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A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models

Published online by Cambridge University Press:  01 January 2025

Gwowen Shieh
Gwowen Shieh*
Affiliation:
National Chiao Tung University
*
Requests for reprints should be sent to Gwowen Shieh, Department of Management Science, National Chiao Tung University, Hsinchu, Taiwan 30050, ROC. E-mail: gwshieh@mail.nctu.edu.tw
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Abstract

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all variables having a joint multivariate normal distribution. This paper presents a unified approach to determining power and sample size for random regression models with arbitrary distribution configurations for explanatory variables. Numerical examples are provided to illustrate the usefulness of the proposed method and Monte Carlo simulation studies are also conducted to assess the accuracy. The results show that the proposed method performs well for various model specifications and explanatory variable distributions.

Keywords

asymptotic distributioneffect sizenoncentral F distribution

Information

Type
Theory and Methods
Information
Psychometrika , Volume 72 , Issue 3 , September 2007, pp. 347 - 360
Copyright
Copyright © 2007 The Psychometric Society

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Footnotes

The author would like to thank the editor, the associate editor, and the referees for drawing attention to pertinent references that led to improved presentation. This research was partially supported by National Science Council grant NSC-94-2118-M-009-004.

References

Aguinis, H., Beaty, J.C., Boik, R.J., Pierce, C.A. (2005). Effect size and power in assessing moderating effects of categorical variables using multiple regression: A 30-year review. Journal of Applied Psychology, 90, 94–107.CrossRefGoogle ScholarPubMed
Aiken, L.S., West, S.G. (1991). Multiple regression: Testing and interpreting interactions, Thousand Oaks: Sage.Google Scholar
Algina, J., Olejnik, S. (2000). Determining sample size for accurate estimation of the squared multiple correlation coefficient. Multivariate Behavioral Research, 35, 119–137.CrossRefGoogle ScholarPubMed
Anderson, T.W. (1999). Asymptotic distribution of the reduced rank regression estimator under general conditions. Annals of Statistics, 27, 1141–1154.CrossRefGoogle Scholar
Cohen, J. (1988). Statistical power analysis for the behavioral sciences, (2nd ed.). Hillsdale: Lawrence Erlbaum.Google Scholar
Gatsonis, C., Sampson, A.R. (1989). Multiple correlation: Exact power and sample size calculations. Psychological Bulletin, 106, 516–524.CrossRefGoogle ScholarPubMed
Kelley, K., Maxwell, S.E. (2003). Sample size for multiple regression: Obtaining regression coefficients that are accurate, not simply significant. Psychological Methods, 8, 305–321.CrossRefGoogle Scholar
Mendoza, J.L., Stafford, K.L. (2001). Confidence interval, power calculation, and sample size estimation for the squared multiple correlation coefficient under the fixed and random regression models: A computer program and useful standard tables. Educational and Psychological Measurement, 61, 650–667.CrossRefGoogle Scholar
Muirhead, R.J. (1982). Aspects of multivariate statistical theory, New York: Wiley.CrossRefGoogle Scholar
Raudenbush, S.W., Liu, X. (2000). Statistical power and optimal design for multisite randomized trials. Psychological Methods, 5, 199–213.CrossRefGoogle ScholarPubMed
Raudenbush, S.W., Liu, X. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401.CrossRefGoogle ScholarPubMed
Rencher, A.C. (2000). Linear models in statistics, New York: Wiley.Google Scholar
Sampson, A.R. (1974). A tale of two regressions. Journal of the American Statistical Association, 69, 682–689.CrossRefGoogle Scholar
SAS Institute (2003). SAS/IML user’s guide, Version 8. Cary, NC: SAS Institute Inc.Google Scholar
Shieh, G. (2003). A comparative study of power and sample size calculations for multivariate general linear models. Multivariate Behavioral Research, 38, 285–307.CrossRefGoogle ScholarPubMed
Shieh, G. (2005). Power and sample size calculations for multivariate linear models with random explanatory variables. Psychometrika, 70, 347–358.CrossRefGoogle Scholar
Shieh, G. (2006). Exact interval estimation, power calculation and sample size determination in normal correlation analysis. Psychometrika, 71, 529–540.CrossRefGoogle Scholar
Steiger, J.H., Fouladi, R.T. (1992). R2: A computer program for interval estimation, power calculations, sample size estimation, and hypothesis testing in multiple regression. Behavioral Research Methods, Instruments, and Computers, 24, 581–582.CrossRefGoogle Scholar