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Missing data are exceedingly common across a variety of disciplines including educational area. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have problems such as leaving the data incomplete and failing to accommodate incomplete covariates with non-linear terms and random effects. We propose a Bayesian latent variable imputation approach to impute missing data due to MNAR (and other missingness mechanisms) and estimate the model of substantive interest simultaneously. Computer simulation results suggest that except when the sample size was small, estimates from the proposed Bayesian latent variable imputation approach tracked closely with those from the complete data analysis.