 2029.9 2.7485 1 0.09735 .
## m4gi 9 2050.5 2087.0 -1016.2 2032.5 0.0000 1 1.00000
## m6gi 12 2051.8 2100.5 -1013.9 2027.8 4.6627 3 0.19823
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m4g, m6g)## Data: dataset
## Models:
## m4g: sqrt(prop_bare) ~ AAA + p_a_r + (1 | area) + (1 | man)
## m6g: sqrt(prop_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4g 7 2046.7 2075.1 -1016.3 2032.7
## m6g 8 2045.9 2078.4 -1015.0 2029.9 2.7485 1 0.09735 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m6g is best# model_prop_bare_AAA <- m6g
# model diagnostics
model <- model_prop_bare_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(prop_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 2024
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.0583 -0.6404 -0.2599 0.4485 2.9563
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.2514 0.5014
## man (Intercept) 0.1072 0.3274
## Residual 6.7489 2.5979
## Number of obs: 426, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.7876 0.3151 5.3570 5.673 0.00189 **
## poly(AAA, 2)1 20.0938 2.7060 415.1171 7.426 6.43e-13 ***
## poly(AAA, 2)2 4.5118 2.6742 420.7026 1.687 0.09231 .
## p_a_rp 1.6448 0.2796 420.5456 5.882 8.27e-09 ***
## p_a_rr -0.2971 0.4321 345.6863 -0.688 0.49220
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 0.030
## ply(AAA,2)2 0.102 0.025
## p_a_rp -0.474 -0.058 -0.159
## p_a_rr -0.369 0.133 -0.062 0.328plot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 33.324 3.636e-14 ***
## 423
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.7003 0.03664 *
## 407
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.7991 0.7019
## 407leveneTest(residuals(model) ~ dataset$man)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 3.4704 0.0162 *
## 422
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$man)
heteroscedasticity in p_a_r, area and man, obvious, but acceptable.
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(prop_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man)
## Data: dataset
##
## REML criterion at convergence: 2024
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.0583 -0.6404 -0.2599 0.4485 2.9563
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.2514 0.5014
## man (Intercept) 0.1072 0.3274
## Residual 6.7489 2.5979
## Number of obs: 426, groups: area, 19; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 1.7876 0.3151 5.3570 5.673 0.00189 **
## poly(AAA, 2)1 20.0938 2.7060 415.1171 7.426 6.43e-13 ***
## poly(AAA, 2)2 4.5118 2.6742 420.7026 1.687 0.09231 .
## p_a_rp 1.6448 0.2796 420.5456 5.882 8.27e-09 ***
## p_a_rr -0.2971 0.4321 345.6863 -0.688 0.49220
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 0.030
## ply(AAA,2)2 0.102 0.025
## p_a_rp -0.474 -0.058 -0.159
## p_a_rr -0.369 0.133 -0.062 0.328r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.228 0.300 0.169
## 2 poly(AAA, 2)1 0.114 0.174 0.064
## 4 p_a_rp 0.075 0.128 0.034
## 3 poly(AAA, 2)2 0.007 0.031 0.000
## 5 p_a_rr 0.001 0.017 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 387.41 193.70 2 414.18 28.701 2.121e-12 ***
## p_a_r 285.44 142.72 2 376.71 21.147 1.977e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(prop_bare) ~ poly(AAA, 2) + p_a_r + (1 |
## area) + (1 | man), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 1.6448 0.2796 5.882 <1e-04 ***
## r - a == 0 -0.2971 0.4321 -0.688 0.766
## r - p == 0 -1.9418 0.4307 -4.509 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.2514 /(0.2514 +0.1072 + 6.7489 ) # area## [1] 0.035371090.1072 /(0.2514 +0.1072 +6.7489 )## [1] 0.01508266yearly increment [cm]
yearly increment (annual growth) was significantly differing in both, intense managements and grazing regimes. Therefore they were both included as random terms
annual growth [cm] - plant age
dataset <- vita_all[complete.cases(vita_all$ann_gro) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_anngro_RA <- dataset
shapiro.test(dataset$ann_gro)##
## Shapiro-Wilk normality test
##
## data: dataset$ann_gro
## W = 0.9156, p-value = 8.346e-10hist(dataset$ann_gro)
shapiro.test(sqrt(dataset$ann_gro)) ##
## Shapiro-Wilk normality test
##
## data: sqrt(dataset$ann_gro)
## W = 0.96144, p-value = 1.24e-05hist(sqrt(dataset$ann_gro))
pairwise.wilcox.test(dataset$ann_gro, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$ann_gro and dataset$man
##
## F Ma none
## Ma 0.00013 - -
## none 7.8e-06 0.23496 -
## S 0.03928 0.23496 0.50330
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$ann_gro, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$ann_gro and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.0000 - - - -
## no 0.8655 0.2345 - - -
## sheep fenced 1.0000 1.0000 0.0068 - -
## sheep trad 1.0000 1.0000 0.0003 0.8655 -
## sheep trad+ 1.0000 0.9741 1.0000 0.5301 0.8925
##
## P value adjustment method: holm# both sign
m8 <- lmer(sqrt(ann_gro) ~ RA + (1|area) + (1|man) + (1|grazing), data = dataset)
m8g <- lmer(sqrt(ann_gro) ~ RA + p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m8gi <- lmer(sqrt(ann_gro) ~ RA * p_a_r + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10 <- lmer(sqrt(ann_gro) ~ poly(RA,2) + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10g <- lmer(sqrt(ann_gro) ~ poly(RA,2) + p_a_r + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10gi <- lmer(sqrt(ann_gro) ~ poly(RA,2) * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: sqrt(ann_gro) ~ RA + (1 | area) + (1 | man) + (1 | grazing)
## m10: sqrt(ann_gro) ~ poly(RA, 2) + (1 | area) + (1 | man) + (1 | grazing)
## m8g: sqrt(ann_gro) ~ RA + p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## m10g: sqrt(ann_gro) ~ poly(RA, 2) + p_a_r + (1 | area) + (1 | man) +
## m10g: (1 | grazing)
## m8gi: sqrt(ann_gro) ~ RA * p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## m10gi: sqrt(ann_gro) ~ poly(RA, 2) * p_a_r + (1 | area) + (1 | man) +
## m10gi: (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 6 600.06 620.37 -294.03 588.06
## m10 7 601.87 625.56 -293.93 587.87 0.1976 1 0.6567044
## m8g 8 592.50 619.58 -288.25 576.50 11.3622 1 0.0007496 ***
## m10g 9 593.13 623.59 -287.56 575.13 1.3774 1 0.2405409
## m8gi 10 595.09 628.93 -287.55 575.09 0.0378 1 0.8458220
## m10gi 13 598.15 642.15 -286.07 572.15 2.9417 3 0.4007008
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m8g, m10g) # m8g## Data: dataset
## Models:
## m8g: sqrt(ann_gro) ~ RA + p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## m10g: sqrt(ann_gro) ~ poly(RA, 2) + p_a_r + (1 | area) + (1 | man) +
## m10g: (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8g 8 592.50 619.58 -288.25 576.50
## m10g 9 593.13 623.59 -287.56 575.13 1.3774 1 0.2405# model_ann_gro_RA <- m8g
# model diagnostics
model <- model_ann_gro_RA
summary(model) ## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(ann_gro) ~ RA + p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 589.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5908 -0.4765 0.0720 0.6070 2.3915
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.09504 0.3083
## grazing (Intercept) 0.01767 0.1329
## man (Intercept) 0.00000 0.0000
## Residual 0.78102 0.8838
## Number of obs: 218, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.15481 0.23807 64.70747 13.252 < 2e-16 ***
## RA -0.06110 0.01337 205.52490 -4.570 8.41e-06 ***
## p_a_rp -0.32779 0.16342 212.76535 -2.006 0.0461 *
## p_a_rr 0.20502 0.19867 212.33837 1.032 0.3033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.699
## p_a_rp -0.578 0.148
## p_a_rr -0.482 0.139 0.619
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 2.1229 0.1222
## 215boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.2871 0.1991
## 199boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 23 0.9601 0.5188
## 194ok
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(ann_gro) ~ RA + p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 589.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.5908 -0.4765 0.0720 0.6070 2.3915
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.09504 0.3083
## grazing (Intercept) 0.01767 0.1329
## man (Intercept) 0.00000 0.0000
## Residual 0.78102 0.8838
## Number of obs: 218, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 3.15481 0.23807 64.70747 13.252 < 2e-16 ***
## RA -0.06110 0.01337 205.52490 -4.570 8.41e-06 ***
## p_a_rp -0.32779 0.16342 212.76535 -2.006 0.0461 *
## p_a_rr 0.20502 0.19867 212.33837 1.032 0.3033
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) RA p_a_rp
## RA -0.699
## p_a_rp -0.578 0.148
## p_a_rr -0.482 0.139 0.619
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.142 0.239 0.075
## 2 RA 0.096 0.179 0.035
## 3 p_a_rp 0.018 0.069 0.000
## 4 p_a_rr 0.005 0.040 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## RA 16.3110 16.3110 1 205.53 20.8841 8.412e-06 ***
## p_a_r 9.6836 4.8418 2 212.76 6.1993 0.002417 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(ann_gro) ~ RA + p_a_r + (1 | area) + (1 |
## man) + (1 | grazing), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.3278 0.1634 -2.006 0.10897
## r - a == 0 0.2050 0.1987 1.032 0.55295
## r - p == 0 0.5328 0.1612 3.305 0.00259 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.09504 /(0.09504 +0.01767 +0.78102 ) # area## [1] 0.10634080.01767 /(0.09504 +0.01767 +0.78102 ) # grazing## [1] 0.01977107annual growth [cm] - stem age
dataset <- vita_all[complete.cases(vita_all$ann_gro) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_anngro_AAA <- dataset
hist(dataset$ann_gro)
hist(sqrt(dataset$ann_gro))
pairwise.wilcox.test(dataset$ann_gro, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$ann_gro and dataset$man
##
## F Ma none
## Ma 8.6e-05 - -
## none 2.2e-06 0.26 -
## S 0.10 0.22 0.34
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$ann_gro, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$ann_gro and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.00000 - - - -
## no 0.07807 0.07675 - - -
## sheep fenced 1.00000 1.00000 0.00033 - -
## sheep trad 1.00000 1.00000 4.8e-05 0.24508 -
## sheep trad+ 1.00000 1.00000 1.00000 0.61375 1.00000
##
## P value adjustment method: holm# both sign
m8 <- lmer(sqrt(ann_gro) ~ AAA + (1|area) + (1|man) + (1|grazing), data = dataset)
m8g <- lmer(sqrt(ann_gro) ~ AAA + p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m8gi <- lmer(sqrt(ann_gro) ~ AAA * p_a_r + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10 <- lmer(sqrt(ann_gro) ~ poly(AAA,2) + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10g <- lmer(sqrt(ann_gro) ~ poly(AAA,2) + p_a_r + (1|area)+ (1|man) + (1|grazing), data = dataset)
m10gi <- lmer(sqrt(ann_gro) ~ poly(AAA,2) * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
anova(m8, m8g, m8gi, m10, m10g, m10gi)## Data: dataset
## Models:
## m8: sqrt(ann_gro) ~ AAA + (1 | area) + (1 | man) + (1 | grazing)
## m10: sqrt(ann_gro) ~ poly(AAA, 2) + (1 | area) + (1 | man) + (1 |
## m10: grazing)
## m8g: sqrt(ann_gro) ~ AAA + p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## m10g: sqrt(ann_gro) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man) +
## m10g: (1 | grazing)
## m8gi: sqrt(ann_gro) ~ AAA * p_a_r + (1 | area) + (1 | man) + (1 | grazing)
## m10gi: sqrt(ann_gro) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man) +
## m10gi: (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m8 6 1227.0 1251.6 -607.49 1215.0
## m10 7 1216.0 1244.7 -600.98 1202.0 13.0181 1 0.0003085 ***
## m8g 8 1191.3 1224.1 -587.64 1175.3 26.6871 1 2.392e-07 ***
## m10g 9 1184.0 1220.9 -583.01 1166.0 9.2543 1 0.0023495 **
## m8gi 10 1190.5 1231.5 -585.23 1170.5 0.0000 1 1.0000000
## m10gi 13 1180.6 1233.9 -577.30 1154.6 15.8680 3 0.0012069 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m10g, m10gi)## Data: dataset
## Models:
## m10g: sqrt(ann_gro) ~ poly(AAA, 2) + p_a_r + (1 | area) + (1 | man) +
## m10g: (1 | grazing)
## m10gi: sqrt(ann_gro) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man) +
## m10gi: (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m10g 9 1184.0 1220.9 -583.01 1166.0
## m10gi 13 1180.6 1233.9 -577.30 1154.6 11.419 4 0.02224 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m10gi# model_ann_gro_AAA <- m10gi
# model diagnostics
model <- model_ann_gro_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(ann_gro) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man) +
## (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 1142.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7276 -0.4918 0.0448 0.6387 2.9031
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.1390 0.3729
## grazing (Intercept) 0.0000 0.0000
## man (Intercept) 0.0000 0.0000
## Residual 0.7512 0.8667
## Number of obs: 445, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.38158 0.11449 35.55658 20.802 < 2e-16 ***
## poly(AAA, 2)1 -0.58599 1.60644 428.87076 -0.365 0.7155
## poly(AAA, 2)2 -1.26238 1.57354 431.07229 -0.802 0.4228
## p_a_rp -0.38201 0.09230 429.52788 -4.139 4.2e-05 ***
## p_a_rr 0.05891 0.25019 424.64920 0.235 0.8140
## poly(AAA, 2)1:p_a_rp 4.72041 1.96626 428.69750 2.401 0.0168 *
## poly(AAA, 2)2:p_a_rp -2.87990 1.95983 429.40853 -1.469 0.1424
## poly(AAA, 2)1:p_a_rr -10.81988 7.77348 423.58856 -1.392 0.1647
## poly(AAA, 2)2:p_a_rr -7.84225 5.70810 426.42865 -1.374 0.1702
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.015
## ply(AAA,2)2 0.121 0.120
## p_a_rp -0.480 0.000 -0.171
## p_a_rr -0.169 -0.010 -0.072 0.218
## ply(AAA,2)1:p__rp -0.030 -0.819 -0.095 -0.026 0.008
## ply(AAA,2)2:p__rp -0.096 -0.092 -0.803 0.086 0.058 0.035
## ply(AAA,2)1:p__rr 0.000 -0.201 -0.033 0.003 0.808 0.162
## ply(AAA,2)2:p__rr -0.010 -0.024 -0.280 0.038 0.660 0.015
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.031
## ply(AAA,2)2:p__rr 0.231 0.739
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 15.845 2.26e-07 ***
## 442
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.9815 0.48
## 426boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ dataset$man)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 3 1.3663 0.2525
## 441boxplot(residuals(model) ~ dataset$man)
leveneTest(residuals(model) ~ dataset$grazing)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 5 1.449 0.2055
## 439boxplot(residuals(model) ~ dataset$grazing)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 2.1828 0.003555 **
## 426
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1heteroscedasticity detetcted in p_a_r and AAA, but it looks acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(ann_gro) ~ poly(AAA, 2) * p_a_r + (1 | area) + (1 | man) +
## (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 1142.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.7276 -0.4918 0.0448 0.6387 2.9031
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.1390 0.3729
## grazing (Intercept) 0.0000 0.0000
## man (Intercept) 0.0000 0.0000
## Residual 0.7512 0.8667
## Number of obs: 445, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.38158 0.11449 35.55658 20.802 < 2e-16 ***
## poly(AAA, 2)1 -0.58599 1.60644 428.87076 -0.365 0.7155
## poly(AAA, 2)2 -1.26238 1.57354 431.07229 -0.802 0.4228
## p_a_rp -0.38201 0.09230 429.52788 -4.139 4.2e-05 ***
## p_a_rr 0.05891 0.25019 424.64920 0.235 0.8140
## poly(AAA, 2)1:p_a_rp 4.72041 1.96626 428.69750 2.401 0.0168 *
## poly(AAA, 2)2:p_a_rp -2.87990 1.95983 429.40853 -1.469 0.1424
## poly(AAA, 2)1:p_a_rr -10.81988 7.77348 423.58856 -1.392 0.1647
## poly(AAA, 2)2:p_a_rr -7.84225 5.70810 426.42865 -1.374 0.1702
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(AAA,2)1 pl(AAA,2)2 p_a_rp p_a_rr ply(AAA,2)1:p__rp
## ply(AAA,2)1 0.015
## ply(AAA,2)2 0.121 0.120
## p_a_rp -0.480 0.000 -0.171
## p_a_rr -0.169 -0.010 -0.072 0.218
## ply(AAA,2)1:p__rp -0.030 -0.819 -0.095 -0.026 0.008
## ply(AAA,2)2:p__rp -0.096 -0.092 -0.803 0.086 0.058 0.035
## ply(AAA,2)1:p__rr 0.000 -0.201 -0.033 0.003 0.808 0.162
## ply(AAA,2)2:p__rr -0.010 -0.024 -0.280 0.038 0.660 0.015
## ply(AAA,2)2:p__rp ply(AAA,2)1:p__rr
## ply(AAA,2)1
## ply(AAA,2)2
## p_a_rp
## p_a_rr
## ply(AAA,2)1:p__rp
## ply(AAA,2)2:p__rp
## ply(AAA,2)1:p__rr 0.031
## ply(AAA,2)2:p__rr 0.231 0.739
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.129 0.202 0.089
## 4 p_a_rp 0.036 0.076 0.010
## 6 poly(AAA, 2)1:p_a_rp 0.012 0.041 0.000
## 7 poly(AAA, 2)2:p_a_rp 0.005 0.026 0.000
## 8 poly(AAA, 2)1:p_a_rr 0.004 0.024 0.000
## 9 poly(AAA, 2)2:p_a_rr 0.004 0.024 0.000
## 3 poly(AAA, 2)2 0.001 0.017 0.000
## 2 poly(AAA, 2)1 0.000 0.013 0.000
## 5 p_a_rr 0.000 0.012 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 5.5812 2.7906 2 427.70 3.7148 0.0251501 *
## p_a_r 13.8919 6.9459 2 426.86 9.2463 0.0001172 ***
## poly(AAA, 2):p_a_r 8.6110 2.1528 4 427.60 2.8657 0.0230140 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(ann_gro) ~ poly(AAA, 2) * p_a_r + (1 | area) +
## (1 | man) + (1 | grazing), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.38201 0.09230 -4.139 <0.001 ***
## r - a == 0 0.05891 0.25019 0.235 0.968
## r - p == 0 0.44092 0.24703 1.785 0.160
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.1390 /(0.1390 +0.7512 ) # area## [1] 0.1561447relative yearly increment [%]
initial analysis revealed large differences between Managements; therefore, it is tested as fixed effect, too.
prop_liv_bare: proportion of yearly increment on the total plant height
relative yearly increment [%] - plant age
dataset <- vita_all[complete.cases(vita_all$prop_liv_bare) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_prop_liv_RA <- dataset
hist(dataset$prop_liv_bare)
hist(sqrt(dataset$prop_liv_bare))
pairwise.wilcox.test(dataset$prop_liv_bare, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_liv_bare and dataset$man
##
## F Ma none
## Ma 0.0043 - -
## none 0.0006 1.0000 -
## S 0.0053 1.0000 1.0000
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_liv_bare, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_liv_bare and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.0000 - - - -
## no 1.0000 1.0000 - - -
## sheep fenced 1.0000 1.0000 0.0249 - -
## sheep trad 1.0000 1.0000 0.0065 1.0000 -
## sheep trad+ 0.5466 0.9010 1.0000 0.0411 0.0768
##
## P value adjustment method: holm# both sign
m3 <- lmer(sqrt(dataset$prop_liv_bare) ~ RA + (1|area) + (1|man) + (1|grazing), data = dataset)
m3g <- lmer(sqrt(dataset$prop_liv_bare) ~ RA + p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m3gi <- lmer(sqrt(dataset$prop_liv_bare) ~ RA * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m6 <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(RA,2) + (1|area) + (1|man) + (1|grazing), data = dataset)
m6g <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(RA,2) + p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m6gi <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(RA,2) * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
anova(m3, m3g, m3gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m3: sqrt(dataset$prop_liv_bare) ~ RA + (1 | area) + (1 | man) + (1 |
## m3: grazing)
## m6: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + (1 | area) + (1 |
## m6: man) + (1 | grazing)
## m3g: sqrt(dataset$prop_liv_bare) ~ RA + p_a_r + (1 | area) + (1 |
## m3g: man) + (1 | grazing)
## m6g: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + p_a_r + (1 | area) +
## m6g: (1 | man) + (1 | grazing)
## m3gi: sqrt(dataset$prop_liv_bare) ~ RA * p_a_r + (1 | area) + (1 |
## m3gi: man) + (1 | grazing)
## m6gi: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) * p_a_r + (1 | area) +
## m6gi: (1 | man) + (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m3 6 855.10 875.06 -421.55 843.10
## m6 7 851.77 875.06 -418.88 837.77 5.3305 1 0.0209551 *
## m3g 8 844.44 871.06 -414.22 828.44 9.3260 1 0.0022592 **
## m6g 9 835.01 864.96 -408.50 817.01 11.4322 1 0.0007218 ***
## m3gi 10 842.63 875.90 -411.31 822.63 0.0000 1 1.0000000
## m6gi 13 836.62 879.88 -405.31 810.62 12.0038 3 0.0073702 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m6g, m6gi)## Data: dataset
## Models:
## m6g: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + p_a_r + (1 | area) +
## m6g: (1 | man) + (1 | grazing)
## m6gi: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) * p_a_r + (1 | area) +
## m6gi: (1 | man) + (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m6g 9 835.01 864.96 -408.50 817.01
## m6gi 13 836.62 879.88 -405.31 810.62 6.3854 4 0.1722# m6g is best in the point of residual diagnostics# model_prop_liv_bare_RA <- m6g
model <- model_prop_liv_bare_RA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + p_a_r + (1 | area) +
## (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 812.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2606 -0.6595 -0.0604 0.6962 2.9063
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.17751 0.4213
## grazing (Intercept) 0.23397 0.4837
## man (Intercept) 0.06681 0.2585
## Residual 2.94852 1.7171
## Number of obs: 206, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.0011 0.4014 8.9413 14.950 1.25e-07 ***
## poly(RA, 2)1 -16.9234 1.8971 179.8872 -8.921 5.21e-16 ***
## poly(RA, 2)2 6.3006 1.8376 195.6551 3.429 0.00074 ***
## p_a_rp -0.8543 0.3264 190.6606 -2.617 0.00957 **
## p_a_rr 0.6485 0.3901 194.8940 1.662 0.09802 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(RA,2)1 p(RA,2)2 p_a_rp
## poly(RA,2)1 -0.166
## poly(RA,2)2 0.051 -0.027
## p_a_rp -0.534 0.195 -0.126
## p_a_rr -0.473 0.135 0.095 0.561plot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.3648 0.6948
## 203boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.993 0.4697
## 187boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 22 0.7722 0.7568
## 183leveneTest(residuals(model) ~ dataset$grazing)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 5 0.9242 0.4663
## 200boxplot(residuals(model) ~ dataset$grazing)
perfect
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + p_a_r + (1 | area) +
## (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 812.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2606 -0.6595 -0.0604 0.6962 2.9063
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.17751 0.4213
## grazing (Intercept) 0.23397 0.4837
## man (Intercept) 0.06681 0.2585
## Residual 2.94852 1.7171
## Number of obs: 206, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 6.0011 0.4014 8.9413 14.950 1.25e-07 ***
## poly(RA, 2)1 -16.9234 1.8971 179.8872 -8.921 5.21e-16 ***
## poly(RA, 2)2 6.3006 1.8376 195.6551 3.429 0.00074 ***
## p_a_rp -0.8543 0.3264 190.6606 -2.617 0.00957 **
## p_a_rr 0.6485 0.3901 194.8940 1.662 0.09802 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(RA,2)1 p(RA,2)2 p_a_rp
## poly(RA,2)1 -0.166
## poly(RA,2)2 0.051 -0.027
## p_a_rp -0.534 0.195 -0.126
## p_a_rr -0.473 0.135 0.095 0.561r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.356 0.456 0.268
## 2 poly(RA, 2)1 0.291 0.389 0.197
## 3 poly(RA, 2)2 0.054 0.126 0.010
## 4 p_a_rp 0.032 0.094 0.002
## 5 p_a_rr 0.013 0.060 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(RA, 2) 264.612 132.306 2 187.59 44.872 < 2.2e-16 ***
## p_a_r 62.357 31.179 2 105.51 10.574 6.522e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(dataset$prop_liv_bare) ~ poly(RA, 2) + p_a_r +
## (1 | area) + (1 | man) + (1 | grazing), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.8543 0.3264 -2.617 0.0237 *
## r - a == 0 0.6485 0.3901 1.662 0.2181
## r - p == 0 1.5028 0.3404 4.415 <0.001 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.17751 /(0.17751 +0.23397 +0.06681 +2.94852 )## [1] 0.051800360.23397 /(0.17751 +0.23397 +0.06681 +2.94852 )## [1] 0.068276330.06681 /(0.17751 +0.23397 +0.06681 + 2.94852 )## [1] 0.01949627relative yearly increment [%] - stem age
dataset <- vita_all[complete.cases(vita_all$prop_liv_bare) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_prop_liv_AAA <- dataset
hist(dataset$prop_liv_bare)
hist(sqrt(dataset$prop_liv_bare))
pairwise.wilcox.test(dataset$prop_liv_bare, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_liv_bare and dataset$man
##
## F Ma none
## Ma 0.00013 - -
## none 1.2e-05 0.73079 -
## S 0.02966 0.73079 0.73079
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$prop_liv_bare, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$prop_liv_bare and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.00000 - - - -
## no 0.26816 1.00000 - - -
## sheep fenced 1.00000 1.00000 0.00880 - -
## sheep trad 1.00000 1.00000 0.00042 1.00000 -
## sheep trad+ 0.82884 1.00000 1.00000 0.33944 0.84690
##
## P value adjustment method: holm# both sign
m1 <- lmer(sqrt(dataset$prop_liv_bare) ~ AAA + (1|area) + (1|man) + (1|grazing), data = dataset)
m1g <- lmer(sqrt(dataset$prop_liv_bare) ~ AAA + (1|area) + (1|man) + (1|grazing), data = dataset)
m1gi <- lmer(sqrt(dataset$prop_liv_bare) ~ AAA * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m4 <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(AAA,2) + (1|area) + (1|man) + (1|grazing), data = dataset)
m4g <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(AAA,2) + p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
m4gi <- lmer(sqrt(dataset$prop_liv_bare) ~ poly(AAA,2) * p_a_r + (1|area) + (1|man) + (1|grazing), data = dataset)
anova(m1, m1g, m1gi, m4, m4g, m4gi)## Data: dataset
## Models:
## m1: sqrt(dataset$prop_liv_bare) ~ AAA + (1 | area) + (1 | man) +
## m1: (1 | grazing)
## m1g: sqrt(dataset$prop_liv_bare) ~ AAA + (1 | area) + (1 | man) +
## m1g: (1 | grazing)
## m4: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + (1 | area) + (1 |
## m4: man) + (1 | grazing)
## m4g: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) +
## m4g: (1 | man) + (1 | grazing)
## m1gi: sqrt(dataset$prop_liv_bare) ~ AAA * p_a_r + (1 | area) + (1 |
## m1gi: man) + (1 | grazing)
## m4gi: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) * p_a_r + (1 | area) +
## m4gi: (1 | man) + (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m1 6 1615.2 1639.3 -801.60 1603.2
## m1g 6 1615.2 1639.3 -801.60 1603.2 0.0000 0
## m4 7 1609.9 1638.1 -797.94 1595.9 7.3174 1 0.006829 **
## m4g 9 1607.0 1643.2 -794.49 1589.0 6.8966 2 0.031800 *
## m1gi 10 1614.5 1654.7 -797.23 1594.5 0.0000 1 1.000000
## m4gi 13 1612.5 1664.8 -793.25 1586.5 7.9679 3 0.046679 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m4, m4g) #m4g is diagnostically best## Data: dataset
## Models:
## m4: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + (1 | area) + (1 |
## m4: man) + (1 | grazing)
## m4g: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) +
## m4g: (1 | man) + (1 | grazing)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 7 1609.9 1638.1 -797.94 1595.9
## m4g 9 1607.0 1643.2 -794.49 1589.0 6.8966 2 0.0318 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# model_prop_liv_bare_AAA <- m4g
model <- model_prop_liv_bare_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) +
## (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 1587
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8633 -0.5655 -0.0444 0.6649 3.3981
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.3596 0.5997
## grazing (Intercept) 0.1241 0.3523
## man (Intercept) 0.0000 0.0000
## Residual 2.5765 1.6052
## Number of obs: 414, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.1217 0.2580 8.7869 19.850 1.33e-08 ***
## poly(AAA, 2)1 -24.4390 1.6904 401.2906 -14.458 < 2e-16 ***
## poly(AAA, 2)2 4.6811 1.6750 406.1224 2.795 0.00544 **
## p_a_rp -0.1686 0.1764 402.3995 -0.956 0.33975
## p_a_rr 0.5263 0.2662 406.1515 1.978 0.04865 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 -0.001
## ply(AAA,2)2 0.034 0.010
## p_a_rp -0.369 -0.099 -0.142
## p_a_rr -0.255 0.151 -0.060 0.342
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.9226 0.5512
## 395boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 2.1641 0.004001 **
## 395
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 0.0682 0.9341
## 411boxplot(residuals(model) ~ dataset$p_a_r)
heteroscedasticity in area and AAA… but acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + p_a_r + (1 | area) +
## (1 | man) + (1 | grazing)
## Data: dataset
##
## REML criterion at convergence: 1587
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.8633 -0.5655 -0.0444 0.6649 3.3981
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.3596 0.5997
## grazing (Intercept) 0.1241 0.3523
## man (Intercept) 0.0000 0.0000
## Residual 2.5765 1.6052
## Number of obs: 414, groups: area, 19; grazing, 6; man, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.1217 0.2580 8.7869 19.850 1.33e-08 ***
## poly(AAA, 2)1 -24.4390 1.6904 401.2906 -14.458 < 2e-16 ***
## poly(AAA, 2)2 4.6811 1.6750 406.1224 2.795 0.00544 **
## p_a_rp -0.1686 0.1764 402.3995 -0.956 0.33975
## p_a_rr 0.5263 0.2662 406.1515 1.978 0.04865 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1 p(AAA,2)2 p_a_rp
## ply(AAA,2)1 -0.001
## ply(AAA,2)2 0.034 0.010
## p_a_rp -0.369 -0.099 -0.142
## p_a_rr -0.255 0.151 -0.060 0.342
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.373 0.442 0.310
## 2 poly(AAA, 2)1 0.326 0.395 0.259
## 3 poly(AAA, 2)2 0.018 0.052 0.002
## 5 p_a_rr 0.009 0.036 0.000
## 4 p_a_rp 0.002 0.020 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 560.79 280.395 2 404.11 108.8257 < 2e-16 ***
## p_a_r 17.84 8.921 2 405.86 3.4623 0.03229 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(dataset$prop_liv_bare) ~ poly(AAA, 2) + p_a_r +
## (1 | area) + (1 | man) + (1 | grazing), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 -0.1686 0.1764 -0.956 0.5991
## r - a == 0 0.5263 0.2662 1.978 0.1143
## r - p == 0 0.6950 0.2643 2.629 0.0224 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)0.3596 /(0.3596 +0.1241 + 2.5765 )## [1] 0.11750870.1241 /(0.3596 +0.1241 + 2.5765 )## [1] 0.04055291plant height [cm]
initial analysis revealed large differences between Managements; therefore, it is tested ad fixes effect, too.
plant height [cm] - plant age
dataset <- vita_all[complete.cases(vita_all$height) & complete.cases(vita_all$RA), ] # clean for NA for considered
dataset_height_RA <- dataset
hist(dataset$height)
hist(sqrt(dataset$height))
pairwise.wilcox.test(dataset$height, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$height and dataset$man
##
## F Ma none
## Ma 1 - -
## none 1 1 -
## S 1 1 1
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$height, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$height and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1.00 - - - -
## no 1.00 1.00 - - -
## sheep fenced 1.00 1.00 1.00 - -
## sheep trad 1.00 1.00 1.00 1.00 -
## sheep trad+ 1.00 1.00 0.39 0.92 0.61
##
## P value adjustment method: holm# both not sign
m3 <- lmer(sqrt(dataset$height) ~ RA + (1|area), data = dataset)
m3g <- lmer(sqrt(dataset$height) ~ RA + p_a_r + (1|area), data = dataset)
m3gi <- lmer(sqrt(dataset$height) ~ RA * p_a_r + (1|area), data = dataset)
m6 <- lmer(sqrt(dataset$height) ~ poly(RA,2) + (1|area), data = dataset)
m6g <- lmer(sqrt(dataset$height) ~ poly(RA,2) + p_a_r + (1|area), data = dataset)
m6gi <- lmer(sqrt(dataset$height) ~ poly(RA,2) * p_a_r + (1|area), data = dataset)
anova(m3, m3g, m3gi, m6, m6g, m6gi)## Data: dataset
## Models:
## m3: sqrt(dataset$height) ~ RA + (1 | area)
## m6: sqrt(dataset$height) ~ poly(RA, 2) + (1 | area)
## m3g: sqrt(dataset$height) ~ RA + p_a_r + (1 | area)
## m6g: sqrt(dataset$height) ~ poly(RA, 2) + p_a_r + (1 | area)
## m3gi: sqrt(dataset$height) ~ RA * p_a_r + (1 | area)
## m6gi: sqrt(dataset$height) ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m3 4 748.59 761.92 -370.30 740.59
## m6 5 750.21 766.87 -370.10 740.21 0.3838 1 0.5356
## m3g 6 733.65 753.64 -360.82 721.65 18.5613 1 1.645e-05 ***
## m6g 7 733.20 756.53 -359.60 719.20 2.4456 1 0.1179
## m3gi 8 718.13 744.79 -351.06 702.13 17.0728 1 3.597e-05 ***
## m6gi 11 722.52 759.18 -350.26 700.52 1.6144 3 0.6561
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m3gi is best in the point of residual diagnostics, but unimodal model is ecologically with more sense
anova(m6, m6g, m6gi)## Data: dataset
## Models:
## m6: sqrt(dataset$height) ~ poly(RA, 2) + (1 | area)
## m6g: sqrt(dataset$height) ~ poly(RA, 2) + p_a_r + (1 | area)
## m6gi: sqrt(dataset$height) ~ poly(RA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m6 5 750.21 766.87 -370.10 740.21
## m6g 7 733.20 756.53 -359.60 719.20 21.007 2 2.744e-05 ***
## m6gi 11 722.52 759.18 -350.26 700.52 18.687 4 0.0009053 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# m6gi#model_height_RA <- m6gi
model <- model_height_RA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$height) ~ poly(RA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 681.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7010 -0.6269 0.0168 0.5618 3.7624
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.000 0.000
## Residual 1.805 1.344
## Number of obs: 207, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.778444 0.237283 198.000000 20.138 < 2e-16 ***
## poly(RA, 2)1 -0.005202 3.574728 198.000000 -0.001 0.998840
## poly(RA, 2)2 1.060047 3.253903 198.000000 0.326 0.744937
## p_a_rp 0.653257 0.267779 198.000000 2.440 0.015587 *
## p_a_rr -0.322087 0.348572 198.000000 -0.924 0.356602
## poly(RA, 2)1:p_a_rp 15.099141 3.931838 198.000000 3.840 0.000165 ***
## poly(RA, 2)2:p_a_rp -2.946548 3.658617 198.000000 -0.805 0.421571
## poly(RA, 2)1:p_a_rr 3.802688 5.907389 198.000000 0.644 0.520504
## poly(RA, 2)2:p_a_rr -3.117723 5.933302 198.000000 -0.525 0.599850
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(RA,2)1 pl(RA,2)2 p_a_rp p_a_rr ply(RA,2)1:p__rp
## poly(RA,2)1 -0.493
## poly(RA,2)2 0.321 -0.462
## p_a_rp -0.886 0.437 -0.285
## p_a_rr -0.681 0.336 -0.219 0.603
## ply(RA,2)1:p__rp 0.448 -0.909 0.420 -0.383 -0.305
## ply(RA,2)2:p__rp -0.286 0.411 -0.889 0.220 0.195 -0.360
## ply(RA,2)1:p__rr 0.298 -0.605 0.280 -0.264 0.028 0.550
## ply(RA,2)2:p__rr -0.176 0.253 -0.548 0.156 0.467 -0.230
## ply(RA,2)2:p__rp ply(RA,2)1:p__rr
## poly(RA,2)1
## poly(RA,2)2
## p_a_rp
## p_a_rr
## ply(RA,2)1:p__rp
## ply(RA,2)2:p__rp
## ply(RA,2)1:p__rr -0.249
## ply(RA,2)2:p__rr 0.488 0.112
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularplot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$p_a_r)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 2 1.1289 0.3254
## 204boxplot(residuals(model) ~ dataset$p_a_r)
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.6637 0.04904 *
## 188
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$RA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 22 1.634 0.04289 *
## 184
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1perfect
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$height) ~ poly(RA, 2) * p_a_r + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 681.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.7010 -0.6269 0.0168 0.5618 3.7624
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.000 0.000
## Residual 1.805 1.344
## Number of obs: 207, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 4.778444 0.237283 198.000000 20.138 < 2e-16 ***
## poly(RA, 2)1 -0.005202 3.574728 198.000000 -0.001 0.998840
## poly(RA, 2)2 1.060047 3.253903 198.000000 0.326 0.744937
## p_a_rp 0.653257 0.267779 198.000000 2.440 0.015587 *
## p_a_rr -0.322087 0.348572 198.000000 -0.924 0.356602
## poly(RA, 2)1:p_a_rp 15.099141 3.931838 198.000000 3.840 0.000165 ***
## poly(RA, 2)2:p_a_rp -2.946548 3.658617 198.000000 -0.805 0.421571
## poly(RA, 2)1:p_a_rr 3.802688 5.907389 198.000000 0.644 0.520504
## poly(RA, 2)2:p_a_rr -3.117723 5.933302 198.000000 -0.525 0.599850
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) pl(RA,2)1 pl(RA,2)2 p_a_rp p_a_rr ply(RA,2)1:p__rp
## poly(RA,2)1 -0.493
## poly(RA,2)2 0.321 -0.462
## p_a_rp -0.886 0.437 -0.285
## p_a_rr -0.681 0.336 -0.219 0.603
## ply(RA,2)1:p__rp 0.448 -0.909 0.420 -0.383 -0.305
## ply(RA,2)2:p__rp -0.286 0.411 -0.889 0.220 0.195 -0.360
## ply(RA,2)1:p__rr 0.298 -0.605 0.280 -0.264 0.028 0.550
## ply(RA,2)2:p__rr -0.176 0.253 -0.548 0.156 0.467 -0.230
## ply(RA,2)2:p__rp ply(RA,2)1:p__rr
## poly(RA,2)1
## poly(RA,2)2
## p_a_rp
## p_a_rr
## ply(RA,2)1:p__rp
## ply(RA,2)2:p__rp
## ply(RA,2)1:p__rr -0.249
## ply(RA,2)2:p__rr 0.488 0.112
## optimizer (nloptwrap) convergence code: 0 (OK)
## boundary (singular) fit: see ?isSingularr2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.440 0.563 0.347
## 6 poly(RA, 2)1:p_a_rp 0.100 0.210 0.026
## 4 p_a_rp 0.043 0.132 0.002
## 5 p_a_rr 0.006 0.061 0.000
## 7 poly(RA, 2)2:p_a_rp 0.005 0.056 0.000
## 8 poly(RA, 2)1:p_a_rr 0.003 0.050 0.000
## 9 poly(RA, 2)2:p_a_rr 0.002 0.046 0.000
## 3 poly(RA, 2)2 0.001 0.041 0.000
## 2 poly(RA, 2)1 0.000 0.037 0.000anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(RA, 2) 18.316 9.1580 2 198 5.0729 0.0071030 **
## p_a_r 27.029 13.5144 2 198 7.4861 0.0007343 ***
## poly(RA, 2):p_a_r 33.770 8.4425 4 198 4.6766 0.0012542 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Plot_test <- confint(glht(model, mcp(p_a_r = "Tukey")))
summary(Plot_test)##
## Simultaneous Tests for General Linear Hypotheses
##
## Multiple Comparisons of Means: Tukey Contrasts
##
##
## Fit: lmer(formula = sqrt(dataset$height) ~ poly(RA, 2) * p_a_r + (1 |
## area), data = dataset)
##
## Linear Hypotheses:
## Estimate Std. Error z value Pr(>|z|)
## p - a == 0 0.6533 0.2678 2.440 0.03805 *
## r - a == 0 -0.3221 0.3486 -0.924 0.62010
## r - p == 0 -0.9753 0.2839 -3.435 0.00162 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## (Adjusted p values reported -- single-step method)plant height [cm] - stem age
dataset <- vita_all[complete.cases(vita_all$height) & complete.cases(vita_all$AAA), ] # clean for NA for considered
dataset_height_AAA <- dataset
hist(dataset$height)
hist(sqrt(dataset$height))
pairwise.wilcox.test(dataset$height, dataset$man)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$height and dataset$man
##
## F Ma none
## Ma 1 - -
## none 1 1 -
## S 1 1 1
##
## P value adjustment method: holmpairwise.wilcox.test(dataset$height, dataset$grazing)##
## Pairwise comparisons using Wilcoxon rank sum test with continuity correction
##
## data: dataset$height and dataset$grazing
##
## deer horses/cattle no sheep fenced sheep trad
## horses/cattle 1 - - - -
## no 1 1 - - -
## sheep fenced 1 1 1 - -
## sheep trad 1 1 1 1 -
## sheep trad+ 1 1 1 1 1
##
## P value adjustment method: holm# both not sign
m1 <- lmer(sqrt(dataset$height) ~ AAA + (1|area), data = dataset)
m1g <- lmer(sqrt(dataset$height) ~ AAA + (1|area), data = dataset)
m1gi <- lmer(sqrt(dataset$height) ~ AAA * p_a_r + (1|area), data = dataset)
m4 <- lmer(sqrt(dataset$height) ~ poly(AAA,2) + (1|area), data = dataset)
m4g <- lmer(sqrt(dataset$height) ~ poly(AAA,2) + p_a_r + (1|area), data = dataset)
m4gi <- lmer(sqrt(dataset$height) ~ poly(AAA,2) * p_a_r + (1|area), data = dataset)
anova(m1, m1g, m1gi, m4, m4g, m4gi)## Data: dataset
## Models:
## m1: sqrt(dataset$height) ~ AAA + (1 | area)
## m1g: sqrt(dataset$height) ~ AAA + (1 | area)
## m4: sqrt(dataset$height) ~ poly(AAA, 2) + (1 | area)
## m4g: sqrt(dataset$height) ~ poly(AAA, 2) + p_a_r + (1 | area)
## m1gi: sqrt(dataset$height) ~ AAA * p_a_r + (1 | area)
## m4gi: sqrt(dataset$height) ~ poly(AAA, 2) * p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m1 4 1328.3 1344.4 -660.16 1320.3
## m1g 4 1328.3 1344.4 -660.16 1320.3 0.0000 0
## m4 5 1313.0 1333.1 -651.49 1303.0 17.3222 1 3.155e-05 ***
## m4g 7 1314.7 1342.9 -650.35 1300.7 2.2831 2 0.3193276
## m1gi 8 1331.6 1363.8 -657.80 1315.6 0.0000 1 1.0000000
## m4gi 11 1316.7 1361.0 -647.36 1294.7 20.8690 3 0.0001121 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1anova(m4, m4g) #m4 is diagnostically best## Data: dataset
## Models:
## m4: sqrt(dataset$height) ~ poly(AAA, 2) + (1 | area)
## m4g: sqrt(dataset$height) ~ poly(AAA, 2) + p_a_r + (1 | area)
## npar AIC BIC logLik deviance Chisq Df Pr(>Chisq)
## m4 5 1313.0 1333.1 -651.49 1303.0
## m4g 7 1314.7 1342.9 -650.35 1300.7 2.2831 2 0.3193#model_height_AAA <- m4
model <- model_height_AAA
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$height) ~ poly(AAA, 2) + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 1302.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6610 -0.6619 -0.0472 0.5598 4.3521
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.02278 0.1509
## Residual 1.34509 1.1598
## Number of obs: 415, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.23682 0.07207 5.21503 72.663 4.84e-09 ***
## poly(AAA, 2)1 24.55036 1.16905 410.00242 21.000 < 2e-16 ***
## poly(AAA, 2)2 -4.92437 1.16916 409.22008 -4.212 3.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1
## ply(AAA,2)1 -0.021
## ply(AAA,2)2 0.001 -0.001plot(model)
qqnorm(residuals(model))
qqline(residuals(model))
leveneTest(residuals(model) ~ dataset$area)## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 0.5725 0.9189
## 396boxplot(residuals(model) ~ dataset$area)
leveneTest(residuals(model) ~ as.factor(dataset$AAA))## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 18 1.4089 0.1229
## 396heteroscedasticity in area and AAA… but looks acceptable
summary(model)## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: sqrt(dataset$height) ~ poly(AAA, 2) + (1 | area)
## Data: dataset
##
## REML criterion at convergence: 1302.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.6610 -0.6619 -0.0472 0.5598 4.3521
##
## Random effects:
## Groups Name Variance Std.Dev.
## area (Intercept) 0.02278 0.1509
## Residual 1.34509 1.1598
## Number of obs: 415, groups: area, 19
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 5.23682 0.07207 5.21503 72.663 4.84e-09 ***
## poly(AAA, 2)1 24.55036 1.16905 410.00242 21.000 < 2e-16 ***
## poly(AAA, 2)2 -4.92437 1.16916 409.22008 -4.212 3.12e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) p(AAA,2)1
## ply(AAA,2)1 -0.021
## ply(AAA,2)2 0.001 -0.001r2beta(model)## Effect Rsq upper.CL lower.CL
## 1 Model 0.526 0.582 0.469
## 2 poly(AAA, 2)1 0.516 0.573 0.457
## 3 poly(AAA, 2)2 0.041 0.086 0.012anova(model)## Type III Analysis of Variance Table with Satterthwaite's method
## Sum Sq Mean Sq NumDF DenDF F value Pr(>F)
## poly(AAA, 2) 616.83 308.42 2 409.47 229.29 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 10.02278 /(0.02278 +1.34509 )## [1] 0.01665363