Numerical computing and graphics for the power method transformation using mathematica

Journal of Statistical Software

Volumn 19, Issue 3, 2007, Pages 1-17

  Headrick, Todd C ^a   Sheng, Yanyan ^a   Hodis, Flaviu Adrian ^a  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Cumulants; Mathematica; Monte Carlo; Non normal; Polynomial; Simulation

Indexed keywords

EID: 34247520620     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v019.i03     Document Type: Article

References (40)

1. Beasley TM (2002). "Multivariate Aligned Rank Test for Interactions in Multiple Group Repeated Measures." Multivariate Behavioral Research, 37, 197-226.
2. Beasley TM, Zumbo BD (2003). "Comparison of Aligned Friedman Rank and Parametric Methods For Testing Interactions in Split-plot Designs." Computational Statistics & Data Analysis, 42, 569-593.
3. Blair RC (1987). Rangen. IBM, Boca Raton, FL.
4. Finch H (2005). "Comparison of the Performance of Nonparametric and Parametric MANOVA Test Statistics with Assumptions are Violated." Methodology, 1, 27-38.
5. Fleishman AI (1978). "A Method for Simulating Non-normal Distributions." Psychometrika, 43, 521-532.
6. Habib AR, Harwell MR (1989). "An Empirical Study of the Type I Error Rate and Power of Some Selected Normal Theory and Nonparametric Tests of Independence of Two Sets of Variables." Communications in Statistics: Simulation and Computation, 18, 793-826.
7. Harwell MR, Serlin RC (1988). "An Experimental Study of a Proposed Test of Nonparametric Analysis of Covariance." Psychological Bulletin, 104, 268-281.
8. Headrick TC (2002). "Fast Fifth-order Polynomial Transforms for Generating Univariate and Multivariate Non-normal Distributions." Computational Statistics & Data Analysis, 40, 685-711.
9. Headrick TC (2004). "On Polynomial Transformations for Simulating Multivariate Non-normal Distributions." Journal of Modern Applied Statistical Methods, 3, 65-71.
10. Headrick TC, Beasley TM (2003). "A Method for Simulating Correlated Structures of Continuous and Ranked Data." Paper presented at the annual meeting of the American Educational Research Association, Chicago, April 2003.
11. Headrick TC, Beasley TM (2004). "A Method for Simulating Correlated Non-normal Systems of Linear Statistical Equations." Communications in Statistics: Simulation and Computation, 33, 19-33.
12. Headrick TC, Kowalchuk RK (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. Preprint available at URL http://www.siu.edu/~epsel/ headrick/JSCS-PowerMethod.pdf.
13. Headrick TC, Mudgadi A (2006). "On Simulating Multivariate Non-normal Distributions from the Generalized Lambda Distribution." Computational Statistics & Data Analysis, 50, 3343-3353.
14. Headrick TC, Rotou O (2001). "An Investigation of the Rank Transformation in Multiple Regression." Computational Statistics & Data Analysis, 38, 203-215.
15. Headrick TC, Sawilowsky SS (1999). "Simulating Correlated Non-normal Distributions: Extending the Fleishman Power Method." Psychometrika, 64, 25-35.
16. Headrick TC, Sawilowsky SS (2000a). "Properties of the Rank Transformation in Factorial Analysis of Covariance." Communications in Statistics: Simulation and Computation, 29, 1059-1088.
17. Headrick TC, Sawilowsky SS (2000b). "Weighted Simplex Procedures for Determining Boundary Points and Constants for the Univariate and Multivariate Power Methods." Journal of Educational and Behavioral Statistics, 25, 417-436.
18. Headrick TC, Vineyard G (2001). "An Empirical Investigation of Four Tests for Interaction in the Context of Factorial Analysis of Covariance." Multiple Linear Regression Viewpoints, 27, 3-15.
19. Headrick TC, Zumbo BD (2004). "A Method for Simulating Multivariate Non-normal Distributions with Specified Intraclass Correlations." In "Proceedings of the Statistical Computing Section, American Statistical Association," pp. 2462-2467.
20. Hess B, Olejnik S, Huberty CJ (2001). "The Efficacy of Two Improvement-over-chance Effect Sizes for Two Group Univariate Comparisons under Variance Heterogeneity and Nonnormality." Educational and Psychological Measurement, 61, 909-936.
21. Hipp JR, Bollen KA (2003). "Model Fit in Structural Equation Models with Censored, Ordinal, and Dichotomous variables: Testing Vanishing Tetrads." Sociological Methodology, 33, 267-305.
22. Karian ZA, Dudewicz EJ (2000). Fitting Statistical Distributions: The Generalized Lamda Distribution and Generalized Bootstrap Method. Boca Raton: Chapman & Hall/CRC.
23. Klockars AJ, Moses TP (2002). "Type I Error Rates for Rank-based Tests of Homogeneity of Regression Slopes." Journal of Modern Applied Statistical Methods, 1, 452-460.
24. Kotz S, Balakrishnan N, Johnson NL (2000). Continuous Multivariate Distributions. New York: John Wiley, 2nd edition.
25. Kowalchuk RK, Keselman HJ, Algina J (2003). "Repeated Measures Interaction Test with Aligned Ranks." Multivariate Behavioral Research, 38, 433-461.
26. Lix LM, Algina J, Keselman HJ (2003). "Analyzing Multivariate Repeated Measures Designs: A Comparison of Two Approximate Degrees of Freedom Procedures." Multivariate Behavioral Research, 38, 403-431.
27. Olejnik SF, Algina J (1987). "An Analysis of Statistical Power for Parametric ANCOVA and Rank Transform ANCOVA." Communications in Statistics: Theory and Methods, 16, 1923-1949.
28. Powell DA, Anderson LM, Chen RYS, Alvord WG (2002). "Robustness of the Chen-Dougherty-Bittner Procedure against Non-normality and Heterogeneity in the Coefficient of Variation." Journal of Biomedical Optics, 7, 650-660.
29. Ramberg JS, Tadikamalla PR, Dudewicz EJ, Mykytka EF (1979). "A Probability Distribution and its use in Fitting Data." Technometrics, 21, 201-214.
30. Rasch D, Guiard V (2004). "The Robustness of Parametric Statistical Methods." Psychology Science, 46, 175-208.
31. Reinartz WJ, Echambadi R, Chin WW (2002). "Generating Non-normal Data for Simulation of Structural Equation Models Using Mattson's Method." Multivariate Behavioral Research, 37, 227-244.
32. Shieh Y (2000). "The Effects of Distributional Characteristics on Multi-level Modeling Parameter Estimates and Type I Error Control of Parameter Tests under Conditions of Non-normality." Paper prented at the annual meeting of the American Educational Research Association, New Orleans, April 2000.
33. Steyn HS (1993). "On the Problem of More than One Kurtosis Parameter in Multivariate Analysis." Journal of Multivariate Analysis, 44, 1-22.
34. Stone C (2003). "Empirical Power and Type I Error Rates for an IRT Fit Statistic that Considers the Precision and Ability Estimates." Educational and Psychological Measurement, 63, 566-583.
35. Tadikamalla PR (1980). "On Simulating Nonnormal Distributions." Psychometrika, 45, 273-279.
36. Vale CD, Maurelli VA (1983). "Simulating Multivariate Nonnormal Distributions." Psychometrika, 48, 465-471.
37. Welch G, Kim KH (2004). "An Evaluation of the Fleishman Transformation for Simulating Non-normal Data in Structural Equation Modeling." Paper presented at the International Meeting of the Psychometric Society, Monterey, CA, May 2004.
38. Wolfram S (2003). The Mathematica Book. Wolfram Media, Inc, 5th edition.
39. Yaun K, Bentler PM (2002). "On Robustness of the Normal-Theory Based Asymptotic Distributions of Three Reliability Coefficient Estimates." Psychometrika, 67, 251-259.
40. Zhu R, Yu F, Liu S (2002). "Statistical Indexes for Monitoring Item Behavior under Computer Adaptive Testing Environment." Paper presented at the annual meeting of the American Educational Research Association, New Orleans, April 2002.