Journal
STATISTICAL MODELLING
Volume 22, Issue 4, Pages 297-326Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1471082X20966919
Keywords
Box-Cox transformation; Random effects model; variance component model; nonparametric maximum likelihood; EM algorithm
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Funding
- Qassim University
- CRoNoS COST Action [IC1408]
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Random effect models and response transformation models are widely used statistical techniques. However, the methodology for simultaneously including both random effects and response transformation has been limited. This study develops a nonparametric profile maximum likelihood technique to address this issue.
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.
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