The Goodness of Fit of the Maximum-Likelihood Estimation Procedure in Factor Analysis

Several goodness of fit measures for factor analysis were applied to the results of maximum-likelihood factor analyses of data with known factors. Results showed that p was a fairly good measure of the degree to which the factor analytic model held in the population, although some values were large for smaller sample sizes. Two measures, c and r, were used to compare the obtained sample factors with the population factors. These measures could be used in confirmatory studies, when an hypothesized factor matrix could be written down. They showed that fairly good agreement with an hypothesis can be obtained, even when the factor analytic model does not exactly hold in the population. This would require that the investigator have a large sample size, variables with high communalities, and a low ratio of number of factors to number of variables.