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Power and Sample Size Calculations for Multivariate Linear Models with Random Explanatory Variables

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, R.O.C., E-mail: gwshieh@mail.nctu.edu.tw
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Abstract

This article considers the problem of power and sample size calculations for normal outcomes within the framework of multivariate linear models. The emphasis is placed on the practical situation that not only the values of response variables for each subject are just available after the observations are made, but also the levels of explanatory variables cannot be predetermined before data collection. Using analytic justification, it is shown that the proposed methods extend the existing approaches to accommodate the extra variability and arbitrary configurations of the explanatory variables. The major modification involves the noncentrality parameters associated with the F approximations to the transformations of Wilks likelihood ratio, Pillai trace and Hotelling-Lawley trace statistics. A treatment of multivariate analysis of covariance models is employed to demonstrate the distinct features of the proposed extension. Monte Carlo simulation studies are conducted to assess the accuracy using a child’s intellectual development model. The results update and expand upon current work in the literature.

Keywords

MANCOVAMANOVAmultivariate regressionnoncentral F distribution.
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 2 , June 2005 , pp. 347 - 358
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

The author wishes to thank the associate editor and the referees for comments which improve the paper considerably. This research was partially supported by a grant from the Natural Science Council of Taiwan.

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