Bayesian analysis of two-part nonlinear latent variable model: Semiparametric method

Abstract

Two-part model (TPM) is a widely appreciated statistical method for analyzing semi-continuous data. Semi-continuous data can be viewed as arising from two distinct stochastic processes: one governs the occurrence or binary part of data and the other determines the intensity or continuous part. In the regression setting with the semi-continuous outcome as functions of covariates, the binary part is commonly modelled via logistic regression and the continuous component via a log-normal model. The conventional TPM, still imposes assumptions such as log-normal distribution of the continuous part, with no unobserved heterogeneity among the response, and no collinearity among covariates, which are quite often unrealistic in practical applications. In this article, we develop a two-part nonlinear latent variable model (TPNLVM) with mixed multiple semi-continuous and continuous variables. The semi-continuous variables are treated as indicators of the latent factor analysis along with other manifest variables. This reduces the dimensionality of the regression model and alleviates the potential multicollinearity problems. Our TPNLVM can accommodate the nonlinear relationships among latent variables extracted from the factor analysis. To downweight the influence of distribution deviations and extreme observations, we develop a Bayesian semiparametric analysis procedure. The conventional parametric assumptions on the related distributions are relaxed and the Dirichlet process (DP) prior is used to improve model fitting. By taking advantage of the discreteness of DP, our method is effective in capturing the heterogeneity underlying population. Within the Bayesian paradigm, posterior inferences including parameters estimates and model assessment are carried out through Markov Chains Monte Carlo (MCMC) sampling method. To facilitate posterior sampling, we adapt the Polya-Gamma stochastic representation for the logistic model. Using simulation studies, we examine properties and merits of our proposed methods and illustrate our approach by evaluating the effect of treatment on cocaine use and examining whether the treatment effect is moderated by psychiatric problems.

Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations

“…In particular, both methods support that 'family culture' is relevant to the amount of household finance debt being held. This fact is also revealed by [18] in an analysis of the CHFS using a two-part nonlinear latent variable model. Further interpretation is omitted in order to save space.…”

“…[17] incorporated a two-part regression model into a general latent variable model framework and analyzed the internal relationships between multiple factors longitudinally. These methods have brought significant attention to two-part models in behavioral science, economics, psychology, and medicine in recent years: see, for example [14,18,19], and references therein for further developments of two-part models.…”

Assessing Heterogeneity of Two-Part Model via Bayesian Model-Based Clustering with Its Application to Cocaine Use Data

“…By taking advantage of series sampling method [54], Polson et al [53] devised a rejection algorithm for generating observations from such type of distribution. Their method can be adapted to draw ω iℓ , see also [55].…”

Bayesian Feature Extraction for Two-Part Latent Variable Model with Polytomous Manifestations

“…[17] incorporated a two-part regression model into a general latent variable model framework and analyzed the internal relationships between multiple factors longitudinally. These methods have brought significant attention to two-part models in behavioral science, economics, psychology, and medicine in recent years: see, for example [14,18,19], and references therein for further developments of two-part models.…”