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Statistical power estimation for studies with multiple model parameters isinherently a multivariate problem. Power for individual parameters of interestcannot be reliably estimated univariately since correlation and varianceexplained relative to one parameter will impact the power for anotherparameter, all usual univariate considerations being equal. Explicit solutionsin such cases, especially for models with many parameters, are eitherimpractical or impossible to solve, leaving researchers to the prevailingmethod of simulating power. However, the point estimates for a vector of modelparameters are uncertain, and the impact of inaccuracy is unknown. In suchcases, sensitivity analysis is recommended such that multiple combinations ofpossible observable parameter vectors are simulated to understand powertrade-offs. A limitation to this approach is that it is computationallyexpensive to generate sufficient sensitivity combinations to accurately map thepower trade-off function in increasingly high-dimensional spaces for the modelsthat social scientists estimate. This paper explores the efficient estimationand graphing of statistical power for a study over varying model parametercombinations. We propose a simple and generalizable machine learning inspiredsolution to cut the computational cost to less than 10% of the brute forcemethod while providing F1 scores above 90%. We further motivate the impact oftransfer learning in learning power manifolds across varying distributions.

PowerGraph: Using neural networks and principal components to determine multivariate statistical power trade-offs