Polychoric correlations can be impacted by conditions that easily produce tables with zero-frequency cells. To elucidate this association, we reexamined the quality of polychoric correlations by evaluating L-shaped and non-L-shaped tables with zero cells (L and NL), as well as tables without zero cells, in our simulations. This reexamination aimed to (1) identify which table types mostly impact estimation quality and to (2) determine if remediating zero cells in L and NL tables improves their estimates. Part 1 found that L tables, invariably yielding estimates beyond −0.90, emerged as the primary source of poor estimation quality. Despite the inherent decrease in their bias with more negative correlations, their proportion instead increases, even rising significantly with greater skewness, which substantially impacts overall quality in data under severe skewness with moderate correlations (i.e., −0.3 to 0.5). As demonstrated in Part 2, remediating only L tables, instead of all tables with zero cells (i.e., L and NL), improves the quality under conditions identified in Part 1, since the NL tables are not the main cause of poor estimation quality. In conclusion, researchers should exercise caution when interpreting polychoric correlations, particularly in severely skewed data with moderate correlations, where L tables appear frequently and exhibit severe bias. Remediating L tables in these conditions can effectively reduce the bias.
Keywords: polychoric correlations; zero-frequency cells; L-shaped tables