In
statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...
, polychoric correlation
[{{Cite web, url=https://support.sas.com/documentation/cdl/en/procstat/65543/HTML/default/viewer.htm#procstat_corr_details14.htm, title=Base SAS(R) 9.3 Procedures Guide: Statistical Procedures, Second Edition, website=support.sas.com, language=en, access-date=2018-01-10] is a technique for estimating the
correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistic ...
between two hypothesised
normally distributed continuous
latent variables, 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 which are used for estimation of these correlations.
Applications and examples
This technique is frequently applied when analysing items on self-report instruments such as
personality tests and
surveys that often use
rating 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. Kiwanuka and colleagues (2022) have also illustrated the application of polychoric correlations and polychoric confirmatory factor analysis in nursing science. 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. In some disciplines, the statistical technique is rarely applied however, some scholar
have demonstrated how it can be used as an alternative to the Pearson correlation.
Software
* Mplus by Muthen and Muthe
* polycor package in R by John Fo
* psych package in R by William Revell
* lavaan package in R by Yves Rossee
* PRELIS
POLYCORR program* PROC CORR in SAS (with POLYCHORIC or OUTPLC= options
* An extensive list of software for computing the polychoric correlation, by John Uebersa
* package polychoric in Stata by Stas Koleniko
See also
*
Liability threshold model In mathematical or statistical modeling a threshold model is any model where a threshold value, or set of threshold values, is used to distinguish ranges of values where the behaviour predicted by the model varies in some important way. A particula ...
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.
* Bonett, D. G., & Price R. M. (2005). "Inferential Methods for the Tetrachoric Correlation Coefficient". ''Journal of Educational and Behavioral Statistics'', 30, 213.
* Drasgow, F. (1986). ''Polychoric and polyserial correlations''. In Kotz, Samuel, Narayanaswamy Balakrishnan, Campbell B. Read, Brani Vidakovic & Norman L. Johnson (Eds), ''Encyclopedia of Statistical Sciences'', Vol. 7. New York, NY: John Wiley, pp. 68–74.
*Kiwanuka, F., Kopra, J., Sak-Dankosky, N., Nanyonga, R. C., & Kvist, T. (2022). "Polychoric Correlation with Ordinal Data in Nursing Research". ''Nursing research, 10.1097/NNR.0000000000000614''. Advance online publication. https://doi.org/10.1097/NNR.0000000000000614.
External links
The Tetrachoric and Polychoric Correlation Coefficients
Summary statistics
Covariance and correlation
Summary statistics for contingency tables
Latent variable models