  A split questionnaire design (SQD), an alternative to full questionnaires,
can reduce the response burden and improve survey quality. One can design a
split questionnaire to reduce the information loss from missing data induced by
the split questionnaire. This study develops a methodology for finding optimal
SQD (OSQD) for multivariate continuous variables, applying a probabilistic
design and optimality criterion approach. Our method employs previous survey
data to compute the Fisher information matrix and A-optimality criterion to
find OSQD for the current survey study. We derive theoretical findings on the
relationship between the correlation structure and OSQD and the robustness of
local OSQD. We conduct simulation studies to compare local and two global
OSQDs; mini-max OSQD and Bayes OSQD) to baselines. We also apply our method to
the 2016 Pet Demographic Survey (PDS) data. In both simulation studies and the
real data application, local and global OSQDs outperform the baselines.
