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

TL;DR

This paper explores convolution models combining normal and Laplace distributions for robust and standard statistical analysis of clustered data, demonstrating their practical applications through real-world examples.

Contribution

It introduces a simple 2x2 convolution scheme for mixed-effects models using normal and Laplace distributions, expanding the toolkit for applied research.

Findings

Models provide robust alternatives for clustered data analysis

Application to epidemiological and biological datasets demonstrates usefulness

Some models are less known but practically relevant

Abstract

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