On The Robustness Of Factor Analysis Against Crude Classification Of The Observations

Abstract

The paper is concerned with the consequences for maximum likelihood factor analysis which may follow if the observed variables are ordinal with only a few scale steps, which are assigned integer values. It is hypothesized that the observed variables are obtained through a classification of some true variables, which are multivariate normal and for which a factor model holds. Using simple formulas for the relations between true correlations and correlations based on the classified variables, we demonstrate numerically the relationships between true factor models and results obtained from classified data. This is done for several choices of thresholds, true factor loadings and numbers of variables, assuming a one-factor model. The results indicate that classification may lead to a substantial lack of fit of the model, i.e. an erroneous indication that more factors are needed. This is especially true if the variables are skewed in opposite direction and have high true loadings, but does not depend much on the number of scale steps. The classification also attenuates the loading estimates, and this effect is increased with a decreasing number of scale steps and increasing variation in skewness among the variables.