Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method
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A procedure for generating multivariate nonnormal distributions is proposed. Our procedure generates average values of intercorrelations much closer to population parameters than competing procedures for skewed and/or heavy tailed distributions and for small sample sizes. Also, it eliminates the necessity of conducting a factorization procedure on the population correlation matrix that underlies the random deviates, and it is simpler to code in a programming language (e.g., FORTRAN). Numerical examples demonstrating the procedures are given. Monte Carlo results indicate our procedure yields excellent agreement between population parameters and average values of intercorrelation, skew, and kurtosis.
- Blair, R.C. (1987).RANGEN. Boca Raton, FL: IBM.
- Blair, R.C., & Higgins, J.J. (1985). Comparison of the power of the paired samplest test to that of the Wilcoxon's signed-ranks test under various population shapes.Psychological Bulletin, 97, 119–127.
- Burr, I.W. (1942). Cumulative frequency functions.Annals of Mathematical Statistics, 13, 215–232.
- Fleishman, A. I. (1978). A method for simulating non-normal distributions.Psychometrika, 43, 521–532.
- Harwell, M.R., & Serlin, R.C. (1988). An experimental study of a proposed test of non-parametric analysis of covariance.Psychological Bulletin, 104(2), 268–281.
- Harwell, M.R., & Serlin, R.C. (1989). A nonparametric test statistic for the general linear model.Journal of Educational Statistics, 14(4), 351–371.
- Iman, R.L., & Conover, W.J. (1979). The use of the rank transform in regression.Technometrics, 21(4), 499–509.
- Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation.Biometrika, 36, 149–176.
- Kaiser, H.F., & Dickman, K. (1962). Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix.Psychometrika, 27, 179–182.
- Knapp, T.R., & Swoyer, V.H. (1967). Some empirical results concerning the power of Bartlett's test of the significance of a correlation matrix.American Educational Research Journal, 4(1), 13–17.
- Levy, K.J. (1980). A Monte Carlo study of analysis of covariance under violations of the assumptions of normality and equal regression slopes.Educational and Psychological Measurement, 40, 835–840.
- Olejnik, S.F., & Algina, J. (1984). Parametric ANCOVA and the rank transform ANCOVA when the data are conditionally non-normal and heteroscedastic.Journal of Educational Statistics, 9(2), 129–150.
- Olejnik, S.F., & Algina, J. (1987). An analysis of statistical power for parametric ANCOVA and rank transform ANCOVA.Communications in Statistics: Theory and Methods, 16(7), 1923–1949.
- Ramberg, J.S., & Schmeiser, B.W. (1974). An approximate method for generating asymmetric random variables.Communications of the ACM, 17, 78–82.
- Sawilowsky, S. S., Kelley, D. L., Blair, R. C., & Markman, B. S. (1994). Meta-analysis and the Solomon four-group design.Journal of Experimental Education, 62(4), 361–376.
- Schmeiser, B. W., & Deutch, S. J. (1977). A versatile four parameter family of probability distributions suitable for simulation.AIIE Transactions, 9, 176–182.
- Seamen, S., Algina, J., & Olejnik, S. F. (1985). Type I error probabilities and power of rank and parametric ANCOVA procedures.Journal of Educational Statistics, 10(4), 345–367.
- Tadikamalla, P. R. (1980). On simulating nonnormal distributions.Psychometrika, 45, 273–279.
- Tadikamalla, P. R., & Johnson, N. L. (1979). Systems of frequency curves generated by transformations of logistic variables (Mimeo Series No. 1126). Chapel Hill, NC: University of North Carolina at Chapel Hill, Department of Statistics.
- Tukey, J. W. (1960). The practical relationship between the common transformations of percentages of counts and of amounts (Technical Report 36). Princeton, NJ: Princeton University, Statistical Techniques Research Group.
- Vale, D. C., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions.Psychometrika, 48, 465–471.
- Visual Numerics. (1994). IMSL Math/Library: FORTRAN subroutines for mathematical applications, Volume II. Houston, TX: Author.
- Simulating correlated multivariate nonnormal distributions: Extending the fleishman power method
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