  Multiple matrix sampling is a survey methodology technique that randomly
chooses a relatively small subset of items to be presented to survey
respondents for the purpose of reducing respondent burden. The data produced
are missing completely at random (MCAR), and special missing data techniques
should be used in linear regression and other multivariate statistical
analysis. We derive asymptotic variances of regression parameter estimates that
allow us to conduct power analysis for linear regression models fit to the data
obtained via a multiple matrix sampling design. The ideas are demonstrated with
a variation of the Big Five Inventory of psychological traits. An exploration
of the regression parameter space demonstrates instability of the sample size
requirements, and substantial losses of precision with matrix-sampled
regressors. A simulation with non-normal data demonstrates the advantages of a
semi-parametric multiple imputation scheme.
