Iteratively Reweighted Least Squares Method for Estimating Polyserial and Polychoric Correlation Coefficients

References

• Albert, J. H. (1992), “Bayesian Estimation of the Polychoric Correlation Coefficient,” Journal of Statistical Computation and Simulation, 44, 47–61. DOI: 10.1080/00949659208811448.
   Google Scholar
• Bollen, K. A., and Barb, K. H. (1981), “Pearson’s R and Coarsely Categorized Measures,” American Sociological Review, 46, 232–239. DOI: 10.2307/2094981.
   Web of Science ®Google Scholar
• Chen, J., and Choi, J. (2009), “A Comparison of Maximum Likelihood and Expected A Posteriori Estimation for Polychoric Correlation Using Monte Carlo Simulation,” Journal of Modern Applied Statistical Methods, 8, 32. DOI: 10.22237/jmasm/1241137860.
   Google Scholar
• Choi, J., Kim, S., Chen, J., and Dannels, S. (2011), “A Comparison of Maximum Likelihood and Bayesian Estimation for Polychoric Correlation Using Monte Carlo Simulation,” Journal of Educational and Behavioral Statistics, 36, 523–549. DOI: 10.3102/1076998610381398.
   Web of Science ®Google Scholar
• Cox, N. (1974), “Estimation of the Correlation between a Continuous and a Discrete Variable,” Biometrics, 30, 171–178. DOI: 10.2307/2529626.
   PubMed Web of Science ®Google Scholar
• Epskamp, S., Borsboom, D., and Fried, E. I. (2018), “Estimating Psychological Networks and their Accuracy: A Tutorial Paper,” Behavior Research Methods, 50, 195–212. DOI: 10.3758/s13428-017-0862-1.
   PubMed Web of Science ®Google Scholar
• Fox, J. (2010), Polycor: Polychoric and Polyserial Correlations r package version 0.7-8. Online http://www.cran.r-project.org/web/packages/polycor/index.html (Accessed on 31 August 2010). bibr12, 69.
   Google Scholar
• Gilley, W. F., and Uhlig, G. E. (1993), “Factor Analysis and Ordinal Data,” Education, 114, 258–265.
   Google Scholar
• Holgado-Tello, F. P., Chacón-Moscoso, S., Barbero-García, I., and Vila-Abad, E. (2010), “Polychoric versus Pearson Correlations in Exploratory and Confirmatory Factor Analysis of Ordinal Variables,” Quality & Quantity, 44, 153–166.
   Web of Science ®Google Scholar
• Institute, S. (2017), Base SAS 9.4 Procedures Guide: Statistical Procedures, SAS Institute.
   Google Scholar
• Jöreskog, K. G. (2005), “Structural Equation Modeling with Ordinal Variables Using Lisrel.” Technical report.
   Google Scholar
• Kirk, D. B. (1973), “On the Numerical Approximation of the Bivariate Normal (tetrachoric) Correlation Coefficient,” Psychometrika, 38, 259–268. DOI: 10.1007/BF02291118.
   Web of Science ®Google Scholar
• Lauritzen, S. L. (1996), Graphical Models (Vol. 17), Oxford: Clarendon Press.
   Google Scholar
• Likert, R., Roslow, S., and Murphy, G. (1934), “A Simple and Reliable Method of Scoring the Thurstone Attitude Scales,” The Journal of Social Psychology, 5, 228–238. DOI: 10.1080/00224545.1934.9919450.
   Web of Science ®Google Scholar
• Moustaki, I. (2000), “A Latent Variable Model for Ordinal Variables,” Applied Psychological Measurement, 24, 211–223. DOI: 10.1177/01466210022031679.
   Web of Science ®Google Scholar
• Muthén, B. O. (1984), “A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators,” Psychometrika, 49, 115–132. DOI: 10.1007/BF02294210.
   Web of Science ®Google Scholar
• Muthén, L. K., and Muthén, B. O. (2005), Mplus: Statistical Analysis with Latent Variables: User’s Guide, Los Angeles: Muthén & Muthén.
   Google Scholar
• Olsson, U. (1979), “Maximum Likelihood Estimation of the Polychoric Correlation Coefficient,” Psychometrika, 44, 443–460. DOI: 10.1007/BF02296207.
   Web of Science ®Google Scholar
• Olsson, U., Drasgow, F., and Dorans, N. J. (1982), “The Polyserial Correlation Coefficient,” Psychometrika, 47, 337–347. DOI: 10.1007/BF02294164.
   Web of Science ®Google Scholar
• Pearson, K. (1900), “Mathematical Contribution to the Theory of Evolution. VII. On the Correlation of Characters not Quantitatively Measurable,” Philosophical Transactions of the Royal Society of London, 195, 1–47.
   Google Scholar
• Pearson, K., and Pearson, E. S. (1922), “On Polychoric Coefficients of Correlation,” Biometrika, 14, 127–156. DOI: 10.1093/biomet/14.1-2.127.
   Google Scholar
• Revelle, W. R. (2017), “psych: Procedures for Personality and Psychological Research.” Software.
   Google Scholar
• Ritchie-Scott, A. (1918), “The Correlation Coefficient of a Polychoric Table,” Biometrika, 12, 93–133. DOI: 10.1093/biomet/12.1-2.93.
   Google Scholar
• Robitzsch, A. (2020), “Why Ordinal Variables Can (Almost) Always Be Treated as Continuous Variables: Clarifying Assumptions of Robust Continuous and Ordinal Factor Analysis Estimation Methods,” Frontiers in Education, 5, 589965. DOI: 10.3389/feduc.2020.589965.
   Google Scholar
• Uebersax, J. S. (2006), “Introduction to the Tetrachoric and Polychoric Correlation Coefficients,” Obtenido de http://www.john-uebersax.com/stat/tetra.htm. [Links].
   Google Scholar
• Uebersax, J. S. (2010), “User Guide for polycorr 1.1” (advanced version).
   Google Scholar