Bayesian semiparametric approach to quantile nonlinear dynamic factor analysis models with mixed ordered and nonignorable missing data

• Published in: Statistics (Berlin, DDR) Vol. 56; no. 5; pp. 1166 - 1192
• Main Authors: Tuerde, Mulati, Tang, Niansheng
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 03.09.2022; Taylor & Francis Ltd
• Subjects: Bayesian analysis; Bayesian local influence; Dirichlet problem; Dirichlet process prior; Factor analysis; Missing data; nonignorable missing data; nonlinear dynamic factor analysis; Nonlinear dynamics; Normal distribution; Perturbation; Primary 62F15; quantile regression; Secondary 62P15
• ISSN: 0233-1888; 1029-4910
• DOI: 10.1080/02331888.2022.2121399

In classical nonlinear dynamic factor analysis models (NDFAMs),  we assume manifest variables follow the normal distribution. However, in some applications, the normality assumption may be unreasonable or questionable. This paper proposes a quantile NDFAM in which manifest variables may be observed or unobserved but associated with the observed ordinal indicators or subject to missingness, and develops a Bayesian semiparametric method to estimate unknown parameters and latent variables by utilizing the Dirichlet process prior to approximate unknown distribution of random effects. Logistic and probit models are adopted to specify propensity scores for missing manifests and covariates, respectively. An exponential family distribution is assumed for missing covariates. Bayesian local influence is presented to assess the effect of minor perturbations to data, priors, and sampling distributions. Several simulation studies and a real example are illustrated by the proposed methodologies.