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In statistical applications, the normal and the Laplace distributions areoften contrasted: the former as a standard tool of analysis, the latter as itsrobust counterpart. I discuss the convolutions of these two populardistributions and their applications in research. I consider four models withina simple $2\times 2$ scheme which is of practical interest in the analysis ofclustered (e.g., longitudinal) data. In my view, these models, some of whichare less known than others by the majority of applied researchers, constitute a'family' of sensible alternatives when modelling issues arise. In threeexamples, I revisit data published recently in the epidemiological and clinicalliterature as well as a classic biological dataset.

Mixed-effects models using the normal and the Laplace distributions: A $\mathbf{2 \times 2}$ convolution scheme for applied research