Modelling heterogeneity: on the problem of group comparisons with logistic regression and the potential of the heterogeneous choice model

The comparison of coefficients of logit models obtained for different groups is widely considered as problematic because of possible heterogeneity of residual variances in latent variables. It is shown that the heterogeneous logit model can be used to account for this type of heterogeneity by considering reduced models that are identified. A model selection strategy is proposed that can distinguish between effects that are due to heterogeneity and substantial interaction effects. In contrast to the common understanding, the heterogeneous logit model is considered as a model that contains effect modifying terms, which are not necessarily linked to variances but can also represent other types of heterogeneity in the population. The alternative interpretation of the parameters in the heterogeneous logit model makes it a flexible tool that can account for various sources of heterogeneity. Although the model is typically derived from latent variables it is important that for the interpretation of parameters the reference to latent variables is not needed. Latent variables are considered as a motivation for binary models, but the effects in the models can be interpreted as effects on the binary response.