Polychoric correlation

When variables are measured using ordinal measurement, but there is an assumed continuous latent variable, polychoric correlations are a way of estimating the correlations between the underlying latent variables.

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 be attenuated. Lee, Poon & Bentler (1995) have recommended this a two step approach to factor analysis for assessing the factor structure of tests involving ordinally measured items.

Software

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

References Lee, S.-Y., Poon, W. Y., & Bentler, P. M. (1995). A two-stage estimation of structural equation models with continuous and polytomous variables. British Journal of Mathematical and Statistical Psychology, 48, 339–358.

See http://ourworld.compuserve.com/homepages/jsuebersax/tetra.htm