Title: Optimal Split Questionnaire Designs based on Multivariate Ordinal Data

Abstract: In surveys, questionnaires are frequently used to collect data for statistical inference. Split questionnaire design (SQD) is an alternate method for increasing the quality of responses by reducing the stress of responding to a lengthy questionnaire. Due to the prevalence of Likert scale questions, surveys frequently contain many ordinal variables. We develop log-linear models to study and estimate population proportions using multivariate ordinal survey data. Then, given the values of the true parameters, we find the local optimal SQD. To examine the robustness of the optimal design, we determine the global optimal SQDs using Bayesian Design or Minimax Design. We conduct simulations to examine the relationship between the gain of an optimal SQD and other variables such as population proportions or correlations.