<p>This paper aims to develop a unified Bayesian approach for clustered data analysis when observations are subject to missingness at random. The authors consider a general framework in which the parameters of interest are defined through estimating equations, and the probability of missingness follows a general parametric form. The generalized method of moments framework is employed to derive an optimal combination of inverse-probability-weighted estimating equations for the parameters of interest and score equations for propensity score. Using this framework, the authors develop a quasi-Bayesian analysis for clustered samples with missing values. A unified model selection approach is also proposed to compare models characterized by different moment conditions. The authors systematically evaluate the large-sample properties of the proposed quasi-posterior density with both fixed and shrinking priors and establish the selection consistency of the proposed model selection criterion. The proposed results are valid under very mild conditions and offer significant advantages for parameters defined through non-smooth estimating functions. Extensive numerical studies demonstrate that the proposed method performs exceptionally well in finite samples.</p>