Latent trait shared-parameter mixed models for missing ecological momentary assessment data

Latent trait shared-parameter mixed models for ecological momentary assessment (EMA) data containing missing values are developed in which data are collected in an intermittent manner. In such studies, data are often missing due to unanswered prompts. Using item response theory models, a latent trait is used to represent the missing prompts and modeled jointly with a mixed model for bivariate longitudinal outcomes. Both one- and two-parameter latent trait shared-parameter mixed models are presented. These new models offer a unique way to analyze missing EMA data with many response patterns. Here, the proposed models represent missingness via a latent trait that corresponds to the students' "ability" to respond to the prompting device. Data containing more than 10 300 observations from an EMA study involving high school students' positive and negative affects are presented. The latent trait representing missingness was a significant predictor of both positive affect and negative affect outcomes. The models are compared to a missing at random mixed model. A simulation study indicates that the proposed models can provide lower bias and increased efficiency compared to the standard missing at random approach commonly used with intermittent missing longitudinal data.