  Ecological Momentary Assessments (EMA) capture real-time thoughts and
behaviors in natural settings, producing rich longitudinal data for statistical
and physiological analyses. However, the robustness of these analyses can be
compromised by the large amount of missing in EMA data sets. To address this,
multiple imputation, a method that replaces missing values with several
plausible alternatives, has become increasingly popular. In this paper, we
introduce a two-step Bayesian multiple imputation framework which leverages the
configuration of mixed models. We adopt the Random Intercept Linear Mixed
model, the Mixed-effect Location Scale model which accounts for subject
variance influenced by covariates and random effects, and the Shared Parameter
Location Scale Mixed Effect model which links the missing data to the response
variable through a random intercept logistic model, to complete the posterior
distribution within the framework. In the simulation study and an application
on data from a study on caregivers of dementia patients, we further adapt this
two-step Bayesian multiple imputation strategy to handle simultaneous missing
variables in EMA data sets and compare the effectiveness of multiple
imputations across different mixed models. The analyses highlight the
advantages of multiple imputations over single imputations. Furthermore, we
propose two pivotal considerations in selecting the optimal mixed model for the
two-step imputation: the influence of covariates as well as random effects on
the within-variance, and the nature of missing data in relation to the response
variable.
