PolychoricRM: A Computationally Efficient R Function for Estimating Polychoric Correlations and their Asymptotic Covariance Matrix

ABSTRACT

Many applications of structural equation modeling involve ordinal (e.g., Likert) variables. A popular way of dealing with ordinal variables is to estimate the model with polychoric correlations rather than Pearson correlations. Such an estimation also requires the asymptotic covariance matrix of polychoric correlations. It is computationally intensive to estimate polychoric correlations and their asymptotic covariance matrices. We describe a computationally efficient R function PolychoricRM to estimate polychoric correlations and their asymptotic covariance matrix. The function invokes the computing power of modern Fortran and exploits multiple-core (multiple-thread) CPUs on nearly all current computers.

KEYWORDS:

• Factor analysis
• ordinal data
• polychoric correlations
• tetrachoric correlations

Notes

¹ One can speed up EFA with ordinal variables by passing the polychoric correlation matrix and the ACM to an EFA function directly. Example R code is provided in Appendix C.

² Olsson (1979a) presented the correlation-related equation before threshold-related equations. We reverse the order and present threshold-related relations first for a more intuitive description of the two-stage method.

³ The scoring method is like the Newton method but with an approximated Hessian matrix.

⁴ Some example R code are provided in Appendix C.

⁵ We also compared the two functions with the whole IPIP data set, which contains 50 5-category items and 19,376 participants. The computing cost for PolychoricRM was 7.43 seconds and the computing cost for lavCor was 67.53 seconds.

⁶ An online support file (https://drive.google.com/file/d/1Mdme5NLScg6IywQUhVl1egYgjTuHlE8r/view?usp=sharing) contains details of the comparisons.