Model selection in linear mixed-effect models
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Model selection in linear mixed-effect models Simona Buscemi1 · Antonella Plaia1 Received: 19 September 2018 / Accepted: 17 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or random), the dimensionality of models and the structure of variance and covariance matrices, and also, wherever possible, the existence of an implemented application of the methodologies set out. Keywords Linear mixed model · Mixed model selection · AIC · BIC · MCP · LASSO · Shrinkage methods · MDL
1 Introduction Linear mixed-effects models (LMM) represent one of the most wide instruments for modeling data in applied statistics, and increasing research on linear mixed models has been rapidly in the last 10–15 years. This is due to the wide range of its applications to different types of data (clustered data such as repeated measures, longitudinal data, panel data, and small area estimation), which involve the fields of agriculture, economics, medicine, biology, sociology etc. Some practical issues usually encountered in statistical analysis concern the choice of an appropriate model, estimating parameters of interest and measuring the order
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Antonella Plaia [email protected] Simona Buscemi [email protected]
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Department of Economics, Business and Statistics, University of Palermo, Viale delle Scienze, Ed. 13, 90128 Palermo, Italy
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S. Buscemi, A. Plaia
or dimension of a model. This paper focuses on model selection, which is essential for making valid inference. The principle of model selection or model evaluation is to choose the “best approximating” model within a class of competing models, characterized by a different number of parameters, a suitable model selection criterion given a data set (Bozdogan 1987). The ideal selection procedure should lead to the “true” model, i.e., the unknown model behind the true process generating the observed data. In practice, one seeks, among a set of plausible candidate models, the parsimonious one that best approximates the “true” model. The selection of only one model among a pool of candidate models is not a trivial issue in LMMs, and the different methods proposed in the literature over time are, often, not directly comparable. In fact, not only there is a different notation among papers and great confusion as regards the software (R, SAS, MATLAB, etc.) to be us
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