Response transformations for random effect and variance component models

Almohaimeed, Amani; Einbeck, Jochen

Abstract

Random effect models have been popularly used as a mainstream statistical technique over several decades; and the same can be said for response transformation models such as the Box–Cox transformation. The latter aims at ensuring that the assumptions of normality and of homoscedasticity of the response distribution are fulfilled, which are essential conditions for inference based on a linear model or a linear mixed model. However, methodology for response transformation and simultaneous inclusion of random effects has been developed and implemented only scarcely, and is so far restricted to Gaussian random effects. We develop such methodology, thereby not requiring parametric assumptions on the distribution of the random effects. This is achieved by extending the ‘Nonparametric Maximum Likelihood’ towards a ‘Nonparametric profile maximum likelihood’ technique, allowing to deal with overdispersion as well as two-level data scenarios.

Citation

Almohaimeed, A., & Einbeck, J. (2022). Response transformations for random effect and variance component models. Statistical Modelling, 22(4), 297-326. https://doi.org/10.1177/1471082x20966919

• Journal Article Type: Article
• Acceptance Date: Sep 28, 2020
• Online Publication Date: Dec 13, 2020
• Publication Date: Aug 1, 2022
• Deposit Date: Jan 20, 2021
• Publicly Available Date: Feb 23, 2021
• Journal: Statistical Modelling
• Print ISSN: 1471-082X
• Electronic ISSN: 1477-0342
• Publisher: SAGE Publications
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 4
• Pages: 297-326
• DOI: https://doi.org/10.1177/1471082x20966919
• Keywords: Box-Cox transformation, Random effects model, variance component model, nonparametric maximum likelihood, EM algorithm
• Public URL: https://durham-repository.worktribe.com/output/1253593