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Logistic regression analysis with multidimensional random effects : A comparison of three approaches

This paper investigates the performance of three types of random coefficients logistic regression models; that is, models using parametric, semi-parametric, and nonparametric specifications of the distribution of the random effects. Whereas earlier studies focussed on models with a single random effect, here we look at models with multidimensional random effects (intercepts and slopes). Moreover, also the performance of a semi-parametric approach – using mixture regression models with number of latent classes is selected using the BIC – is investigated. One of the main conclusions of our study is that the good results obtained with the nonparametric approach in the unidimensional case do not generalize to the multidimensional case. Parametric and semi-parametric approaches are much better in terms of bias and relative efficiency than the nonparametric approach. For the fixed-effects estimation, a parametric approach is the preferred method when the underlying assumption of the parametric model holds. In other situations, the semi-parametric approach is the best choice.