Mixed Model Selection: Theory and Application

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AbstractDMS-0203676 & 0203724PIs: Jiang/RaoThis research involves development of model selection procedures for linear and generalized linear mixed models. The focus of this research will be on studying asymptotic properties and finite sample performance of the procedures, which will include comparisons to commonly used ad hoc methods. The research will also develop applications of the selection methodology to selecting factors in longitudinal data, genetic screening of genes related to quantitative traits of interest, and to model selection in small area estimation problems from surveys. In addition, the methods developed will be made accessible through the development of freely available software. The research will also improve work recently completed by the investigators where the conditions for consistent factor selection in linear mixed models were established. These improvements will include developing a more efficient method for linear mixed model selection, and studying some adaptive procedures. Linear and generalized linear mixed models are important classes of models which allow relaxation of standard assumptions like independence or homogeneity of variances of observations, and take into account more complicated data structures in quite general ways. Typical applications include repeated measurements made on a patient over time or screening of candidate genes that might be related to a quantitative trait of interest. Selecting which factors should or should not be in the model can be of importance for model inference and predictions, yet little if anything has been developed to formally study this problem. This research attempts to fill this important gap in the field of developing new procedures for correct factor selection from a theoretical perspective, and evaluating real-world performance via extensive simulations. Another important component of this research is to apply it in a variety of real-world settings including longitudinal data, genetic screening, and small area estimation in survey sampling.