Multilevel analysis of matching behavior: A comparison of maximum likelihood and Bayesian estimation
Use maximum-likelihood estimation when you stack matching-law data inside subjects.
01Research in Context
What this study did
Ilagan et al. (2023) ran a computer simulation to test two ways of crunching matching-law data.
They compared plain-vanilla maximum-likelihood (ML) estimation against flat-prior Bayesian estimation in multilevel models.
The goal was to see which method gives cleaner answers when behavior data are stacked inside subjects.
What they found
ML won.
The simulations showed ML estimates were more accurate and less wobbly than flat-prior Bayesian ones.
In short, skip the flat priors when you model matching behavior across levels.
How this fits with other research
Older papers like Houston (1982) already warned that matching math can break if the model is sloppy.
Ilagan et al. answer that worry by giving analysts a cleaner tool—ML—to keep the math tight.
Schenk et al. (2020) and Johnson et al. (2009) both fit matching equations to real basketball shots; they could re-run their data with Ilagan’s ML approach for sharper standard errors.
No clash here—just an upgrade kit for anyone who studies choice.
Why it matters
If you write grants or papers using multilevel matching models, run them with maximum likelihood, not flat-prior Bayes. Your stats reviewer will smile and your error bars will shrink.
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02At a glance
03Original abstract
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.
Journal of the Experimental Analysis of Behavior, 2023 · doi:10.1002/jeab.872