A primer on distributional assumptions and model linearity in repeated measures data analysis

Repeated measures data are widely used in social and behavioral sciences, e.g., to investigate the trajectory of an underlying phenomenon over time. A variety of different mixed-effects models, a type of statistical modeling approach for repeated measures data, have been proposed and they differ mainly in two aspects: (1) the distributional assumption of the dependent variable and (2) the linearity of the model. Distinct combinations of these characteristics encompass a variety of modeling techniques. Although these models have been independently discussed in the literature, the most flexible framework - the generalized nonlinear mixed-effects model (GNLMEM) - can be used as a modeling umbrella to encompass these modeling options for repeated measures data. Therefore, the aim of this paper is to explicate on the different mixed-effects modeling techniques guided by the distributional assumption and model linearity choices using the GNLMEM as a general framework. Additionally, empirical examples are used to illustrate the versatility of this framework.