Title: Unsupervised Learning of Mixture Regression Models for Longitudinal Data,
Abstract: This paper is concerned with learning of mixture regression models for
individuals that are measured repeatedly. The adjective "unsupervised" implies
that the number of mixing components is unknown and has to be determined,
ideally by data driven tools. For this purpose, a novel penalized method is
proposed to simultaneously select the number of mixing components and to
estimate the mixing proportions and unknown parameters in the models. The
proposed method is capable of handling both continuous and discrete responses
by only requiring the first two moment conditions of the model distribution. It
is shown to be consistent in both selecting the number of components and
estimating the mixing proportions and unknown regression parameters. Further, a
modified EM algorithm is developed to seamlessly integrate model selection and
estimation. Simulation studies are conducted to evaluate the finite sample
performance of the proposed procedure. And it is further illustrated via an
analysis of a primary biliary cirrhosis data set.