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Multiple matrix sampling is a survey methodology technique that randomlychooses a relatively small subset of items to be presented to surveyrespondents for the purpose of reducing respondent burden. The data producedare missing completely at random (MCAR), and special missing data techniquesshould be used in linear regression and other multivariate statisticalanalysis. We derive asymptotic variances of regression parameter estimates thatallow us to conduct power analysis for linear regression models fit to the dataobtained via a multiple matrix sampling design. The ideas are demonstrated witha variation of the Big Five Inventory of psychological traits. An explorationof the regression parameter space demonstrates instability of the sample sizerequirements, and substantial losses of precision with matrix-sampledregressors. A simulation with non-normal data demonstrates the advantages of asemi-parametric multiple imputation scheme.

Power analysis for a linear regression model when regressors are matrix sampled