# A Bayesian Two‐Step Multiple Imputation Approach Based on Mixed Models for Missing EMA Data

## TL;DR

This paper introduces a Bayesian two-step multiple imputation method using mixed models to handle missing data in Ecological Momentary Assessment (EMA) studies.

## Contribution

The novel contribution is a Bayesian framework that compares three mixed models for imputing missing EMA data.

## Key findings

- Multiple imputation outperforms single imputation in handling missing EMA data.
- Modeling within-subject variance and linking missingness to the response improves imputation performance.
- The MELS models show distinct imputation results compared to the Random Intercept Linear Mixed model in real-world data.

## Abstract

Ecological Momentary Assessments (EMA) capture real‐time thoughts and behaviors in natural settings, producing rich longitudinal data for statistical analyses. However, the robustness of these analyses can be compromised by the large amount of missing data in EMA studies. To address this, multiple imputation, a method that replaces missing values with several plausible alternatives, has become increasingly popular. In this article, we introduce a two‐step Bayesian multiple imputation framework which leverages the configuration of mixed models. We adopt and compare: (1) the Random Intercept Linear Mixed model; (2) the Mixed‐effect Location Scale (MELS) model which accounts for subject variance influenced by covariates and random effects; and (3) the Shared Parameter MELS model which additionally links the missing data to the response variable through a random intercept logistic model. Each of these three can be used to complete the posterior distribution within the framework. In the simulation study, we extend this two‐step Bayesian multiple imputation strategy to handle simultaneous missing variables in EMA data and compare the effectiveness of the multiple imputations across the three mixed models. Our analyses highlight the advantages of multiple imputations over single imputations and underscore the importance of selecting an appropriate model for the imputation process. Specifically, modeling within‐subject variance and linking the missingness mechanism to the response will greatly improve the performance in certain scenarios. Furthermore, we applied our techniques to the “Make Better Choices 1 (MBC1)” study, highlighting the distinction, in particular, of imputation results between the Random Intercept Linear Mixed model and the two MELS models in terms of modeling within‐subject variance.