Response transformations for random effect and variance component models. (August 2022)

• Record Type: Journal Article
• Authors: Almohaimeed, Amani; Einbeck, Jochen
• Is Part Of: Statistical modelling. Volume 22:Number 4(2022)
• Page Start: 297
• Page End: 326
• Publication Date: 2022-08
• Subjects: Box-Cox transformation -- Random effects model -- variance component model -- nonparametric maximum likelihood -- EM algorithm; Linear models (Statistics) -- Periodicals; Mathematical models -- Periodicals; Modèles linéaires (Statistique) -- Périodiques; Modèles mathématiques -- Périodiques; Modèle statistique; Modèle linéaire; Modélisation statistique; Périodique électronique (Descripteur de forme); Ressource Internet (Descripteur de forme); 519.5011
• DOI: 10.1177/1471082X20966919
• Languages: English
• ISSNs: 1471-082X

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.