Applying Mixed-Effects Tobit Models to Right-Skewed ESM/EMA Data

Intensive longitudinal data collection methods like the Experience Sampling Method (ESM) and Ecological Momentary Assessment (EMA) are used to repeatedly assess people’s emotional states, behaviors, and context to examine their associations. Many variables of interest, such as negative affect and psychopathological symptoms, are measured with bounded scales that can produce right-skewed data. Standard linear mixed-effects models do not account for this intricacy, potentially producing biased parameter estimates.This study proposes to conceptualize skewed observations as censored manifestations of underlying latent variables, using mixed-effects tobit models as an alternative analytical approach. Using data from N = 322 participants from three mental health groups (controls, depressed, psychotic) who completed mood assessments ten times daily for six days, we examined parameter recovery capabilities of the standard linear and tobit mixed-effects models by inducing increasing skewness into an originally roughly normally distributed outcome variable (positive affect). Results indicated that the tobit model provided relatively stable parameter estimates under progressive censoring conditions, while the standard linear model showed deterioration in slope estimates approaching zero.When applied to a naturally skewed outcome variable (negative affect), the tobit model again estimated larger associations across all groups, with the greatest differences observed in controls, where floor effects were most pronounced. Tobit models also revealed greater between-person variability and reduced intercept-slope correlations.While computational complexity presents implementation challenges, these findings suggest that tobit models offer important advantages for analyzing bounded psychological constructs in ESM research. However, further research across diverse contexts is needed to establish implementation guidelines.