Lan Liu, University of Minnesota at Twin Cities

“Parsimonious Regressions for Repeated Measure Analysis” 

Abstract: Longitudinal data with repeated measures frequently arises in various
disciplines. The standard methods typically impose a mean outcome model as
a function of individual features, time and their interactions. However,
the validity of the estimators relies on the correct specifications of the
time dependency. The envelope method is recently proposed as a sufficient
dimension reduction (SDR) method in multivariate regressions. In this
paper, we demonstrate the use of the envelope method as a new parsimonious
regression method for repeated measures analysis, where the specification
of the underlying pattern of time trend is not required by the model. We
found that if there is enough prior information to support the
specification of the functional dependency of the mean outcome on time and
if the dimension of the prespecified functional form is low, then the
standard method is advantageous as an efficient and unbiased estimator.
Otherwise, the envelope method is appealing as a more robust and
potentially efficient parsimonious regression method in repeated measure
analysis. We compare the performance of the envelope estimators with the
existing estimators in simulation study and in an application to the China
Health and Nutrition Survey