Bayesian quantile regression for ordinal longitudinal data

Abstract

Since the pioneering work by Koenker and Bassett (1978), quantile regression models and its applications have become increasingly popular and important for research in many areas. In this paper, a random effects ordinal quantile regression model is proposed for analysis of longitudinal data with ordinal outcome of interest. An efficient Gibbs sampling algorithm was derived for fitting the model to the data based on a location-scale mixture representation of the skewed double exponential distribution. The proposed approach is illustrated using simulated data and a real data example. This is the first work to discuss quantile regression for analysis of longitudinal data with ordinal outcome.

Do Online Courses Provide an Equal Educational Value Compared to In-Person Classroom Teaching? Evidence from US Survey Data Using Quantile Regression

“…2 Binary quantile regression is a special of ordinal quantile regression considered in Rahman (2016) and can be linked to the random utility theory in economics (Train, 2009;Jeliazkov and Rahman, 2012). For other developments on Bayesian quantile regression with discrete outcomes, please see Alhamzawi and Ali (2018a) (henceforth, the subscript p is dropped for notational convenience), ǫ i follows an AL distribution i.e., ǫ i ∼ AL(0, 1, p), and n denotes the number of observations. In our study, the latent variable z i can be interpreted as the latent utility differential between online learning relative to in-person classroom learning.…”

Estimation and Applications of Quantile Regression for Binary Longitudinal Data

“…A normal prior on β implies a ℓ 2 penalty and has been used in Yuan and Yin (2010), and Luo et al (2012). One may also employ a Laplace prior distribution on β that imposes ℓ 1 penalization, as used in several articles such as Alhamzawi and Ali (2018). While Alhamzawi and Ali (2018) also work with quantile regression for discrete panel data (ordered, in particular), our work contributes by considering multivariate heterogeneity (not just intercept heterogeneity), and introducing computational improvements outlined below.…”

“…One may also employ a Laplace prior distribution on β that imposes ℓ 1 penalization, as used in several articles such as Alhamzawi and Ali (2018). While Alhamzawi and Ali (2018) also work with quantile regression for discrete panel data (ordered, in particular), our work contributes by considering multivariate heterogeneity (not just intercept heterogeneity), and introducing computational improvements outlined below. By Bayes' theorem, we express the "complete joint posterior" density as proportional to the product of likelihood function and the prior distributions as follows,…”

“…The paper touches on three growing econometric literatures -discrete panel data, quantile regression for panel data, and quantile regression for discrete data. In reference to the latter, quantile regression has been implemented in binary data models (Kordas, 2006;Benoit and Poel, 2012), ordered data models (Rahman, 2016;Alhamzawi and Ali, 2018), count data models (Machado and Silva, 2005;Harding and Lamarche, 2015), and censored data models (Portnoy, 2003;Harding and Lamarche, 2012). For limited dependent variables, the concern is modeling the latent utility differential in the quantile framework, since the response variable takes limited values and does not yield continuous quantiles.…”

Fully Bayesian Estimation of Simultaneous Regression Quantiles under Asymmetric Laplace Distribution Specification

“…In continuous dependent variable case and for variable selection and coefficient estimation, Alhamzawi et al [18] used adaptive LASSO quantile regression and, recently, Sayed-Ahmed [19] applied this approach for small sample sizes, whereas Abbas and Thaher [20] developed Bayesian adaptive Tobit regression. Benoit and Van den Poel [21] proposed Bayesian quantile regression methods for binary response data and Alhamzawi and Ali [22] adapted the quantile regression model to deal with longitudinal ordinal data.…”