TreeBUGS: An R package for hierarchical multinomial-processing-tree modeling

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.

A New Model for Acquiescence at the Interface of Psychometrics and Cognitive Psychology

“…The proposed model belongs to the general class of hierarchical MPT models (Heck, Arnold, & Arnold, 2018;Klauer, 2010;Matzke et al, 2015), which subsume psychometric IR-tree models as special cases (Böckenholt, 2012a;De Boeck & Partchev, 2012;Tutz, 1990). We believe that hierarchical MPT models provide a general and fruitful framework for future developments and applications based on the idea and principles of "cognitive psychometrics" (Riefer et al, 2002).…”

A Simple Method for Comparing Complex Models: Bayesian Model Comparison for Hierarchical Multinomial Processing Tree Models using Warp-III Bridge Sampling

“…We believe that Warp-III may be especially useful for so-called sloppy models with highly correlated parameters (Brown & Sethna, 2003), including but not limited to race models of response times, which often yield skewed posterior distributions (e.g., Brown & Heathcote, 2008;Matzke, Love, & Heathcote, 2017). The Warp-III methodology also lends itself to model comparison in extensions of hierarchical cognitive models that impose on the model parameters a statistical structure such as a linear regression, factor analysis, or analysis of variance (e.g., Boehm, Steingroever, & Wagenmakers, 2017;Heck et al, 2018a;Turner, Wang, & Merkle, 2017;Vandekerckhove, 2014). The application of Warp-III to complex experimental designs is ongoing work in our laboratory.…”

“…Priors are assigned to μ and . We follow earlier implementations of the latent-trait approach and assign independent standard normal distributions to the P components of μ (Heck, Arnold, & Arnold, 2018a;Matzke et al, 2015). This choice corresponds to uniform priors on the probability scale for the grand means.…”

“…We follow Klauer (2010) and assign Q an inverse Wishart prior with degrees of freedom ν = P + 1 and scale matrix I P (i.e., P × P identity matrix). For the P components of ξ , we follow Heck et al (2018a) and use independent uniform priors that range from zero to ten. These choices correspond to relatively diffuse priors for the standard deviations of the random effects on the probit scale and uniform priors for the correlations between the random effects.…”

“…The choice of the prior for ξ is less straightforward. We report the results corresponding to the default setting of the recently developed MPT software package TreeBUGS (Heck et al, 2018a), but we probed the robustness of our conclusions with a sensitivity analysis using ξ p ∼ Uniform(0, ξ max ) ∀ p ∈ {1, 2, . .…”