Choosing an appropriate number of factors in factor analysis with incomplete data

When we conduct factor analysis, the number of factors is often unknown in advance. Among many decision rules for an appropriate number of factors, it is easy to find approaches that make use of the estimated covariance matrix. When data include missing values, the estimated covariance matrix using either complete cases or available cases may not accurately represent the true covariance matrix, and decision based on the estimated covariance matrix may be misleading. We discuss how to apply model selection techniques using AIC or BIC to choose an appropriate number of factors when data include missing values. In the simulation study, it is shown that the suggested methods select the correct number of factors for simulated data with known number of factors.