Abstract
Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes. Traditionally, data are aggregated across participants and analyzed under the assumption of independently and identically distributed observations. Hierarchical Bayesian extensions of MPT models explicitly account for participant heterogeneity by assuming that the individual parameters follow a continuous hierarchical distribution. We provide an accessible introduction to hierarchical MPT modeling and present the user-friendly and comprehensive R package TreeBUGS, which implements the two most important hierarchical MPT approaches for participant heterogeneity—the beta-MPT approach (Smith & Batchelder, Journal of Mathematical Psychology 54:167-183, 2010) and the latent-trait MPT approach (Klauer, Psychometrika 75:70-98, 2010). TreeBUGS reads standard MPT model files and obtains Markov-chain Monte Carlo samples that approximate the posterior distribution. The functionality and output are tailored to the specific needs of MPT modelers and provide tests for the homogeneity of items and participants, individual and group parameter estimates, fit statistics, and within- and between-subjects comparisons, as well as goodness-of-fit and summary plots. We also propose and implement novel statistical extensions to include continuous and discrete predictors (as either fixed or random effects) in the latent-trait MPT model.
Highlights
Multinomial processing tree modelsBefore describing the statistical details of the MPT model class in general, we introduce the source-monitoring model, which serves as a running example
Multinomial processing tree (MPT) models are a class of measurement models that account for categorical data by assuming a finite number of underlying cognitive processes
Multinomial processing tree (MPT) models are a class of measurement models that estimate the probability of underlying latent cognitive processes on the basis of categorical data (Batchelder & Riefer, 1999)
Summary
Before describing the statistical details of the MPT model class in general, we introduce the source-monitoring model, which serves as a running example. On item recognition, the source memory parameter dA gives the probability of correctly remembering the item’s source, which results in a correct response (i.e., A). If one of these two memory processes fails, participants are assumed to guess. Whereas the profession schemata were activated at the time of encoding for half of the participants (encoding condition), the other half were told about the professions of the sources just before the test (retrieval condition) Overall, this resulted in a 2 (Source; within subjects) × 3 (Expectancy; within subjects) × 2 (Time of Schema Activation; between subjects) mixed factorial design. On the basis of the latenttrait approach, we (a) first analyze data from the retrieval condition; (b) show how to check for convergence and model fit, and perform within-subjects comparisons; (c) compare the parameter estimates to those from the beta-MPT approach; (d) include perceived contingency as a continuous predictor for the source-guessing parameter a; and (e) discuss two approaches for modeling a between-subjects factor (i.e., Time of Schema Activation)
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