Circumplex Models With Ordinal Data. Issue 6 (2nd November 2022) - Lee, Dayoung; Zhang, Guangjian
Abstract: Circumplex models arrange personality or mood variables around a circle such that the relative locations of these variables reflect their correlations. Although circumplex models were originally developed for continuous variables, their applications often involve ordinal variables. To accommodate ordinal variables, we propose estimating Browne's circumplex correlation structure with polychoric correlations instead of Pearson correlations. We consider ordinary least squares estimation due to its computational robustness with polychoric correlation matrices. We illustrate the newly developed method with an empirical study that involves 18 binary variables and 12, 108 participants. We also conduct a simulation study to explore its statistical property and compare it with maximum likelihood estimation with polychoric correlations, ordinary least squares estimation with Pearson correlations, and maximum likelihood estimation with Pearson correlations. The new method provides essentially unbiased point estimates and more satisfactory confidence intervals than other methods.