Mixtures of factor analyzers with covariates for modeling multiply censored dependent variables

• Published in: Statistical papers (Berlin, Germany) Vol. 62; no. 5; pp. 2119 - 2145
• Main Authors: Wang, Wan-Lun, Castro, Luis M., Hsieh, Wan-Chen, Lin, Tsung-I
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2021; Springer Nature B.V
• Subjects: Algorithms; Analyzers; Asymptotic methods; Clustering; Dependent variables; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Educational evaluation; Finance; Insurance; Management; Mathematics and Statistics; Maximum likelihood estimates; Normal distribution; Operations Research/Decision Theory; Parameter estimation; Probability Theory and Stochastic Processes; Quantitative psychology; Regression coefficients; Regular Article; Statistics; Statistics for Business; Variables; Censored data; AECM algorithm; Factor analysis; ML estimation; Truncated multivariate normal distribution; Detection limit
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-020-01177-1

Censored data arise frequently in diverse applications in which observations to be measured may be subject to some upper and lower detection limits due to the restriction of experimental apparatus such that they are not exactly quantifiable. Mixtures of factor analyzers with censored data (MFAC) have been recently proposed for model-based density estimation and clustering of high-dimensional data in the presence of censored observations. In this paper, we consider an extended version of MFAC by considering regression equations to describe the relationship between covariates and multiply censored dependent variables. Two analytically feasible EM-type algorithms are developed for  computing maximum likelihood estimates of model parameters with closed-form expressions. Moreover, we provide an information-based method to compute asymptotic standard errors of mixing proportions and regression coefficients. The utility and performance of our proposed methodology are illustrated through a simulation study and two real data examples.