| Summary: | 碩士 === 逢甲大學 === 統計學系統計與精算碩士班 === 102 === Mixture of common factor analyzers (MCFA), which is a fusion of Gaussian mixture models and factor analysis models, provides the ability to analyze high-dimensional data from a heterogeneous population. The model considerably reduces the number of parameters in the specification of component-covariance matrices through factor-analytic representation of the component-covariance matrices and common component-factor loadings. For the data with clusters of having nonnormality or heavy tails, a robust extension of MCFA, called the mixture of common t-factor analyzers (MCtFA), has become a more flexible approach due to less than ideal sensitivity to outliers. Unfortunately, the existing MCtFA model does not allow to handle missing values that frequently occur in many scientific investigations. The thesis accommodates the analysts with a general framework for fitting the MCtFA with incomplete data. To carry out maximum likelihood estimation of the model parameters, we develop an efficient ECME and AECM algorithm under a missing at random mechanism. A visualization tool for clustering, a classification rule for allocating new individuals, a diagnostic guideline for outliers, and an imputation method for filling in missing data under the proposed approach are also provided.Illustrative examples are presented to describe the usefulness of our methodology and compare the finite sample performance of various competing models.
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