RE: st: Tetrachoric correlations and survey data

[Cameron McIntosh <cnm100@hotmail.com>]

I don't know of a specific Stata command to do all that at once, but essentially you would just need to estimate the thresholds and rho's from weighted frequencies... so I would imagine you could weight first and then feed the tetrachoric procedure the weighted frequency tables.  As for stratification, I think that would pertain more to standard errors of the rho's, which you could get by bootstrapping.  You may want to see:
Choi, J., Kim, S., Chen, J., & 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(4), 523-549.http://www.education.umd.edu/EDMS/events/Choi_et_al_2011_JEBS.pdf
Li, C., & Shepherd, B.E. (2010). Test of Association between Two Ordinal Variables while Adjusting for Covariates.  Journal of the American Statistical Association, 105(490), 612-620. 

Aguinis, H., Pierce, C. A., & Culpepper, S. A. (2009). Scale coarseness as a methodological artifact: Correcting correlation coefficients attenuated from using coarse scales. Organizational Research Methods, 12(4), 623-652.
http://mypage.iu.edu/~haguinis/Coarseness2009.pdf

Bentler, P.M. (2011). Can Interval-level Scores be Obtained from Binary Responses? UCLA Preprint #622.http://preprints.stat.ucla.edu/622/Bentler%20Interval%20Scores%20from%20Binary%20Responses.pdf

Ulrich, R., & Wirtz, M. (2004). On the correlation of a naturally and an artificially dichotomized variable. British Journal of Mathematical and Statistical Psychology, 57(2), 235–251. 

Ogasawara, H. (2010). Accurate distribution and its asymptotic expansion for the tetrachoric correlation coefficient. Journal of Multivariate Analysis, 101(4), 936-948. 

Ledesma, R.D., Macbeth, G., & Valero-Mora, P. (2011). Software for Computing the Tetrachoric Correlation Coefficient. Revista Latinoamericana de Psicología, 43(1), 181-189. http://openjournal.konradlorenz.edu.co/index.php/rlpsi/article/viewFile/459/463

Greer, T., Dunlap, W.P., & Beatty, G.O. (2003). A Monte Carlo Evaluation of the Tetrachoric Correlation Coefficient. Educational and Psychological Measurement, 63(6), 931-950.

Bonett, D.G., & Price, R.M. (2005). Inferential Methods for the Tetrachoric Correlation Coefficient. Journal of Educational and Behavioral Statistics, 30(2), 213-225.

Long, M.A., Berry, K.J., & Milke, P.W., Jr. (2009). Tetrachoric Correlation: A Permutation Alternative. Educational and Psychological Measurement, 69(3), 429-437.

Genest, C., & Lévesque, J.-M. (2009). Estimating correlation from dichotomized normal variables. Journal of Statistical Planning and Inference, 139(11), 3785-3794.

Fox, J. (January 2, 2012). Polychoric and Polyserial Correlations: Package ‘polycor’, Version 0.7-8.http://cran.r-project.org/web/packages/polycor/

Savalei, V. (2011). What to Do About Zero Frequency Cells When Estimating Polychoric Correlations. Structural Equation Modeling, 18(2), 253-273.

Choi, J., Peters, M., & Mueller, R.O. (2010). Correlational analysis of ordinal data: from Pearson’s r to Bayesian polychoric correlation. Asia Pacific Education Review, 11(4), 459-466. 

Maydeu-Olivares, A. García-Forero, C., Gallardo-Pujol, D. & Renom, J. (2009). Testing categorized bivariate normality with two-stage polychoric correlation estimates. Methodology, 5, 131-136.

Chen, B.-W., & Xu, B.-Y. (2009). Comparison of coefficients among polychoric correlation, Pearson correlation and rank correlation of rank data. Modern Preventive Medicine, 36(17), 3206-3208.

Cam

> From: McDowell-R3@email.ulster.ac.uk
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Tetrachoric correlations and survey data
> Date: Tue, 31 Jan 2012 11:49:00 +0000
> 
> Is it possible to compute tetrachoric correlations of ordinal data in STATA to take account of survey weights and stratification?
> 
> 
> -----------------------------------------
> 
> Ron McDowell
> 
> Institute of Nursing Research
> 
> University of Ulster, Coleraine
> 
> McDowell-R3@email.ulster.ac.uk
> 
> 
> 
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