  We consider the problem of full information maximum likelihood (FIML)
estimation in a factor analysis model 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 observed variables are included
in complete data. However, the EM algorithm has an extremely high computational
cost when the number of observations is large and/or plenty of missing values
are involved. 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 observed variables as a part of complete data. Our algorithm is
applied to a real data set collected from a Web questionnaire that asks about
first impressions of human; almost $90\%$ of the data values are missing. When
there are many missing data values, it is not clear if the FIML procedure can
achieve good estimation accuracy even if the number of observations is large.
In order to investigate this, we conduct Monte Carlo simulations under a wide
variety of sample sizes.
