Abstract: When choosing a parametric statistical model two important considerations are mathematical soundness and substantive relevance. In this paper, we illustrate and exemplify that a number of issues arise from these considerations, even in relatively simple settings, such as ordinal regression, linear mixed models, models for cross-classified data and generalized linear mixed models. Many of our points are illustrated with data.
Key words and phrases: Binary data, conditional model, generalized linear mixed model, likelihood ratio test, linear mixed model, logistic regression, marginal model, ordinal data, random effects, score test, variance components.