A Bayesian two-stage regression approach of analysing longitudinal outcomes with endogeneity and incompleteness

Abstract

Two-stage regression methods are typically used for handling endogeneity in the simultaneous equations models in economics and other social sciences. However, the problem is challenging in the presence of incomplete response and/or incomplete endogenous covariate(s). We propose a Bayesian approach for the joint modelling of incomplete longitudinal continuous response and an incomplete count endogenous covariate, where the incompleteness is caused by the censorship through a selection mechanism. We define latent continuous variables which are left-censored at zero and develop a Gibbs sampling algorithm for the simultaneous estimation of the model parameters. We consider partially varying coefficients regression models containing covariates with fixed and time-varying effects on the response. Our work is motivated by a sample dataset from the Health and Retirement Study (HRS) for modelling the out-of-pocket medical cost, where the number of hospital admissions is considered as an endogenous covariate. Our analysis addresses some of the previously unanswered questions on the physical and financial health of the older population based on HRS data. Simulation studies are performed for assessing the usefulness of the proposed method compared to its competitors.

A Bayesian approach of analysing semi-continuous longitudinal data with monotone missingness

“…We consider a non-parametric modelling based on Legendre orthogonal polynomials (LOP). These polynomials are well-behaved basis functions (Hušková and Sen, 1985;Meyer, 2000) and have been used in non-parametric regression (Cui et al, 2006;Bhuyan et al, 2018).…”

“…Brown et al (2015) proposed a Bayesian two-part model for household debt based on the HRS data. Bhuyan et al (2018) proposed a two-stage regression model for handling endogeneity and incompleteness due to censoring for the HRS data. They used a Bayesian Tobit model for the response and the endogenous covariate.…”

An automated patient monitoring using discrete‐time wireless sensor networks

“…This general effect of time includes the effects of unobserved covariates on the biomarkers. For a sophisticated modeling of , one can use penalized splines, B‐splines, wavelets, and other nonparametric approaches . However, in our presentation, we model using a polynomial function of time for the sake of simplicity and computational ease .…”

Estimation of random-effects model for longitudinal data with nonignorable missingness using Gibbs sampling

“…Since parametric nature of β j (t) and θ k (t) is not known in advance, we consider semi-parametric approach of modelling the time-varying coefficients using Legendre polynomials (LP) basis functions. These Polynomials have already been proven as powerful tool by several authors for semiparametric regression (Marie and Sen 1985;Meyer 2000;Cui and Zhu 2006;Bhuyan et al 2019).…”