Logistic regression examines the relationship of an outcome variable to a set of potential predictor variables considered simultaneously. This technique determines the association of each potential predictor to the outcome variable when the effects of the other potential predictors are taken into account. That is, it determines the independent predictors of the outcome variable from the set of predictors examined (Agresti 1996; Hosmer & Lemeshow 2000; Menard 2002).
Logistic regression models were run, comparing the five disability type sub-groups, on three outcome variables:
Two types of logistic regression models were run for each of these outcome variables:
1. Preliminary logistic regression model. The preliminary model examined all potential predictors simultaneously with the exception of disability type.
2. Final logistic regression model. The final model included disability type as a potential predictor together with all the predictors that were significant (p<0.05) in the preliminary model.
This two-step approach was used to maximise the statistical power of the final models by excluding variables which were not significant predictors of the outcome variables. In each (preliminary and final) model, all of the outcome variables were treated as binary variables and all of the predictors were treated as categorical variables. Table A2 summarises the potential predictor and outcome variables in each preliminary and final regression model.
Standard versus mixed-effects logistic regression
Standard binary logistic regression was used for the outcome variable of reporting legal events, while mixed-effects binary logistic regression (Hedeker 1999) was used for the other two outcome variables. Standard logistic regression assumes the independence of observations, and was appropriate for the outcome variable of reporting legal events because there was only one observation for each participant (i.e. each participant reported either experiencing legal events or not experiencing them). The Statistical Package for the Social Sciences (SPSS) was used to run the standard logistic regressions (Green & Salkind 2003).
Mixed-effects logistic regression can be used to analyse binary outcome variables where the data are correlated as a result of clustered designs (Hedeker 1999). The outcome variables of action taken and resolution status involved potentially correlated observations because some participants had multiple legal events. The mixed-effects model allows for the possibility that the present data (for events) within clusters (participants) are dependent (e.g. a participant may respond in similar ways to the different types of events he or she experiences). The model treats participants as a random effect, estimates the degree of dependence within participants, and adjusts for this level of dependence. Adjusting for any dependence means that the model avoids falsely rejecting the null hypothesis too often, that is, it avoids falsely concluding that predictors are significant when they are not (Gibbons & Hedeker 1997). The mixed-effects logistic regression models were run using the package MIXNO (Hedeker 1999).
With the exception of two predictor variables (disability type and legal event group), comparisons were made between one chosen category of each predictor (the reference category) and each other category of that predictor (e.g. the oldest age group was compared to each other age group).
Basing comparisons on a single reference category considerably limits the interpretation of nominal (non-ordered categorical) predictors that have numerous categories because many of these categories are not directly compared against each other (Menard 2002). Disability type and legal event group were the only such predictors in the present study. For these variables, comparisons were made between each category and the average of all categories (e.g. each disability type sub-group was compared to the average effect of all disability type sub-groups).
The significance of each predictor and comparison was examined at the 0.05 level. For the standard regression, the Wald statistic (as outputted by SPSS) was used to examine the significance of each predictor and comparison. For the mixed-effects regressions, the Z statistic (as outputted by MIXNO) was examined for each comparison, and the likelihood ratio test statistic (?2) was examined for predictors with three or more categories. (MIXNO does not provide statistics on the overall significance of each predictor). For each comparison, the odds ratio and its 95 per cent confidence interval are also detailed in Appendix 3.
To address Aim 2, a single chi-square test was conducted between disability type and type of first adviser.
Although logistic regression analyses would have been appropriate for addressing Aim 4, there were insufficient numbers to conduct such analyses. Instead, a separate chi-square test was conducted on each of the 15 legal event groups between disability type and reporting legal events of that type.
The chi-square test is a non-parametric test that examines whether there is a significant relationship between two or more categorical variables, without taking into account the influence of other factors. The test is based on the cross-tabulation of the relevant variables, and compares the observed frequencies in each cell of the cross-tabulation with the frequencies expected if there were no relationship between the variables. The statistical significance of each chi-square test was examined at the 0.05 level. The standard residual of each cell was examined to determine which cells in the cross-tabulation had higher than expected frequencies, with absolute standard residuals of greater or equal to 2.0 being deemed to be significantly higher than expected (e.g. Siegel & Castellan 1988).
Mann-Whitney and Kruskal-Wallis analyses
A Mann-Whitney test was conducted to compare the number of legal events experienced by participants with a disability who reported at least one event legal as opposed to the number experienced by other participants who reported at least one legal event (Aim 1). A Kruskal-Wallis test was conducted on participants with a disability who reported at least one legal event to compare the number of legal events reported by each of the five disability type sub-groups (Aim 3). These tests are both non-parametric tests which compare independent samples (e.g. disability type sub-groups) on a single variable using ranked scores. The Mann-Whitney test is suitable for comparing two independent samples, while the Kruskal-Wallis test is suitable for comparing more than two independent samples (e.g. Green & Salkind 2003).