Likelihood-Based Confidence Intervals in Exploratory Factor Analysis

In exploratory or unrestricted factor analysis, all factor loadings are free to be estimated. In oblique solutions, the correlations between common factors are free to be estimated as well. The purpose of this article is to show how likelihood-based confidence intervals can be obtained for rotated factor loadings and factor correlations, by applying maximum likelihood factor analysis subject to scaling and rotation constraints. As an illustrative example, an oblique 5-factor model will be fitted to the variance-covariance matrix of the 30 personality facets measured by the Revised NEO Personality Inventory, and confidence intervals will be estimated for all factor loadings and factor correlations, as well as for the associated reliability and validity coefficients.