Multinomial processing tree models are widely used in many areas of psychology. A hierarchical extension of the model class is proposed, using a multivariate normal distribution of person-level parameters with the mean and covariance matrix to be estimated from the data. The hierarchical model allows one to take variability between persons into account and to assess parameter correlations. The model is estimated using Bayesian methods with weakly informative hyperprior distribution and a Gibbs sampler based on two steps of data augmentation. Estimation, model checks, and hypotheses tests are discussed. The new method is illustrated using a real data set, and its performance is evaluated in a simulation study.

The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining $S-R$\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$S-R$$\end{document} parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss–Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach.

One prominent model in the realm of memory-based judgments and decisions is the recognition heuristic. Under certain preconditions, it presumes that choices are based on recognition in a one-cue non-compensatory manner and that other information is ignored. This claim has been studied widely—and received, at best, mixed support—in probabilistic inferences. By contrast, only a small number of recent investigations have taken the RH to the realm of preferential decisions (i.e. consumer choice). So far, the conclusion has been that the RH cannot satisfactorily account for aggregate data patterns, but no fully specified alternative model has been demonstrated to provide a better account. Herein, the data from a recent consumer-choice study (Thoma & Williams, 2013) are re-analyzed with the outcome-based maximum-likelihood strategy classification method, thus testing several competing models on individual data. Results revealed that an alternative compensatory model (an equal weights strategy) accounted best for a larger number of datasets than the RH. Thereby, the findings further specify prior results and answer the call for comparative model testing on individual data that has been voiced repeatedly.

According to the recognition heuristic (RH), for decision domains where recognition is a valid predictor of a choice criterion, recognition alone is used to make inferences whenever one object is recognized and the other is not, irrespective of further knowledge. Erdfelder, Küpper-Tetzel, and Mattern (2011) questioned whether the recognition judgment itself affects decisions or rather the memory strength underlying it. Specifically, they proposed to extend the RH to the memory state heuristic (MSH), which assumes a third memory state of uncertainty in addition to recognition certainty and rejection certainty. While the MSH already gathered significant support, one of its basic and more counterintuitive predictions has not been tested so far: In guessing pairs (none of the objects recognized), the object more slowly judged as unrecognized should be preferred, since it is more likely to be in a higher memory state. In this paper, we test this prediction along with other recognition latency predictions of the MSH, thereby adding to the body of research supporting the MSH.