The utility of hierarchical logistic regression for predicting repeated measures binary responses

This report will employ a hierarchical logistic regression model with mixed effects as an alternative to the traditional analysis of variance (ANOVA) approach that is often used when repeated observations are taken for each treatment. In the case of a binary response variable, ANOVA approaches typically require the user to first convert responses to an appropriate continuous variable, often a total score. The data used in this report include responses from 83 participants and are coded binary. Each participant was asked to make 12 separate decisions based on information received from videos of adult informants. The original purpose of the study was to determine the effect of subjects’ age (between-subjects) and of video characteristics (within-subjects) on the likelihood that children will make the correct choice. The purpose of this report was instead methodological in nature. The results of the hierarchical model are compared to the results of a traditional mixed design analysis of variance to illustrate the strengths gained from applying hierarchical models to data that includes repeated observations per subject and to compare results when the dichotomous nature of the outcomes is appropriately modeled.