Title: Box-Cox transformation for regression models with random effects
Authors: Amani Almohaimeed - Durham University (United Kingdom) [presenting]
Jochen Einbeck - Durham University (United Kingdom)
Abstract: Regression analyses can help us to detect trends, examine relationships and draw meaningful conclusions from experimental data. However, the assumptions of normality and of homoscedasticity of the response must be fulfilled prior to starting to analyze the data. The aim is to ensure the validity of a normal response distribution using the Box-Cox power transformation. The extension of this transformation to the linear mixed effects model was previously proposed in the case of a Gaussian random effect distribution. An obvious concern of assuming a normal random effect distribution is whether there are any harmful effects of a potential misspecification. This problem can be avoided by estimating this distribution implicitly via the EM algorithm, through the use of a technique known as Nonparametric Maximum Likelihood, which, for our purposes, is adapted towards a Nonparametric Profile Maximum Likelihood technique. The feasibility of the approach is demonstrated through examples using a new R package, boxcoxmix, to be available on the Comprehensive R Archive Network (CRAN).