Revisiting Savalei’s (2011) Research on Remediating Zero-Frequency Cells in Estimating Polychoric Correlations: A Data Distribution Perspective

Abstract

In Savalei’s (2011 Savalei, V. (2011). What to do about zero frequency cells when estimating polychoric correlations. Structural Equation Modeling, 18, 253–273. https://doi.org/10.1080/10705511.2011.557339[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) simulation that evaluated the performance of polychoric correlation estimates in small samples, two methods for treating zero-frequency cells, adding 0.5 (ADD) and doing nothing (NONE), were compared. Savalei tentatively suggested using ADD for binary data and NONE for data with three or more categories. Yet, Savalei’s suggestion could be explained by the skewness of the data distribution being severe for binary data and slight for three-category data. To rule out this alternative explanation, we extended Savalei’s design by incorporating the degree of skewness into our simulation. With slightly skewed data, NONE is recommended due to its high-quality estimates. With severely skewed data, only ADD is recommended for binary data when the skewness of two variables is the same-signed and the underlying correlation is expected to be strong. Methods for improving the polychoric correlation estimates with severely skewed data merit further study.