Several nonparametric and semiparametric approaches to linear mixed model regression

Abstract

Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric (P) models, correctness of the assumed model is critical for the validity of the ensuing inference. An incorrectly specified P means model may be improved by using a local, or nonparametric (NP), model. Two local models are proposed by a pointwise weighting of the marginal and conditional variance–covariance matrices. However, NP models tend to fit to irregularities in the data and may provide fits with high variance. Model robust regression techniques estimate mean response as a convex combination of a P and a NP model fit to the data. It is a semiparametric method by which incomplete or incorrectly specified P models can be improved by adding an appropriate amount of the NP fit. We compare the approximate integrated mean square error of the P, NP, and mixed model robust methods via a simulation study and apply these methods to two real data sets: the monthly wind speed data from countries in Ireland and the engine speed data.

Keywords:

• semiparametric
• nonparametric
• mixed effects
• robust

Notes

1. Removal of some, but not all, of the observations in a cluster results in a BLUP not equal to zero for that cluster. See [30] for formulas.

2. The model studied here is similar to the model of [31], except that in this work the cluster correlated, random coefficient case is considered.