Instrumental variables regression with latent variables: Accounting for treatment-based differential itemfunctioning as item-level heterogeneity or item parametermoderation

Recent research has highlighted that modeling heterogeneous treatment effects across the indi-vidual items on an outcome measure can yield additional insights into interventions’ effectsbeyond what is available from comparisons of average scores. So far, this work has generallyfocused on randomized controlled trials. However, in social science research, randomizationoften does not hold perfectly, or may be impossible or impractical. This can lead to treatmentendogeneity—correlation between the predictor and the error term of the outcome. Instrumentalvariables regression (IVR) is a popular method for correcting the resulting bias by introducingan exogenous variable that drives change in the predictor but is otherwise uncorrelated with theoutcome. Though typically estimated via two-stage least squares, IVR can also be estimated ina latent variable framework. We develop two models for estimating treatment effects that areheterogeneous across the items used to measure a latent outcome in an IVR, supporting validcausal inferences about impacts of nonrandom treatments/dosages on test items. We presentmethods for modeling items as fixed when most items are equally sensitive to treatment, or ran-dom when item-level variation in treatment sensitivity is pervasive. We outline the affordancesand tradeoffs of the two approaches. We illustrate the use of these models via an empiricalexample analyzing potential item-level variability in sensitivity to time spent on homeworkusing data a large-scale international assessment of high school mathematics.