HMMTree: A computer program for latent-class hierarchical multinomial processing tree models

Latent-class hierarchical multinomial models are an important extension of the widely used family of multinomial processing tree models, in that they allow for testing the parameter homogeneity assumption and provide a framework for modeling parameter heterogeneity. In this article, the computer program HMMTree is introduced as a means of implementing latent-class hierarchical multinomial processing tree models. HMMTree computes parameter estimates, confidence intervals, and goodness-of-fit statistics for such models, as well as the Fisher information, expected category means and variances, and posterior probabilities for class membership. A brief guide to using the program is provided.     

Hierarchical Multinomial Processing Tree Models: A Latent-Class Approach

Multinomial processing tree models are widely used in many areas of psychology. Their application relies on the assumption of parameter homogeneity, that is, on the assumption that participants do not differ in their parameter values. Tests for parameter homogeneity are proposed that can be routinely used as part of multinomial model analyses to defend the assumption. If parameter homogeneity is found to be violated, a new family of models, termed latent-class multinomial processing tree models, can be applied that accommodates parameter heterogeneity and correlated parameters, yet preserves most of the advantages of the traditional multinomial method. Estimation, goodness-of-fit tests, and tests of other hypotheses of interest are considered for the new family of models. The author thanks Bill Batchelder, Edgar Erdfelder, Thorsten Meiser, and Christoph Stahl for helpful comments on a previous version of this paper. The author is also grateful to Edgar Erdfelder for making available the data set analyzed in this paper.     

The role of orthographic and phonological codes in the word and the pseudoword superiority effect: an analysis by means of multinomial processing tree models

Central to the current accounts of the word and the pseudoword superiority effect (WSE and PWSE, respectively) is the concept of a unitized code that is less susceptible to masking than single-letter codes. Current explanations of the WSE and PWSE assume that this unitized code is orthographic, explaining these phenomena by the assumption of dual read-out from unitized and single-letter codes. In this article, orthographic dual read-out models are compared with a phonological dual read-out model (which is based on the assumption that the 1st unitized code is phonological). From this phonological code, an orthographic code is derived, through either lexical access or assembly. Comparison of the orthographic and phonological dual read-out models was performed by formulating both models as multinomial processing tree models. From an application of these models to the data of 2 letter identification experiments, it was clear that the orthographic dual read-out models are insufficient as an explanation of the PWSE, whereas the phonological dual read-out model is sufficient.     

Beta-MPT: Multinomial processing tree models for addressing individual differences

Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate random effects assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These beta-MPT models are ‘hierarchical models’, and their statistical inference is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to statistical inference for beta-MPT models. In simple cases the likelihood function can be obtained analytically; however, for more complex cases, Markov Chain Monte Carlo algorithms are constructed to assist both approaches to inference. Examples based on clinical assessment studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.     

Adding a speed–accuracy trade-off to discrete-state models: A comment on Heck and Erdfelder (2016)

Psychonomic Bulletin & Review - Heck and Erdfelder (2016) developed a model that extends discrete-state multinomial processing tree models to response time (RT) data. Their model is an...     

MPTinR: Analysis of multinomial processing tree models in R

We introduce MPTinR, a software package developed for the analysis of multinomial processing tree (MPT) models. MPT models represent a prominent class of cognitive measurement models for categorical data with applications in a wide variety of fields. MPTinR is the first software for the analysis of MPT models in the statistical programming language R, providing a modeling framework that is more flexible than standalone software packages. MPTinR also introduces important features such as (1) the ability to calculate the Fisher information approximation measure of model complexity for MPT models, (2) the ability to fit models for categorical data outside the MPT model class, such as signal detection models, (3) a function for model selection across a set of nested and nonnested candidate models (using several model selection indices), and (4) multicore fitting. MPTinR is available from the Comprehensive R Archive Network at http://cran.r-project.org/web/packages/MPTinR/.     

Theoretical and empirical review of multinomial process tree modeling

We review a current and popular class of cognitive models calledmultinomial processing tree (MPT) models. MPT models are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. We formally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPT models to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPT models, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.     

Pooling data versus averaging model fits for some prototypical multinomial processing tree models

For a study with multinomial data where there are n_g individuals and with each person having n_r test trials, the question arises as to how to fit the parameters of a multinomial processing tree (MPT) model. Should each parameter be estimated for each individual and then averaged to obtain a group estimate, or should the frequencies in the multinomial categories be pooled so that the model is fit once for the entire group? This basic question is explored with a series of Monte Carlo simulations for some prototypical MPT models. There is a general finding of a pooling advantage for the case where there is a single experimental condition. Also when there are different experimental conditions, there is reduced bias for detecting condition differences for a method based on the pooled data. Although the focus of the paper is on multinomial models, a general theorem is advanced that establishes a basic condition that determines whether there is or is not a difference between the averaging of individual estimates and the estimate based on the pooled data.     

A novel method for assessing rival models of recognition memory

A general comparison is made between the multinomial processing tree (MPT) approach and a strength-based approach for modeling recognition memory measurement. Strength models include the signal-detection model and the dual-process model. Existing MPT models for recognition memory and a new generic MPT model, called the Multistate (MS) model, are contrasted with the strength models. Although the ROC curves for the MS model and strength model are similar, there is a critical difference between existing strength models and MPT models that goes beyond the assessment of the ROC. This difference concerns the question of stochastic mixtures for foil test trials. The hazard function and the reverse hazard function are powerful methods for detecting the presence of a probabilistic mixture. Several new theorems establish a novel method for obtaining information about the hazard function and reverse hazard function for the latent continuous distributions that are assumed in the strength approach to recognition memory. Evidence is provided that foil test trials involve a stochastic mixture. This finding occurred for both short-term memory procedures, such as the Brown–Peterson task, and long-term list-learning procedures, such as the paired-associate task. The effect of mixtures on foil trials is problematic for existing strength models but can be readily handled by MPT models such as the MS model. Other phenomena, such as the mirror effect and the effect of target-foil similarity, are also predicted accurately by the MPT modeling framework.     

A context-free language for binary multinomial processing tree models

This paper provides a new formalization for the class of binary multinomial processing tree (BMPT) models, and theorems for the class are developed using the formalism. MPT models are a popular class of information processing models for categorical data in specific cognitive paradigms. They have a recursive structure that is productively described with the tools of formal language and computation theory. We provide an axiomatization that characterizes BMPT models as strings in a context-free language, and then we add model-theoretic axioms and definitions to interpret the strings as parameterized probabilistic models for categorical data. The language for BMPT models is related to the Full Binary Tree language, a well-studied context-free language. Once BMPT models are viewed from the perspective of the Full Binary Tree language, a number of theoretical and computational results can be developed. In particular, we have a number of results concerning the enumerations of BMPT models as well as the identifiability of subclasses of these models.     

Applying processing trees in social psychology

Processing tree models offer a powerful research framework by which the contributions of cognitive processes to a task can be separated and quantified. The present article reviews a number of applications of processing tree models in the domain of social psychology in order to illustrate the steps to be taken in developing and validating a given model and applying it to the measurement and comparison of processes across experimental and quasi-experimental conditions. Process dissociation models are discussed as special cases of processing tree models. Crucial assumptions of processing tree models are considered and methods to overcome violations of such assumptions are reviewed. In addition to the application of processing tree models for the analysis of social and cognitive processes, their value is also discussed for the elicitation of truthful responses to socially sensitive questions.     

Appletree: A multinomial processing tree modeling program for macintosh computers

Multinomial processing tree (MPT) models are statistical models that allow for the prediction of categorical frequency data by sets of unobservable (cognitive) states. In MPT models, the probability that an event belongs to a certain category is a sum of products of state probabilities. AppleTree is a computer program for Macintosh for testing user-defined MPT models. It can fit model parameters to empirical frequency data, provide confidence intervals for the parameters, generate tree graphs for the models, and perform identifiability checks. In this article, the algorithms used by AppleTree and the handling of the program are described.     

A constrained Rasch model of trace redintegration in serial recall

The notion that verbal short-term memory tasks, such as serial recall, make use of information in long-term as well as in short-term memory is instantiated in many models of these tasks. Such models incorporate a process in which degraded traces retrieved from a short-term store are reconstructed, or redintegrated (Schweickert, 1993), through the use of information in long-term memory. This article presents a conceptual and mathematical model of this process based on a class of item-response theory models. It is demonstrated that this model provides a better fit to three sets of data than does the multinomial processing tree model of redintegration (Schweickert, 1993) and that a number of conceptual accounts of serial recall can be related to the parameters of the model.     

单字法有意遗忘的内部心理机制：基于多项式加工树模型的分析

通过构建使用单个双字词作为实验材料,并在测验阶段全面考察记忆提取过程的MPT模型,考察单字法有意遗忘的心理机制。结果发现,对于TBF/R项目,遗忘组的储存能力和提取能力均弱于记忆组;对于TBR/R项目,遗忘组的储存能力强于记忆组。并且无论对于短时SOA还是长时SOA,遗忘组对TBF项目后探测刺激的反应时都显著长于TBR项目。研究表明,单字法有意遗忘现象是由选择性复述、注意抑制和提取抑制三种机制共同作用的结果。     

简化的联合再认范式中情绪对错误记忆影响的年龄差异

以康奈尔情绪DRM词表为主要实验材料, 使用简化的联合再认范式(DRM范式的变式), 结合多项式加工树建模的统计手段, 对34名年轻人(23 ± 2岁)和28名老年人(68 ± 5岁)的再认记忆进行比较, 以考察不同年龄组中情绪效价对错误记忆的作用机制。结果发现材料的情绪效价对错误记忆的影响存在显著年龄差异：(1) 积极情绪能够有效降低老年人的错误记忆, 其作用机制为积极情绪增强了老年人的字面痕迹而减弱了要点痕迹提取; (2) 消极情绪能够有效地降低年轻人的错误记忆, 其作用机制为消极情绪使年轻人反应偏向降低, 但不影响其记忆痕迹的提取。结果表明, 简化的联合再认范式下, 情绪效价对错误记忆的效应存在明显的年龄差异：老年人表现出积极情绪降低错误记忆的积极偏向; 年轻人表现出消极情绪降低错误记忆的消极偏向; 情绪效应对错误记忆的认知机制存在年龄差异。     

The multinomial model of prospective memory: validity of ongoing-task parameters

The objective of this research was to provide additional experimental validation of the multinomial processing tree (MPT) model of event-based prospective memory (Smith & Bayen, 2004). In particular, the parameters that measure trial-type detection in the ongoing task were examined. In three experiments with different response instructions, event-based prospective memory tasks were embedded in ongoing color-matching tasks. The results support the validity of the MPT model, that is, manipulations of ongoing-task difficulty affected the ongoing-task parameters of the MPT model, while leaving the estimates for the prospective and the retrospective components of prospective memory unaffected.     

How framing statistical statements affects subjective veracity: Validation and application of a multinomial model for judgments of truth

Extending the well-established negativity bias in human cognition to truth judgments, it was recently shown that negatively framed statistical statements are more likely to be considered true than formally equivalent statements framed positively. However, the underlying processes responsible for this effect are insufficiently understood. Therefore, a multinomial processing tree model is herein proposed to distinguish between differences in (a) knowledge or (b) response bias that may account for the framing effect. Three model validation experiments supported the psychological interpretability of model parameters. Model application revealed that the framing effect can be considered a bias: Given insufficient knowledge, individuals more likely guessed "true" when faced with a negatively framed statistical statement. The probability of conclusive knowledge, however, remained constant across frames. In summary, this article puts forwards and validates a formal model that can be used more generally to investigate processes underlying truth judgments. Based on this model, it is herein shown that one particular phenomenon - framing effects observed for statistical statements - can be considered a response bias, rather than the upshot of differential knowledge.     

Multinomial processing tree models: An implementation

Multinomial processing tree (MPT) models have been widely used by researchers in cognitive psychology. This paper introduces MBT.EXE, a computer program that makes MPT easy to use for researchers. MBT.EXE implements the statistical theory developed by Hu and Batchelder (1994). This user-friendly software can be used to construct MPT models and conduct statistical inferences, including point and interval estimation, hypothesis testing, and goodness of fit. Furthermore, this program can be used to examine the robustness of MPT models. Algorithms for parameter estimation, hypothesis testing, and Monte Carlo simulation are presented.     

Dissociating automatic associations: Comparing two implicit measurements of race bias

Weak correspondence across different implicit bias tasks may arise from the contribution of unique forms of automatic and controlled processes to response behavior. Here, we examined the correspondence between estimates of automatic and controlled processing derived from two sequential priming tasks with identical structure and timing designed to separately measure stereotypic (Weapons Identification Task; WIT) and evaluative (Affective Priming Task; APT) associations. Across two studies using predominantly White samples, three consistent patterns emerged in the data: (a) stereotypic bias was stronger for Black targets, whereas evaluative bias was stronger for White targets; (b) overall response accuracy bias correlated modestly across the two tasks; and (c) multinomial processing tree estimates of controlled processing corresponded much more strongly than estimates of automatic processing. These findings support models positing distinct learning and memory systems for different forms of race bias, and suggest that these differing forms contribute to estimates of automatic associations.     

Cognitive processes in implicit attitude tasks: An experimental validation of the Trip Model

Implicit attitude tasks have become very popular in various areas of psychology. However, little is known about the cognitive processes they involve. To address this issue, we investigated the underlying processes of the Go/No‐go Association Task (GNAT), a go/no‐go variant of the well‐known Implicit Association Test (IAT). More precisely, we tested two alternative multinomial processing tree (MPT) models of GNAT performance, the Trip Model and the generalized Quad Model. Both models assume that GNAT performance is influenced not only by automatic associations but also by response biases and a controlled discrimination process. However, the two models differ with respect to an additional overcoming bias process. In contrast to the Quad Model, the Trip Model assumes that overcoming bias does not play a major role in GNAT performance. Instead, the Trip Model emphasizes the role of response biases. We report three experiments that demonstrate the validity of the Trip Model for GNAT data. Copyright © 2010 John Wiley & Sons, Ltd.