Modeling repeated measures of dichotomous data: Testing whether the within-person trajectory of change varies across levels of between-person factors

In this paper, we consider the following question for the analysis of data obtained in longitudinal panel designs: How should repeated-measures data be modeled and interpreted when the outcome or dependent variable is dichotomous and the objective is to determine whether the within-person rate of change over time varies across levels of one or more between-person factors? Standard approaches address this issue by means of generalized estimating equations or generalized linear mixed models with logistic links. Using an empirical example and simulated data, we show (1) that cross-level product terms from these models can produce misleading results with respect to whether the within-person rate of change varies across levels of a dichotomous between-person factor; and (2) that subgroup differences in the rate of change should be assessed on an additive scale (using group differences in the effects of predictors on the probability of disease) rather than on a multiplicative scale (using group differences in the effects of predictors on the odds of disease). Because usual approaches do not provide a significance test for whether the rate of additive change varies across levels of a between-person factor, sample differences in the rate of additive change may be due to sampling error. We illustrate how standard software can be used to estimate and test whether additive changes vary across levels of a between-person factor.