Polychoric correlation

In statistics, polychoric correlation is a technique for estimating the correlation between two theorised normally distributed continuous latent variables, from two ordinal variables.

Applications and examples
This technique is frequently applied when analysing items on self-report instruments such as personality tests and surveys that often use response scales with a small number of response options (e.g., strongly disagree to strongly agree). The smaller the number of response categories, the more a correlation between latent continuous variables will tend to be attenuated. Lee, Poon & Bentler (1995) have recommended a two step approach to factor analysis for assessing the factor structure of tests involving ordinally measured items. This aims to reduce the effect of statistical artifacts, such as the number of response scales or skewness of variables leading to items grouping together in factors.

Software

 * polycor package in R by John Fox http://rss.acs.unt.edu/Rdoc/library/polycor/html/polychor.html
 * PRELIS

John Ubersax (http://ourworld.compuserve.com/homepages/jsuebersax/tetra.htm) provides an extensive list of software for computing the polychoric correlation.