Unreliable Continuous Treatment Indicators in Propensity Score Analysis

Propensity score analyses (PSA) of continuous treatments often operationalize the treatment as a multi-indicator composite, and its composite reliability is unreported. Latent variables or factor scores accounting for this unreliability are seldom used as alternatives to composites. This study examines the effects of the unreliability of indicators of a latent treatment in PSA using the generalized propensity score (GPS). A Monte Carlo simulation study was conducted varying composite reliability, continuous treatment representation, variability of factor loadings, sample size, and number of treatment indicators to assess whether Average Treatment Effect (ATE) estimates differed in their relative bias, Root Mean Squared Error, and coverage rates. Results indicate that low composite reliability leads to underestimation of the ATE of latent continuous treatments, while the number of treatment indicators and variability of factor loadings show little effect on ATE estimates, after controlling for overall composite reliability. The results also show that, in correctly specified GPS models, the effects of low composite reliability can be somewhat ameliorated by using factor scores that were estimated including covariates. An illustrative example is provided using survey data to estimate the effect of teacher adoption of a workbook related to a virtual learning environment in the classroom.