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Response transformations for random effect and variance component models.

Almohaimeed, Amani and Einbeck, Jochen (2022) 'Response transformations for random effect and variance component models.', Statistical modelling., 22 (4). pp. 297-326.

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.

Item Type:Article
Keywords:Box-Cox transformation, Random effects model, variance component model, nonparametric maximum likelihood, EM algorithm
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1177/1471082X20966919
Publisher statement:Almohaimeed A, Einbeck J. Response transformations for random effect and variance component models. Statistical Modelling. 2022;22(4):297-326. doi:10.1177/1471082X20966919
Date accepted:28 September 2020
Date deposited:23 February 2021
Date of first online publication:13 December 2020
Date first made open access:23 February 2021

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