Statistical Modelling 22 (6) (2022), 485–508
Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach
Luca Merlo,
Department of Statistical Sciences,
Sapienza University of Rome,
Rome,
Italy.
e-mail: luca.merlo@uniroma1.it
Antonello Maruotti,
Department of Mathematics,
University of Bergen,
Bergen,
Norway.
Lea Petrella,
MEMOTEF Department,
Sapienza University of Rome,
Rome,
Italy.
Abstract:
This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.
Keywords:
correlated random effect models, LASSO, Nonparametric ML estimation, quantile regression mixture models, semi-continuous longitudinal data, two-part models
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