“Polychoric correlation”的意思、由来-开放百科全书

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Polychoric correlation

释义

Applications and examples
Software
References
External links

In statistics, polychoric correlation^[1] is a technique for estimating the correlation between two theorised 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. These series were mathematical expansions once but not anymore.

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. 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

Mplus by Muthen and Muthen [https://www.statmodel.com/]
polycor package in R by John Fox [https://cran.r-project.org/web/packages/polycor/]
psych package in R by William Revelle [https://cran.r-project.org/web/packages/psych/index.html]
PRELIS
POLYCORR program
PROC CORR in SAS (with POLYCHORIC or OUTPLC= options)
An extensive list of software for computing the polychoric correlation, by John Uebersax
package polychoric in Stata by Stas Kolenikov [https://web.archive.org/web/20160327054012/http://web.missouri.edu/~kolenikovs/stata/]

References

1. ^{{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}}

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 S. Kotz and N.L. Johnson (Eds), Encyclopedia of Statistical Sciences, Vol. 7. New York, NY: John Wiley, pp. 68-74.

External links

The Tetrachoric and Polychoric Correlation Coefficients

3 : Summary statistics|Psychometrics|Summary statistics for contingency tables

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