Matching Law and Sensitivity to Therapist’s Attention in Children with Autism Spectrum Disorders

Treatments for undefined log ratios in matching analyses

A challenge in carrying out matching analyses is to deal with undefined log ratios. If any reinforcer or response rate equals zero, the logarithm of the ratio is undefined: data are unsuitable for analyses. There have been some tentative solutions, but they had not been thoroughly investigated. The purpose of this article is to assess the adequacy of five treatments: omit undefined ratios, use full information maximum likelihood, replace undefined ratios by the mean divided by 100, replace them by a constant 1/10, and add the constant .50 to ratios. Based on simulations, the treatments are compared on their estimations of variance accounted for, sensitivity, and bias. The results show that full information maximum likelihood and omiting undefined ratios had the best overall performance, with negligibly biased and more accurate estimates than mean divided by 100, constant 1/10, and constant .50. The study suggests that mean divided by 100, constant 1/10, and constant .50 should be avoided and recommends full information maximum likelihood to deal with undefined log ratios in matching analyses.

Multilevel analysis of matching behavior: A comparison of maximum likelihood and Bayesian estimation

While trying to infer laws of behavior, accounting for both within-subjects and between-subjects variance is often overlooked. It has been advocated recently to use multilevel modeling to analyze matching behavior. Using multilevel modeling within behavior analysis has its own challenges though. Adequate sample sizes are required (at both levels) for unbiased parameter estimates. The purpose of the current study is to compare parameter recovery and hypothesis rejection rates of maximum likelihood (ML) estimation and Bayesian estimation (BE) of multilevel models for matching behavior studies. Four factors were investigated through simulations: number of subjects, number of measurements by subject, sensitivity (slope), and variance of the random effect. Results showed that both ML estimation and BE with flat priors yielded acceptable statistical properties for intercept and slope fixed effects. The ML estimation procedure generally had less bias, lower RMSE, more power, and false-positive rates closer to the nominal rate. Thus, we recommend ML estimation over BE with uninformative priors, considering our results. The BE procedure requires more informative priors to be used in multilevel modeling of matching behavior, which will require further studies.

Matching Behaviours and Rewards

Matching describes how behaviour is related to rewards. The matching law holds when the ratio of an individual's behaviours equals the ratio of the rewards obtained. From its origins in the study of pigeons working for food in the laboratory, the law has been applied to a range of species, both in the laboratory and outside it (e.g., human sporting decisions). Probability matching occurs when the probability of a behaviour equals the probability of being rewarded. Input matching predicts the distribution of individuals across habitats. We evaluate the rationality of the matching law and probability matching, expose the logic of matching in real-world cases, review how recent neuroscience findings relate to matching, and suggest future research directions.