Generalized Processing Tree Models: Jointly Modeling Discrete and Continuous Variables

Benefits of multinomial processing tree models with discrete and continuous variables in memory research: an alternative modeling proposal to Juola et al. (2019)

Signal detection theory (SDT) and two-high threshold models (2HT) are often used to analyze accuracy data in recognition memory paradigms. However, when reaction times (RTs) and/or confidence levels (CLs) are also measured, they usually are analyzed separately or not at all as dependent variables (DVs). We propose a new approach to include these variables based on multinomial processing tree models for discrete and continuous variables (MPT-DC) with the aim to compare fits of SDT and 2HT models. Using Juola et al.'s (2019, Memory & Cognition, 47[4], 855-876) data we have found that including CLs and RTs reduces the standard errors of parameter estimates and accounts for interactions among accuracy, CLs, and RTs that classical versions of SDT and 2HT models do not. In addition, according to the simulations, there is an increase in the proportion of correct model selections when relevant DV are included. We highlight the methodological and substantive advantages of MPT-DC in the disentanglement of contributing processes in recognition memory.

Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation

In this paper, we propose a joint modeling approach to analyze dependency in parallel response data. We define two types of dependency: higher-level dependency and within-item conditional dependency. While higher-level dependency can be estimated with common latent variable modeling approaches, within-item conditional dependency is a unique kind of information that is often not captured with extant methods, despite its potential to shed new insights into the relationship between the two types of response data. We differentiate three ways of modeling within-item conditional dependency by conditioning on raw values, expected values, or residual values of the response data, which have different implications in terms of response processes. The proposed approach is illustrated with the example of analyzing parallel data on response accuracy and brain activations from a Theory of Mind assessment. The consequence of ignoring within-item conditional dependency is investigated with empirical and simulation studies in comparison to conventional dependency analysis that focuses exclusively on relationships between latent variables.

rtmpt: An R package for fitting response-time extended multinomial processing tree models

Response-time extended multinomial processing tree models (RT-MPT; Klauer and Kellen, Journal of Mathematical Psychology, 82, 111-130 2018) provide estimates of process-completion times for cognitive processes modeled by means of multinomial processing tree (MPT) models (Batchelder and Riefer, Psychonomic Bulletin & Review, 6, 57-86 1999). We present the R package rtmpt with which it is possible to fit RT-MPT models easily. The package is free and open source, it can be used with two established MPT syntaxes, and has a number of useful features, such as suppressing process-completion times for specific process outcomes, holding process probabilities constant, and changing some prior parameters. In the background of the R package, an altered version of the original C++ code is used for the MCMC sampling. We provide a guide to using rtmpt, validate the underlying hierarchical Bayesian algorithm of rtmpt using simulation-based calibration and show that previously reported results can be reproduced using rtmpt.

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

Multinomial processing trees (MPTs) are a popular class of cognitive models for categorical data. Typically, researchers compare several MPTs, each equipped with many parameters, especially when the models are implemented in a hierarchical framework. A Bayesian solution is to compute posterior model probabilities and Bayes factors. Both quantities, however, rely on the marginal likelihood, a high-dimensional integral that cannot be evaluated analytically. In this case study, we show how Warp-III bridge sampling can be used to compute the marginal likelihood for hierarchical MPTs. We illustrate the procedure with two published data sets and demonstrate how Warp-III facilitates Bayesian model averaging.