Two-part quantile regression models for semi-continuous longitudinal data: A finite mixture approach

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.

Quantile Mixed Hidden Markov Models for Multivariate Longitudinal Data: An Application to Children's Strengths and Difficulties Questionnaire Scores

“…Since locations and masses are completely free to vary over the corresponding support, this is a flexible method that can readily accommodate a wide range of shapes, including fat‐tailed and asymmetric distributions, and it is more robust against deviations from model assumptions. For the interested reader, a detailed survey about this method can be found in Aitkin and Alfó (1998), Alfò and Aitkin (2000), Aitkin and Alfò (2003), Alfò et al (2017, 2021) and Merlo et al (2021), for example.…”

Neural networks for quantile claim amount estimation: a quantile regression approach

“…In this paper, we focus our attention on the effect of covariates on the quantile of the aggregate claim amount S i . In order to build the two-part quantile model (see Duan et al, 1983;Frees, 2010, andMerlo et al, 2021a), we consider the indicator random variable I N i measuring whether the policyholder has zero claims or positive claims (where N i is the number of claims submitted by the policyholder). If N i > 0 then a positive aggregate claim severity Si is observed.…”

Marginal M-quantile regression for multivariate dependent data

“…In particular, dependency of observations may be seen as a clustering effect (Bergsma et al 2009) which arises in a number of sampling designs, including clustered, multilevel, spatial, and repeated measures (Heagerty et al 2000, Bergsma et al 2009, Geraci & Bottai 2014. In this context, quantile methods for modeling dependent-type data have been considered in a wide range of different applications spanning from medicine (Smith et al 2015, Farcomeni 2012, Alfò et al 2017, Marino et al 2018, Merlo, Maruotti & Petrella 2021, social inequality (Heise & Kotsadam 2015), economics (Bassett & Chen 2002, Kozumi & Kobayashi 2011, Bernardi et al 2015, Giovannetti et al 2018, Merlo, Petrella & Raponi 2021, environmental modeling (Hendricks & Koenker 1992, Pandey & Nguyen 1999, Reich et al 2011) and education (Kelcey et al 2019). When the interest of the research is on the entire conditional distribution, in addition to the classical quantile regression, a possible alternative approach is to consider the M-quantile regression proposed by Breckling & Chambers (1988).…”