A Cautionary Note on the Use of the Vale and Maurelli Method to Generate Multivariate, Nonnormal Data for Simulation Purposes

Educational and Psychological Measurement

Volumn 75, Issue 4, 2015, Pages 541-567

  Olvera Astivia, Oscar L ^a   Zumbo, Bruno D ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

computer simulation; Monte Carlo; multivariate data; nonnormality; robustness studies; Vale and Maurelli

Indexed keywords

EID: 84936122044     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164414548894     Document Type: Article

References (31)

1. A.AzzaliniA.Dalla Valle (1996). The multivariate skew–normal distribution. Biometrika, 84, 715-726.
2. D.L.BandalosW.Leite (2013). The role of simulation in structural equation modeling. In G.R.Hancock andR.O.Mueller (Eds.), Structural equation modeling: A second course (2nd ed., pp. 625-666). Greenwich, CT: Information Age.
3. K.A.Bollen (1989). Structural equations with latent variables. New York, NY: Wiley.
4. P.J.CurranS.G.WestJ.F.Finch (1996). The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis. Psychological Methods, 1, 16-29.
5. J.Dalen (1987). Algebraic bounds on standardized sample moments. Statistics & Probability Letters, 5, 329-331.
6. X.FanS.SivoS.Keenan (2002). SAS for Monte Carlo studies: A guide for quantitative researchers. Cary, NC: SAS Institute.
7. J.F.FinchS.G.WestD.P.MacKinnon (1997). Effects of sample size and nonnormality on the estimation of mediated effects in latent variable models. Structural Equation Modeling, 4, 87-107.
8. A.I.Fleishman (1978). A method for simulating non-normal distributions. Psychometrika, 43, 521-532.
9. D.B.FloraP.J.Curran (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466-491.
10. T.C.Headrick (2002). Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. Computational Statistics & Data Analysis, 40, 685-711.
11. T.C.Headrick (2004). Transformations for simulating multivariate distributions. Journal of Modern Applied Statistical Methods, 3, 65-71.
12. T.C.HeadrickR.K.Kowalchuk (2007). The power method transformation: its probability density function, distribution function, and its further use for fitting data. Journal of Statistical Computation and Simulation, 77, 229-249.
13. T.C.HeadrickS.S.Sawilowsky (1999). Simulating correlated multivariate nonnormal distributions: Extending the Fleishman power method. Psychometrika, 64, 25-35.
14. T.C.HeadrickY.ShengF.A.Hodis (2007). Numerical computing and graphics for the power method transformation using Mathematica. Journal of Statistical Software, 19, 1-17.
15. R.K.KowalchukT.C.Headrick (2010). Simulating multivariate g-and-h distributions. British Journal of Mathematical and Statistical Psychology, 63, 63-74.
16. M.Kraatz (2011). Investigating the performance of procedures for correlations under nonnormality (Unpublished doctoral dissertation). Vanderbilt University, Nashville, TN.
17. J.K.Kruschke (2010). Doing Bayesian data analysis: A tutorial with R and BUGS. New York, NY: Elsevier.
18. T.S.LiJ.L.Hammond (1975). Generation of pseudorandom numbers with specified univariate distributions and correlation coefficients. IEEE Transactions on Systems, Man, and Cybernetics, 5, 557-561.
19. L.M.LixR.T.Fouladi (2007). Robust step-down tests for multivariate independent group designs. British Journal of Mathematical and Statistical Psychology, 60, 245-265.
20. L.M.LixH.J.KeselmanA.M.Hinds (2005). Robust tests for the multivariate Behrens-Fisher problem. Computer Methods and Programs in Biomedicine, 77, 129-139.
21. H.Luo (2011). Some aspects on confirmatory factor analysis of ordinal variables and generating non-normal data (Unpublished doctoral dissertation). Uppsala University, Uppsala, Sweden.
22. P.MairA.SatorraP.M.Bentler (2012). Generating nonnormal multivariate data using copulas: Applications to SEM. Multivariate Behavioral Research, 47, 547-565.
23. S.Mattson (1997). How to generate non-normal data for simulation of structural equation models. Multivariate Behavioral Research, 32, 355-373.
24. L.K.MuthénB.O.Muthén (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.
25. Y.Rosseel (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36
26. J.RuscioW.Kaczetow (2008). Simulating multivariate nonnormal data using an iterative algorithm. Multivariate Behavioral Research, 43, 335-381.
27. 2 effect size. Journal of Experimental Education, 79, 257-278.
28. P.R.Tadikamalla (1980). On simulating non-normal distributions. Psychometrika, 45, 273-279.
29. X.TongP.M.Bentler (2013). Evaluation of a new mean scaled and moment adjusted test statistic for SEM. Structural Equation Modeling, 20, 148-156.
30. C.D.ValeV.A.Maurelli (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48, 465-471.
31. D.WeathersS.SharmaR.W.Niedrich (2005). The impact of the number of scale points, dispositional factors, and the status quo decision heuristic on scale reliability and response accuracy. Journal of Business Research, 58, 1516-1524.