Appendix
In this appendix we present the details of the multilevel analyses that we conducted. Each table in the appendix shows the results for one of the dependent variables in our conceptual model. In our model, all independent variables were divided into a judge level variable and a case level variable (Enders & Tofighi,
2007). The judge level variables were the mean values for all cases adjudicated by a specific judge and were grand-mean centered, that is, the overall mean was subtracted in such a way that the average across all judges was 0. The case level variables consisted of the remaining variance of the original variables within each judge and were group mean centered (here: judge mean centered), that is, the mean value for the judge was subtracted from the original variable (Enders & Tofighi,
2007). This means that the judge level variables and the case level variables were completely unrelated (
r = 0.00), and all variance of the original variables was represented in the sum of the judge level and case level variables.
We tested our conceptual model using a hierarchical regression in the multilevel analysis, in which we entered the variables step-by-step, starting with the first variable in the model (litigant perceptions of outcome importance) and working towards the end (litigant perceptions in procedural justice). First, for each variable in the study, the Intraclass Correlation (ICC) was computed by estimating the random variance in the intercept, i.e., the between-judge variance in the variable (Model 1). In Model 2, the litigants’ perceptions of outcome importance scale (both at judge level and at case level) was entered into the regression. In Model 3, the judicial perceptions of outcome importance scale (both at judge level and case level) was entered into the regression. In Model 4, the judicial perceptions of procedural justice scale (both at judge level and case level) was entered into the regression. In Model 5, the litigants’ perceptions of procedural justice scale (both at judge level and at case level) was entered into the regression. Only when the fit of the model improved by an additional step in the regression was the contribution of the added predictors considered. In all analyses full information maximum likelihood estimation was used, and random slopes were restricted to zero.
The Intraclass Correlation (ICC) is a measure of the extent to which different cases of a single judge resemble each other and indicates the proportion of the variance explained by the nested structure of our data. A high ICC shows that there are differences in the level of a variable between judges, and a low ICC shows that there are differences in the level of a variable between cases, within judges.
The ICCs for our judicial variables were significant. For judicial perceptions of outcome importance, the ICC was 0.46, showing that 46% of the variance in outcome importance as perceived by the judge systematically varied between judges. The ICC for judicial perceptions of procedural justice was 0.67, which means that 67% of the variance in how judges perceived procedural justice varied systematically between judges. This means that the majority of the variance in judicial perceptions of procedural justice is between judges, and to a lesser extent between cases within judges.
On the other hand, ICCs for the variables measured among litigants were not significant, which means that litigants did not differ strongly in their perceptions depending on the judge who adjudicated their case. For litigant perceptions of procedural justice the ICC was 0.13, which means that 13% of the variance in litigant perceptions of procedural justice varied systematically between judges. For litigant perceptions of outcome importance, the ICC was 0.04, which means that 4% of the variance in outcome importance varied systematically between judges. For trust in judges, the ICC was 0.10, which means that 10% of the variance in trust in judges varied systematically between judges.
The ICCs of both judicial perceptions and litigant perceptions thus revealed that, to different degrees, part of the variance of our variables is explained by the nested structure of our data. To do justice to this nested structure, we divided all independent variables into a judge level variable and a case level variable. The judge level variables contain the differences between judges, and the case level variables contain the differences between specific cases within judges.
Table
Table 3
Multilevel regression analysis of judicial perceptions of outcome importance
Judge level | 5.76 | 0.13*** | 5.78 | 0.12*** |
Litigant Perceptions of outcome importance | | | 0.54 | 0.18** |
Case level |
Litigant Perceptions of outcome importance | | | 0.11 | 0.05* |
Fit (−2 log L) | 449.51 | | 435.02 | |
Δ fit | | | 14.49*** | |
Df | | | 2 | |
Variance |
Random intercept (judge level) | 0.48** | | 0.38* | |
Residual (case level) | 0.55*** | | 0.52*** | |
ICC | 0.46 | | | |
Explained variance (%) | 0 | | 13 | |
3 shows the results for judicial perceptions of outcome importance. We found a statistically significant relationship between judge level litigant perceptions of outcome importance and judicial perceptions of outcome importance (
b = 0.54,
p = 0.004), indicating that judges considered the litigants’ outcomes as more important when the litigants in their cases on average considered their outcomes as more important. In other words, if a judge’s caseload consisted of three cases with litigants involved, the average perception of these three litigants was related to the judicial perceptions of outcome importance. Thus, on an aggregate or judge level, we found that litigants and judges correspond in their view on outcome importance.
We further found a statistically significant relationship between case level litigant perceptions of outcome importance and judicial perceptions of outcome importance (b = 0.11, p = 0.013). This indicated that when litigants perceived their outcome in the specific law case as more important, judges also tended to perceive the litigants’ outcome as more important. In other words, both the average outcome importance in their cases and the outcome importance in a specific case as perceived by the litigants influenced how important judges rated their cases on the judicial perceptions of outcome importance scale. These findings support Hypothesis 1. Outcome importance as perceived by litigants was positively associated with how important judges thought the outcome would be for the litigant. When litigants perceived their outcome as relatively important, judges also regarded the outcome as relatively important for the litigant.
Table
Table 4
Multilevel regression analysis of judicial perceptions of procedural justice
Intercept | 6.17 | 0.08*** | 6.17 | 0.08*** | 6.18 | 0.07*** |
Judge level |
Litigant perceptions of outcome importance | | | 0.12 | 0.11 | 0.02 | 0.11 |
Judicial perceptions of outcome importance | | | | | 0.19 | 0.09* |
Case level |
Litigant perceptions of outcome importance | | | 0.01 | 0.02 | −0.00 | 0.02 |
Judicial perceptions of outcome importance | | | | | 0.08 | 0.03* |
Fit (−2 log L) | 156.88 | | 155.5 | | 146.54 | |
Δ fit | | | 1.38 | | 12.96* | |
Df | | | 2 | | 2 | |
Variance |
Random intercept (judge level) | 0.18*** | | 0.18*** | | 0.16*** | |
Residual (case level) | 0.09*** | | 0.09*** | | 0.09*** | |
ICC | 0.67 | | | | | |
Explained variance (%) | 0 | | 2 | | 12 | |
4 shows the results for judicial perceptions of procedural justice. Neither case level litigant perceptions of outcome importance nor judge level litigant perceptions of outcome importance in Model 2 contributed to the regression of judicial perceptions of procedural justice. Adding judicial perceptions of outcome importance in Model 3 showed that both case level judicial perceptions of outcome importance (
b = 0.08,
p = 0.027) and judge level judicial perceptions of outcome importance (
b = 0.19,
p = 0.037) were significantly related to judicial perceptions of procedural justice.
The positive relationship between case level judicial perceptions of outcome importance and judicial perceptions of procedural justice indicates that judges regarded themselves as being especially fair if they regarded the outcome as more important for a specific litigant. In addition, the judge level relationship with judicial perceptions of outcome importance shows that judges who regarded litigants’ outcomes on average as more important perceived themselves as treating litigants more fairly. In other words, the fact that judges rated their behavior as relatively high on the judicial perceptions of procedural justice scale is not only influenced by how important they perceive the outcome for a specific litigant, but also by the fact that some judges perceive litigants’ outcomes on average as important. These findings are consistent with Hypothesis 2. Judicial perceptions of outcome importance were positively related to judicial perceptions of procedural justice. When judges regarded the outcome as relatively important for the litigant, they also perceived their own treatment of the litigant as relatively fair.
Full information maximum likelihood estimation was used, and random slopes were restricted to zero. Table
Table 5
Multilevel regression analysis of litigant perceptions of procedural justice
Intercept | 5.87 | 0.11*** | 5.87 | 0.10*** | 5.88 | 0.10*** | 5.87 | 0.10*** |
Judge level |
Litigant Perceptions of Outcome importance | | | 0.23 | 0.16 | 0.11 | 0.17 | 0.12 | 0.16 |
Judicial Perceptions of Outcome Importance | | | | | 0.27 | 0.14 | 0.34 | 0.15* |
Judicial Perceptions of Procedural Justice | | | | | | | −0.29 | 0.23 |
Case level |
Litigant Perceptions of Outcome Importance | | | 0.30 | 0.06*** | 0.32 | 0.06*** | 0.31 | 0.06*** |
Judicial Perceptions of Outcome Importance | | | | | −0.09 | 0.11 | −0.11 | 0.11 |
Judicial Perceptions of Procedural Justice | | | | | | | 0.35 | 0.26 |
Fit (−2 log L) | 479.23 | | 455.54 | | 451.12 | | 447.94 | |
Δ fit | | | 23.69*** | | 4.42 | | 3.18 | |
Df | | | 2.00 | | 2.00 | | 2.00 | |
Variance | | | | | | | | |
Random intercept (judge level) | 0.15 | | 0.15 | | 0.14 | | 0.12 | |
Residual (case level) | 0.99*** | | 0.85*** | | 0.83*** | | 0.82*** | |
ICC | 0.13 | | | | | | | |
Explained variance (%) | 0 | | 13 | | 16 | | 18 | |
5 shows the results for litigant perceptions of procedural justice. Case level litigant perceptions of outcome importance contributed significantly to the regression of litigant perceptions of procedural justice in Model 2 (
b = 0.30,
p < 0.001), Model 3 (
b = 0.32,
p < 0.001) and Model 4 (
b = 0.31,
p < 0.001). These findings indicate that litigants who perceived their outcome in the specific case as more important were more likely to perceive their treatment as fair. Adding judicial perceptions of outcome importance in Model 3 showed that neither case level nor judge level judicial perceptions of outcome importance were significantly related to litigant perceptions of procedural justice. After adding judicial perceptions of procedural justice in Model 4, judge level judicial perceptions of outcome importance were significantly related to litigant perceptions of procedural justice (
b = 0.34,
p = 0.031). This indicates that judges who perceived the outcome on average to be more important for litigants were more likely to be perceived as fair by litigants. Adding judicial perceptions of procedural justice in Model 4 showed no statistically significant relationship between judicial perceptions of procedural justice and litigant perceptions of procedural justice. Apparently, whether judges considered themselves as acting particularly procedurally fairly or not in a specific case was unrelated to how fair litigants perceived they had been treated by the judge. This means that we did not find support for Hypothesis 3 that judicial perceptions of procedural justice would be positively related to litigant perceptions of procedural justice. Litigant perceptions of procedural justice could not be explained by how fair judges estimated their own behavior.
Table
Table 6
Multilevel regression analysis of trust in judges
Intercept | 5.73 | 0.11*** | 5.74 | 0.10*** | 5.74 | 0.09*** | 5.74 | 0.09*** | 5.76 | 0.06*** | |
Judge level | |
Litigant Perceptions of Outcome Importance | | | 0.32 | 0.15* | 0.19 | 0.16 | 0.19 | 0.15 | 0.12 | 0.10 | |
Judicial Perceptions of Outcome Importance | | | | | 0.28 | 0.14* | 0.35 | 0.15* | 0.09 | 0.11 | |
Judicial Perceptions of Procedural Justice | | | | | | | −0.22 | 0.22 | −0.00 | 0.15 | |
Litigant Perceptions of Procedural Justice | | | | | | | | | 0.76 | 0.10*** | |
Case level | |
Litigant Perceptions of Outcome Importance | | | 0.15 | 0.07* | 0.15 | 0.07* | 0.15 | 0.07* | −0.09 | 0.06 | |
Judicial Perceptions of Outcome Importance | | | | | 0.00 | 0.12 | 0.01 | 0.12 | 0.05 | 0.09 | |
Judicial Perceptions of Procedural Justice | | | | | | | −0.05 | 0.30 | −0.14 | 0.22 | |
Litigant Perceptions of Procedural Justice | | | | | | | | | 0.74 | 0.07*** | |
Fit (−2 log L) | 456.29 | | 447.39 | | 443.20 | | 442.14 | | 335.47 | | |
Δfit | | | 8.90** | | 4.19 | | 1.06 | | 106.67*** | | |
Df | | | 2.00 | | 2.00 | | 2.00 | | 2.00 | | |
Variance | |
Random intercept (judge level) | 0.12 | | 0.08 | | 0.06 | | 0.05 | | − | | |
Residual (case level) | 1.04*** | | 1.01*** | | 0.99*** | | 0.99*** | | 0.52*** | | |
ICC | 0.10 | | | | | | | | | | |
Explained variance (%) | 0 | | 7 | | 9 | | 10 | | 55 | | |
6 shows the results for trust in judges. Case level litigant perceptions of outcome importance in Model 2 contributed significantly to the regression of trust in judges (
b = 0.15,
p = 0.030), indicating that litigants who perceive their outcome in the specific case as more important are more likely to trust judges. Judge level litigant perceptions of outcome importance in Model 2 also contributed significantly to the regression of trust in judges (
b = 0.31,
p = 0.038), indicating that judges with cases that on average are considered to be more important by litigants are more trusted by these litigants. This indicates that litigants who perceived their outcome as more important were more likely to trust judges.
Adding judicial perceptions of outcome importance in Model 3 showed that judge level judicial perceptions of outcome importance was significantly related to trust in judges (b = 0.28, p = 0.043). This finding indicates that judges who on average considered litigants’ outcomes to be more important were more likely to be trusted by litigants. This relationship remained significant when judicial perceptions of procedural justice was added in Model 4 (b = 0.35, p = 0.023).
Adding litigant perceptions of procedural justice in Model 5 shows a statistically significant relationship between case level litigant perceptions of procedural justice and trust in judges (b = 0.74, p < 0.001). Litigants who perceived higher levels of procedural justice in their specific case also stated that they had higher levels of trust in the judge who handled their case. We also found a statistically significant relationship between judge level litigant perceptions of procedural justice and trust in judges (b = 0.76, p < 0.001). This indicates that judges who on average are perceived as procedurally fair by litigants are more trusted by these litigants. These findings are consistent with our Hypothesis 4. Litigant perceptions of procedural justice were positively associated with trust in judges. After controlling for litigant perceptions of procedural justice, the relationships of litigant perceptions of outcome importance and judicial perceptions of outcome importance with trust in judges were no longer significant.
Multilevel Reliability
The two judicial variables had substantial variation at the judge level, which is why multilevel analyses were necessary. This also means that reliability of these variables has to be assessed both at the case level (level 1,
αw), and at the judge level (level 2,
αb). Following the procedure described by Geldhof et al. (
2014), we computed the multilevel reliability with multilevel structural equation modeling in R using the Lavaan-package (version 0.6–9). For judicial perceptions of outcome importance (4 items) the model converged, and resulted in reliability estimates at the case level of
αw = 0.90 and at the judge level
αb = 0.88. However, for judicial perceptions of procedural justice, the model assessing the variance–covariance matrix at both levels did not converge due to the large number of items in the scale (11 items). This large number is especially problematic given the limited number of judges and cases. We therefore constructed 4 indicators of judicial perceptions of procedural justice, each consisting of the mean score of 3 or 2 items. In this way, all 11 items were included. This model converged, and resulted in reliability estimates at the case level (
αw = 0.86) and at the judge level (
αb = 0.95).
Finally, we note that it is not possible to consider the judicial procedural justice scale as a ordinal scale as it is based on the mean value of 11 items. We inspected the distribution of this scale in detail, both at the judge level and at the case level. Despite the high mean value of 6.15, the distribution largely resembled a normal distribution. At the case level (N = 199: skewness = −0.115, SE = 0.172; kurtosis = 0.011, SE = 0.343), at the judge level (N = 38: skewness = 0.168, SE = 0.383; kurtosis = −0.205, SE = 0.750; please note that kurtosis in SPSS has value 0 for a normal distribution rather than value 3). This means that the Maximum Likelihood estimation, which in itself is rather robust against small deviations of normality, is suitable for our analysis.
Influence of Context Variables
In Table
Table 7
The influence of context variables in the multilevel regressions
Intercept | 5.63 | 0.59 | 0.000 | 5.80 | 0.37 | 0.000 | 6.27 | 0.18 | 0.000 |
Case type 1 (landlord-tenant) | 0.76 | 0.36 | 0.034 | 0.15 | 0.38 | 0.705 | 0.15 | 0.20 | 0.469 |
Case type 2 (bankruptcy) | 0.89 | 0.25 | 0.000 | 0.40 | 0.39 | 0.319 | −0.04 | 0.21 | 0.838 |
Case type 3 (administrative, reference) | 0 | – | | 0 | – | | 0 | – | |
Age | 0.00 | 0.01 | 0.658 | −0.00 | 0.00 | 0.795 | −0.00 | 0.00 | 0.133 |
Gender | 0.00 | 0.22 | 0.986 | 0.11 | 0.13 | 0.396 | 0.03 | 0.06 | 0.638 |
Education | −0.04 | 0.04 | 0.342 | 0.01 | 0.03 | 0.757 | 0.00 | 0.01 | 0.834 |
Income | −0.12 | 0.07 | 0.090 | −0.03 | 0.04 | 0.489 | −0.01 | 0.02 | 0.455 |
Experience | −0.19 | 0.21 | 0.367 | −0.11 | 0.12 | 0.363 | 0.03 | 0.05 | 0.539 |
Legal assistance | 0.43 | 0.22 | 0.052 | 0.08 | 0.13 | 0.509 | −0.05 | 0.06 | 0.422 |
Gender of judge | 0.28 | 0.25 | 0.264 | −0.28 | 0.35 | 0.434 | 0.23 | 0.18 | 0.218 |
Judge level—Litigant outcome importance | | | | 0.53 | 0.24 | 0.034 | −0.06 | 0.13 | 0.654 |
Judge level—Judicial outcome importance | | | | | | | 0.21 | 0.10 | 0.033 |
Case level—Litigant outcome importance | | | | 0.12 | 0.05 | 0.011 | 0.00 | 0.02 | 0.870 |
Case level—Judicial outcome importance | | | | | | | 0.05 | 0.04 | 0.229 |
Intercept | 5.52 | 0.46 | 0.000 | 5.24 | 0.34 | 0.000 | | | |
Case type 1 (landlord-tenant) | −0.03 | 0.33 | 0.936 | −0.12 | 0.22 | 0.578 | | | |
Case type 2 (bankruptcy) | 0.00 | 0.30 | 0.988 | −0.18 | 0.19 | 0.354 | | | |
Case type 3 (administrative, reference) | 0 | – | | 0 | – | | | | |
Age | −0.00 | 0.01 | 0.667 | 0.01 | 0.00 | 0.138 | | | |
Gender | 0.01 | 0.18 | 0.959 | 0.02 | 0.13 | 0.870 | | | |
Education | 0.04 | 0.04 | 0.241 | −0.02 | 0.03 | 0.347 | | | |
Income | 0.01 | 0.06 | 0.849 | 0.04 | 0.04 | 0.280 | | | |
Experience | 0.23 | 0.16 | 0.166 | 0.25 | 0.12 | 0.036 | | | |
Legal assistance | 0.02 | 0.18 | 0.893 | 0.12 | 0.13 | 0.369 | | | |
Gender of judge | 0.34 | 0.24 | 0.186 | 0.42 | 0.15 | 0.007 | | | |
Judge level—Litigant outcome importance | −0.01 | 0.20 | 0.944 | 0.07 | 0.13 | 0.598 | | | |
Judge level—Judicial outcome importance | 0.41 | 0.17 | 0.017 | 0.17 | 0.12 | 0.142 | | | |
Judge level—Judicial procedural justice | −0.35 | 0.25 | 0.178 | −0.08 | 0.17 | 0.648 | | | |
Judge level—Litigant procedural justice | | | | 0.64 | 0.11 | 0.000 | | | |
Case level—Litigant outcome importance | 0.35 | 0.07 | 0.000 | −0.10 | 0.06 | 0.076 | | | |
Case level—Judicial outcome importance | −0.06 | 0.13 | 0.659 | 0.08 | 0.09 | 0.412 | | | |
Case level—Judicial procedural justice | 0.10 | 0.30 | 0.746 | −0.21 | 0.22 | 0.341 | | | |
Case level—Litigant procedural justice | | | | 0.74 | 0.07 | 0.000 | | | |
7, details of the influence of context variables on the main analyses are shown.