Instrumental variable estimation of reinforcer effects

Obtained reinforcement (whether measured as counts or as rates) is frequently used as a predictor in regression analyses of behavior. This approach, however, often contradicts the strict requirement that predictors in a regression be statistically independent of behavior. Indeed, by definition, reinforcement in operant scenarios depends on behavior, creating a causal feedback loop. The consequence of this feedback loop is bias in the estimation of regression parameters. This manuscript describes the technique of instrumental variable estimation (IVE), which allows unbiased regression parameters to be obtained through the use of "instruments," variables that are known a priori to be independent of both compromised predictors and of regression outcomes. Instruments also allow the strength of the bias to be assessed. Two examples of this technique are provided (one relying on real data and one relying on simulation) in the context of regression models of generalized matching.