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

Abstract

In Savalei’s (2011) 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.

Keywords:

• Polychoric correlations
• skewness
• zero-frequency cells

Notes

1 Our review revealed that Savalei’s (2011) research has been widely referenced in one of the two contexts: (1) to support the use of ADD (e.g., Disabato et al., 2019; Jenkins et al., 2018; Lacko et al., 2022; Lubbe, 2019; Recio-Román et al., 2021; Schuberth et al., 2018) or (2) to substantiate the argument that tables with zero-frequency cells can result in biased polychoric correlation estimates (e.g., Bainter & Forster, 2019; DiStefano et al., 2018; DiStefano et al., 2021; Flora et al., 2012; Olvera Astivia, 2013; Pendergast et al., 2017; Yang & Xia, 2019).

2 We sincerely thank Dr. Savalei for her constructive comments on expanding the scope of our work to include additional methods and options beyond NONE and ADD that performed poorly under severely skewed data in our simulations.

3 We also examined the performance of the three additional estimators for slightly skewed data and found that neither of them outperformed NONE. Therefore, in slight skewness, NONE is still recommended to be used.

Additional information

Funding

The research was supported in part by grant MOST 110-2410-H-002-123-MY3 from the Ministry of Science and Technology in Taiwan.