Tzavidis, N., Salvati, N., Geraci, M. and Bottai, M.
M-Quantile and expectile random effects regression for multilevel data. Southampton, GB, Southampton Statistical Sciences Research Institute, 26pp.
(S3RI Methodology Working Papers, M10/07).
The analysis of hierarchically structured data is usually carried out by using random effects models. The
primary goal of random effects regression is to model the expected value of the conditional distribution
of an outcome variable given a set of explanatory variables while accounting for the dependence structure
of hierarchical data. The expected value, however, may not offer a complete picture of this conditional
distribution. In this paper we propose using linear M-quantile regression, to model other parts of the
conditional distribution of the outcome variable given the covariates. The proposed random effects
regression model extends M-quantile regression and can be viewed as an alternative to the quantile
random effects model. Inference for estimators of the fixed and random effects parameters is discussed.
The performance of the proposed methods is evaluated in a series of simulation studies. Finally, we
present a case study where M-quantile and expectile random effects regression is employed for analyzing
repeated measures data collected from a rotary pursuit tracking experiment.
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