Full information maximum likelihood estimation in factor analysis with a large number of missing values

Abstract

We consider the problem of full information maximum likelihood (FIML) estimation in factor analysis when a majority of the data values are missing. The expectation–maximization (EM) algorithm is often used to find the FIML estimates, in which the missing values on manifest variables are included in complete data. However, the ordinary EM algorithm has an extremely high computational cost. In this paper, we propose a new algorithm that is based on the EM algorithm but that efficiently computes the FIML estimates. A significant improvement in the computational speed is realized by not treating the missing values on manifest variables as a part of complete data. When there are many missing data values, it is not clear if the FIML procedure can achieve good estimation accuracy. In order to investigate this, we conduct Monte Carlo simulations under a wide variety of sample sizes.

Keywords:

• EM algorithm
• factor analysis
• full information maximum likelihood

AMS Subject Classification:

• 62H25
• 62P25

Acknowledgments

The authors would like to thank an anonymous reviewer for the helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.