One situation where parametric approaches are no longer applicable is the so called ”small n large p” case, where the number of predictor variables p is greater than the number of subjects n. This case is common, e.g., in genetics, where thousands of genes are considered as potential predictors of a disease. However, even in studies with much lower numbers of predictor variables, the combination of all main and interaction effects of interest – especially in the case of categorical predictor variables – may well lead to cell counts too sparse for parameter convergence. Thus, interaction effects of high order usually cannot be included in standard parametric models.
