mixtures of the normal mean-variance of lindley factor analysis model with missing data

For a heterogeneous community comprised of multiple sub-communities‎, ‎the model-based clustering method stands out as a suitable recommendation‎. ‎moreover‎, ‎incomplete data collection and information loss may occur due to a variety of causes‎. ‎in this paper‎, ‎our focus is on investigating the mixture of factor analysis model in the presence of missing data‎. ‎here‎, ‎the latent factors and errors within each sub-cluster exhibit non-normal characteristics and adhere to the normal mean-variance mixture of lindley distribution‎. ‎this model is termed the mixture of normal mean-variance mixture of lindley factor analysis‎. ‎to estimate model parameters and generate a single imputation of potential missing values under the missing with random mechanism‎, ‎we introduce a generalized expectation-maximization algorithm‎. ‎the number of factors and mixture components are determined by the evaluation criteria of the model‎. ‎the proposed model's advantage is validated through a real dataset and simulation studies‎, ‎demonstrating its superior performance compared to existing models.