Calculating Power for the General Linear Multivariate Model With One or More Gaussian Covariates

Area of Science:

• Statistics
• Multivariate Analysis

Background:

• General linear multivariate models (GLMMs) are widely used.
• Accurate power approximations are crucial for study design in GLMMs.
• Existing power approximations have limitations, especially with Gaussian covariates.

Purpose of the Study:

• To develop a novel, accurate noncentral F power approximation for GLMMs.
• To extend existing power approximation methods to include Gaussian covariates.
• To provide a computationally efficient alternative to Monte Carlo simulations for power analysis.

Main Methods:

• Developed a new power approximation using Taylor series expansion for the matrix-variate beta distribution of type I.
• Approximated the noncentrality parameter under the alternative hypothesis.
• Evaluated accuracy via Monte Carlo simulation, considering random predictors and errors.
• Varied key parameters: number of outcomes, hypothesis parameters, sample size, and predictor-outcome correlations.

Main Results:

• The novel approximation demonstrated superior accuracy compared to published methods in both small and large samples.
• The new method significantly reduces computation time from minutes (simulation) to milliseconds (approximation).
• Accuracy was validated across various model complexities and data characteristics.

Conclusions:

• The proposed noncentral F power approximation offers a more accurate and computationally efficient solution for GLMMs.
• This method enhances statistical power analysis for studies involving fixed predictors and Gaussian covariates.
• The rPowerlib package provides accessible implementation of this advanced approximation.