Using FTIR spectra as predictor variables and chemical composition (content of major components or their groups) as response variables, predictive PLSR models for juvenile and mature woods were developed using 70 and 39 samples, respectively. Their performance was evaluated based on the minimum value of the root mean square error of prediction (RMSEP), a measure of the average accuracy of prediction of new observations, i.e. of the difference between the true and estimated values.
R2 was also used as a secondary measure (Table
2). While
R2 is a good indicator of how well a model fits actual data from which it is constructed, the reliability and predictive ability of a model are generally better assessed with the aid of appropriate cross-validation statistics. Aside from the RMSEP, the most widely used statistics for evaluating the performance of predictive models are the standard error of prediction (SEP), which measures the precision of the predictions (i.e. the difference between repeated measurements); the ratio of performance to deviation (RPD), which is the ratio of the standard error in prediction to the standard deviation; and the bias, which is the average difference between the predicted and real values, indicating under- or overestimation (Acquah et al.
2015; Chen et al.
2010; Kutner et al.
2005; Zhou et al.
2015).
In the present study, the RMSEP statistics varied across the studied chemical components, from very high for extractives in juvenile wood and galactose in mature wood, through high to moderate for most variables in both groups down to very low for hemicelluloses, despite
R2s being high across variables and wood types (Table
2). The standardization of raw spectra (consisting of four steps: (1) trimming the spectral region; (2) baseline correction; (3) normalization; and (4) smoothing), generally had a positive effect on model performance, although the minimum values of RMSEP and the corresponding
R2 attained following standardization were not necessarily superior to those obtained using raw spectra. For some variables, the predictive models yielded a slightly lower RMSEP when raw spectra were utilized and thus performed apparently better than those constructed using their standardized counterparts. However, with the exception of
Cel and
Glu in juvenile wood and
Hem and
Man in mature wood, the numbers of retained factors were greater with raw spectra (on average by 2.9 and 2.3 factors per response variable in juvenile and mature woods, respectively). This is likely to be the result of accounting for the baseline shift along with the other standardization steps. Thus, the models obtained with raw spectra were more complex, possessing an increased risk of overfitting. The unstructured patterns of
R2 and
r coefficients obtained from raw spectra (grey lines in Figs.
3 and S1, respectively), which follow nearly straight lines along the whole spectral region, confirm that raw spectra are suboptimal and that a suitable pre-processing procedure, conducted with the aim of making spectra compatible with one another, is desired when FTIR-based predictive models are constructed (see Conrad and Bonello
2016 for a review). For instance, a first derivative treatment (Owen
1995) substantially decreased RMSEP values across response variables in a study by Zhou et al. (
2015), in particular in extractives (from 1.19 to 0.34) and in lignin (from 1.05 to 0.50), with superior results reported by Acquah et al. (
2016b) as well. In the present case, the standardization accentuated differences in IR absorbance intensities among individuals at most wavenumbers for the four variables
Lig,
Cel,
Hem and
Ext in both juvenile and mature woods (Figs.
3 and S1). Therefore, untreated spectra were not used for further calibration of the models and one normalization method among TAN and AMM1–3 was chosen that performed best for each respective response variable (Table
2). The differences between the methods in terms or the minimum RMSEP were often just marginal (Table S1), on average only 1.2% and 2.0% between the first- and second-best methods and 5.1% and 4.4% between the best and worst methods in juvenile and mature woods, respectively. Thus, model performances would not be severely affected if only one normalization method was applied to all response variables and both wood types. It cannot be excluded that normalization of FTIR spectra according to other regions than the three tested in the present study, or other normalization types (e.g. point maximum or offset) could lead to even higher predictive power of the calibration models. However, these were not tested, as the results were satisfying (except for arabinose in mature wood) with these common and spectroscopically accepted procedures. The performance of the four normalization methods remained consistent between models constructed using full data sets and after removing outliers. The only exception was variable
Hem in juvenile wood, where AMM3 provided the best fit using all 70 samples, but turned to be inferior when four outliers were removed. In this case, AMM1 attained 17% lower RMSEP and 66% higher
R2 than AMM3. As to the trimming step, excluding data outside of the fingerprint region (i.e. 5200–1870 and 770–400 cm
−1) did not compromise the predictive ability of the models, similarly to what was reported by Acquah et al. (
2016b). Nearly all models’ fit further improved when all 109 samples (representing the two wood types) were pooled prior to calibration.
The present models had high predictive powers for extractives and lignin, moderate for cellulose and low for hemicelluloses (along with some of their structural monosaccharides), which is in congruence with other studies utilizing FTIR spectroscopy for similar purposes. For instance, Zhou et al. (
2015) obtained robust models for extractives and lignin (RMSEP = 0.34 and 0.50, respectively) and acceptable for cellulose (0.80), but the predictive ability for hemicelluloses was problematic (1.90), despite the
R2 being very high for this component (0.929), indicating a good fit of actual observations. Similarly, the models reported by Acquah et al. (
2016b) were good for the first three components (RPD = 2.83, 2.04 and 1.61, respectively), but unreliable for hemicelluloses (along with mannose and galactose), with RPD values remaining below 1.0. Results from some other studies using NIR spectroscopy (Acquah et al.
2015; Jones et al.
2006), which could be considered as an alternative or complementary method to FTIR, also showed that predicting hemicelluloses with reasonably high accuracies using rapid, non-destructive spectroscopic techniques remains a challenge. In these studies, predictions of hemicelluloses were poor too, with RPD values barely reaching 1.0.