- Polychoric correlation
In
statistics , polychoric correlation is a technique for estimating thecorrelation between two theorised normally distributed continuouslatent variable s, from two observed ordinal variables. Tetrachoric correlation is a special case of the polychoric correlation applicable when both observed variables are dichotomous. These names derive from the polychoric and tetrachoric series, mathematical expansions once, but no longer used for estimation of these correlations.Applications and examples
This technique is frequently applied when analysing items on self-report instruments such as
personality test s and surveys that often useresponse 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 tofactor 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.oftware
*polycor package in R by John Fox http://rss.acs.unt.edu/Rdoc/library/polycor/html/polychor.html
*PRELIS
* [http://ourworld.compuserve.com/homepages/jsuebersax/xpc.htm POLYCORR program]John Uebersax (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.
External links
* [http://ourworld.compuserve.com/homepages/jsuebersax/tetra.htm The Tetrachoric and Polychoric Correlation Coefficients]
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