Statistical Modelling 22 (4) (2022), 297–326
Response transformations for random effect and variance component models
Amani Almohaimeed,
Department of Mathematics,
College of Science and Arts,
Qassim University,
Oyoon Aljawa, Qassim,
Saudi Arabia.
e-mail: ama.almohaimeed@qu.edu.sa
Jochen Einbeck,
Department of Mathematical Sciences and Durham Research Methods Centre,
Durham University,
Durham,
UK.
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.
Keywords:
Box-Cox transformation, Random effects model, variance component model, nonparametric maximum likelihood, EM algorithm
Downloads:
Example data and code in
R package; Vignette ; Please install R package qicharts before installing boxcoxmix.
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