Resurrecting the individual in behavioral analysis: Using mixed effects models to address nonsystematic discounting data.

Delay and probability discounting functions typically take a monotonic form, but some individuals produce functions that are nonsystematic. Johnson and Bickel (2008) developed an algorithm for classifying nonsystematic functions on the basis of two different criteria. Type 1 functions were identified as nonsystematic due to random choices and Type 2 functions were identified as nonsystematic due to relatively shallow slopes, suggesting poor sensitivity to choice parameters. Since their original publication, the algorithm has become widely used in the human discounting literature for removal of participants, with studies often removing approximately 20% of the original sample (Smith & Lawyer, 2017). Because subject removal may not always be feasible due to loss of power or other factors, the present report applied a mixed effects regression modeling technique (Wileyto, Audrain-Mcgovern, Epstein, & Lerman, 2004; Young, 2017) to account for individual differences in DD and PD functions. Assessment of the model estimates for Type 1 and 2 nonsystematic functions indicated that both types of functions deviated systematically from the rest of the sample in that nonsystematic participants were more likely to show shallower slopes and increased biases for larger amounts. The results indicate that removing these participants would fundamentally alter the properties of the final sample in undesirable ways. Because mixed effects models account for between-participant variation with random effects, we advocate for the use of these models for future analyses of a wide range of functions within the behavioral analysis field, with the benefit of avoiding the negative consequences associated with subject removal.