Measuring Correlation in Ordered Two-Way Contingency Tables

1980 ◽  
Vol 17 (3) ◽  
pp. 391-394 ◽  
Author(s):  
Ulf Olsson
Keyword(s):  
Correlation Coefficient ◽  
Ordinal Data ◽  
Contingency Tables ◽  
Tetrachoric Correlation ◽  
Polychoric Correlation

The product moment correlation coefficient is often used even for ordinal data with only a few scale steps. This procedure may lead to biased results, where the bias depends on the number of scale steps and on the skewnesses of the observed variables. The polychoric correlation coefficient, which is a generalization of the tetrachoric correlation to the general case, is discussed as a possible measure of correlation for this kind of data.

scholarly journals Bivariate Distributions Underlying Responses to Ordinal Variables

Psych ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 562-578
Author(s):  
Laura Kolbe ◽  
Frans Oort ◽  
Suzanne Jak
Keyword(s):  
Correlation Coefficient ◽  
Latent Variables ◽  
Ordinal Data ◽  
Bivariate Normal Distribution ◽  
Polychoric Correlation ◽  
Bivariate Distributions ◽  
Normal Distributions ◽  
Ordinal Variables ◽  
Bivariate Normal ◽  
Bivariate Normality

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to ordinal variables are generated by two underlying continuous latent variables with a bivariate normal distribution. When the underlying bivariate normality assumption is violated, the estimated polychoric correlation coefficient may be biased. In such a case, we may consider other distributions. In this paper, we aimed to provide an illustration of fitting various bivariate distributions to empirical ordinal data and examining how estimates of the polychoric correlation may vary under different distributional assumptions. Results suggested that the bivariate normal and skew-normal distributions rarely hold in the empirical datasets. In contrast, mixtures of bivariate normal distributions were often not rejected.

The Performance of the Polychoric Correlation Coefficient and Selected Fitting Functions in Confirmatory Factor Analysis with Ordinal Data

1991 ◽  
Vol 28 (4) ◽  
pp. 491-497 ◽  
Author(s):  
Edward E. Rigdon ◽  
Carl E. Ferguson
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Correlation Coefficient ◽  
Simulation Study ◽  
Ordinal Data ◽  
Standard Errors ◽  
Polychoric Correlation ◽  
Chi Square ◽  
Confirmatory Factor

In a simulation study, no combination of the polychoric correlation coefficient with any LISREL 7 fitting function produced unbiased estimated standard errors or a correctly distributed chi square statistic. However, there were major differences in the performance of the five fitting functions in the analysis of ordinal data.

Inter-rater Variability Interferes with Reproducibility of Splenic Injury Grades Reported to the American College of Surgeons Committee on Trauma

2016 ◽  
Vol 82 (2) ◽  
pp. 171-174
Author(s):  
Eric J. Ferguson ◽  
Michael Walsh ◽  
Megan Brown
Keyword(s):  
Correlation Coefficient ◽  
Intraclass Correlation Coefficient ◽  
Trauma Center ◽  
Ordinal Data ◽  
Injury Severity ◽  
Splenic Injury ◽  
Intraclass Correlation ◽  
American College Of Surgeons ◽  
Level I ◽  
Picture Archiving And Communication

The objective of this study was to determine reproducibility of our splenic injury grading data, previously reported to the American College of Surgeons Committee on Trauma for our most recent site visit. The institutional registry of a Level I trauma center was queried to identify adult patients presenting with blunt splenic injury between January 1, 2013 and December 31, 2013. Original CT scans were scanned into the picture archiving and communication system and subsequently reviewed by four trauma surgeons and two radiologists for clinical impressions of splenic injury grade. Grades assigned by the clinician and the grade recorded in the registry were compared for inter-rater reliability using the intraclass correlation coefficient, as a means of assessing variance of ordinal data. The intraclass correlation coefficient in our model was 0.77, which indicates that 77 per cent of the observed variance was due to true variance and 23 per cent of the variance was due to error. Variability in grading may, in some cases, underestimate injury severity and compromise the clinician's expectation of clinical outcome, both in real-time, as well as during retrospective review processes such as those used during the trauma center reverification process.

A Monte Carlo Evaluation of the Tetrachoric Correlation Coefficient

2003 ◽  
Vol 63 (6) ◽  
pp. 931-950 ◽  
Author(s):  
Tammy Greer ◽  
William P. Dunlap ◽  
Gregory O. Beatty
Keyword(s):  
Monte Carlo ◽  
Correlation Coefficient ◽  
Tetrachoric Correlation ◽  
Monte Carlo Evaluation

Muscle Dissatisfaction and Muscle-Enhancing Substance Use: A Population-Based Twin Study in Young Adult Men

2006 ◽  
Vol 9 (3) ◽  
pp. 431-437 ◽  
Author(s):  
Anu Raevuori ◽  
Anna Keski-Rahkonen ◽  
Richard J. Rose ◽  
Aila Rissanen ◽  
Jaakko Kaprio
Keyword(s):  
Substance Use ◽  
Environmental Factors ◽  
Twin Study ◽  
Genetic Factors ◽  
Population Based ◽  
Tetrachoric Correlation ◽  
Polychoric Correlation ◽  
Adult Men ◽  
Genetic And Environmental Factors ◽  
Best Fit

AbstractIn the population-based FinnTwin16 study, proportions of genetic and environmental factors contributing to muscle dissatisfaction and muscle-enhancing substance use were assessed in 319 pairs of twin brothers: 141 monozygotic (MZ) and 178 dizygotic (DZ) pairs. In addition there were 86 twin individuals from pairs in which only one co-twin responded. Of all respondents, 30% experienced high muscle dissatisfaction. The corresponding proportion of muscle-enhancing substance use was 10%. The subjects were similar in age (23.8 years, 95% confidence interval [CI] 23.76–23.84), body mass index (23.7, 95% CI 23.5–23.9), and waist circumference (84.5 cm, 95% CI 83.7–85.2), independent of their muscle dissatisfaction or muscle-enhancing substance use status and independent of their zygosity. The MZ polychoric correlation for muscle dissatisfaction was .39 (95% CI .17–.58) and .27 for DZ pairs (95% CI .07–.46). The MZ tetrachoric correlation for muscle-enhancing substance use was .65 (95% CI .28–.87) and .56 for DZ pairs (95% CI .26–.78). The AE model, where additive genetic factors (A) accounted for 42% (95% CI .23–.59) and unique environmental factors (E) 58% (95% CI .41–.77) of the liability, provided the best fit for muscle dissatisfaction. The CE model, where common environmental factors (C) accounted for 60% (95% CI .37–.77) and unique environmental factors (E) 40% (95% CI .23–.63) of the liability, provided the best fit for muscle-enhancing substance use. Both genetic and unique (nonfamilial) environmental factors are involved in muscle dissatisfaction in the population. Nongenetic factors (both familial and non-familial) appear to best explain the use of muscle-enhancing substances.

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