To evaluate the ability of the independent variables to predict mean DH log
10 CS, we used a linear mixed-effect model. The model was calculated with the R software environment and the
nlme package.
38,39 There are at least two benefits of linear mixed-effect models over repeated measures analysis of variance (ANOVA). First, mixed-effect models have the benefit of assuming the variance of the residuals are normally distributed and not the data itself. Second, unlike repeated-measures ANOVA designs, mixed-models do not assume homoscedasticity of variance (i.e., that the variance within groups or independent variances is equal).
The full model used DH log10 CS as a dependent variable with VA, diagnosis, age, and VA test type as fixed effects and tester and subject as random effects. In the full mixed-model VA (t = −2.91, P < 0.01) and test type (t = −5.03, P < 0.001) were significant. However, including both age and test type in the model has the disadvantage that the VA test type correlates with both age (0.53) and VA (−0.48). The selection of VA test type was based on the participant's ability to perform the test, which correlated with age. Excluding the VA test type from the model, VA (t = −4.70, P < 0.01) is significant, whereas both age (t = 2.06, P = 0.046) and diagnosis (t = −1.79, P = 0.081) are marginal.
One concern when modeling is overfitting, which arises from including too many model parameters. To address the possibility of overfitting, we used a backward stepwise procedure
40 using the Akaike Information Criterion (AIC). Using AIC penalizes models that have more model parameters, and if a simpler model has a higher AIC, it is preferred over a more highly parameterized model. The full model had an AIC = 32.4, whereas a simple model that includes only VA and diagnosis had an AIC = 53.7. The increased AIC value shows the model with VA and diagnosis is the most parsimonious model for the data. Under this reduced model VA (
t = −4.67,
P < 0.001) is significant, whereas diagnosis remains marginal (
t = −1.59,
P = 0.11).