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

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.