What to Do About Zero Frequency Cells When Estimating Polychoric Correlations

Abstract

Categorical structural equation modeling (SEM) methods that fit the model to estimated polychoric correlations have become popular in the social sciences. When population thresholds are high in absolute value, contingency tables in small samples are likely to contain zero frequency cells. Such cells make the estimation of the polychoric correlations more difficult. Some SEM programs use solutions such as adding .5 to the zero frequency cells. However, the adequacy of this solution has never been systematically explored in the literature. In this article, the frequency with which contingency tables with zero cells occur in small samples is explored. Second, it is explored whether or not adding .5 is in any way preferable to leaving the cell value as zero. Binary and 3-category data and a variety of threshold values and correlation values are considered. The findings suggest that the two methods of dealing with zero frequency cells have quite different properties. With binary data, the method of adding .5 is recommended, unless thresholds are opposite-signed and the underlying correlation is suspected to be large. No adjustment is recommended for greater numbers of categories.

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