Assessing the validity of multinomial models using extraneous variables: an application to prospective memory

The class of multinomial processing tree (MPT) models has been used extensively in cognitive psychology to model latent cognitive processes. Critical for the usefulness of a MPT model is its psychological validity. Generally, the validity of a MPT model is demonstrated by showing that its parameters are selectively and predictably affected by theoretically meaningful experimental manipulations. Another approach is to test the convergent validity of the model parameters and other extraneous measures intended to measure the same cognitive processes. Here, we advance the concept of construct validity (Cronbach & Meehl, 1955 ) as a criterion for model validity in MPT modelling and show how this approach can be fruitfully utilized using the example of a MPT model of event-based prospective memory. For that purpose, we investigated the convergent validity of the model parameters and established extraneous measures of prospective memory processes over a range of experimental settings, and we found a lack of convergent validity between the two indices. On a conceptual level, these results illustrate the importance of testing convergent validity. Additionally, they have implications for prospective memory research, because they demonstrate that the MPT model of event-based prospective memory is not able to differentiate between different processes contributing to prospective memory performance.     

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.     

多项式加工树模型次序约束的量化分析及其应用

多项式加工树（MPT）模型是一种认知测量模型,能够对潜在认知过程进行测量和检验。已有研究探讨了二链MPT模型次序约束的重新参数化问题,本研究探讨了MPT模型次序约束的量化分析方法并从二链推广到多链,同时归纳出MPT模型参数向量内和参数向量间两参数次序约束量化分析的结论。数据分析结果表明该方法不仅在MPT模型框架下验证了潜在参数次序关系,而且给出了约束的量化指标,为潜在认知测量提供更有意义的解释。     

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.     

Representing parametric order constraints in multi-trial applications of multinomial processing tree models

Binary multinomial processing tree (MPT) models parameterize the multinomial distribution over a set of J categories, such that each of its parameters, θ₁,θ₂,…,θ_S, is functionally independent and free to vary in the interval [0,1]. This paper analyzes binary MPT models subject to parametric order-constraints of the form 0?θ_s?θ_t?1. Such constraints arise naturally in multi-trial learning and memory paradigms, where some parameters representing cognitive processes would naturally be expected to be non-decreasing over learning trials or non-increasing over forgetting trials. The paper considers the case of one or more, non-overlapping linear orders of parametric constraints. Several ways to reparameterize the model to reflect the constraints are presented, and for each it is shown how to construct a new binary MPT that has the same number of parameters and is statistically equivalent to the original model with the order constraints. The results both extend the mathematical analysis of the MPT class as well as offering an approach to order restricted inference at the level of the entire class. An empirical example of this approach is provided.     

多项式加工树模型在再认启发式中的应用

摘 要 再认启发式利用再认线索进行决策。以往研究采用一致率、击中率、虚报率和区分指数来表示再认启发式使用,然而这些方法都存在局限。多项式加工树模型能够分离不同的认知加工过程,为了解决再认使用与知识使用的混淆,研究者提出一种多项式加工树模型 r-model 测量再认启发式的使用。本文将重 点介绍 r-model,具体包括 r-model 的内容、数据分析以及考虑个体差异的分层 r-model。最后,从 r-model 的模型修正和边界条件两个方面提出未来研究方向。 关键词 再认启发式;流畅启发式;多项式加工树;贝叶斯分层模型     

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

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.     

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.     

多项式加工树模型在社会心理学中的应用

多项式加工树（multinomial processing tree, MPT）从理论模型出发,使用多项式模型来拟合行为数据并估计理论模型中各个加工过程发生的可能性。该模型能够有效分离和量化不同心理过程,被广泛应用于社会认知研究之中,如态度、刻板印象等。本文首先介绍该模型的基本原理及其实现,并以道德判断为例说明其在社会心理学中的最新应用。最后,总结其对社会心理学研究的意义,即可以作为一种方法提高研究的效度和精度,具有较高的实用价值,并指出其潜在不足。     

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.     

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/.     

Hierarchical Approximate Bayesian Computation

Approximate Bayesian computation (ABC) is a powerful technique for estimating the posterior distribution of a model’s parameters. It is especially important when the model to be fit has no explicit likelihood function, which happens for computational (or simulation-based) models such as those that are popular in cognitive neuroscience and other areas in psychology. However, ABC is usually applied only to models with few parameters. Extending ABC to hierarchical models has been difficult because high-dimensional hierarchical models add computational complexity that conventional ABC cannot accommodate. In this paper, we summarize some current approaches for performing hierarchical ABC and introduce a new algorithm called Gibbs ABC. This new algorithm incorporates well-known Bayesian techniques to improve the accuracy and efficiency of the ABC approach for estimation of hierarchical models. We then use the Gibbs ABC algorithm to estimate the parameters of two models of signal detection, one with and one without a tractable likelihood function.     

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.     

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.     

来源监测实验中的源记忆测量

来源监测实验既涉及到研究项目探测、来源甄别两种不同的认知加工过程,又涉及到研究反应倾向。当研究目的着眼于测量或比较不同来源源记忆或不同控制变量组在同一来源上的源记忆效果时,把来源甄别和项目探测两种认知过程及反应倾向分解开是十分必要的。通常的测量和分析方法对此收效甚微,多项式加工树模型旨在有效地实现这一目标。     

multiTree: A computer program for the analysis of multinomial processing tree models

Multinomial processing tree (MPT) models are a family of stochastic models for psychology and related sciences that can be used to model observed categorical frequencies as a function of a sequence of latent states. For the analysis of such models, the present article presents a platform-independent computer program called multiTree, which simplifies the creation and the analysis of MPT models. This makes them more convenient to implement and analyze. Also, multiTree offers advanced modeling features. It provides estimates of the parameters and their variability, goodness-of-fit statistics, hypothesis testing, checks for identifiability, parametric and nonparametric bootstrapping, and power analyses. In this article, the algorithms underlying multiTree are given, and a user guide is provided. The multiTree program can be downloaded from http://psycho3.uni-mannheim.de/multitree.     

Parameter identification in multinomial processing tree models

Multinomial processing tree models form a popular class of statistical models for categorical data that have applications in various areas of psychological research. As in all statistical models, establishing which parameters are identified is necessary for model inference and selection on the basis of the likelihood function, and for the interpretation of the results. The required calculations to establish global identification can become intractable in complex models. We show how to establish local identification in multinomial processing tree models, based on formal methods independently proposed by Catchpole and Morgan (1997) and by Bekker, Merckens, and Wansbeek (1994). This approach is illustrated with multinomial processing tree models for the source-monitoring paradigm in memory research.     

MPT模型在事件性前瞻记忆研究中的应用

前瞻性记忆是指对将要进行的活动或事件的记忆。前瞻记忆中,包含了前瞻成分和回溯成分。前人研究中,缺乏对前瞻成分和回溯成分有效的分离手段,使得对前瞻记忆机制的探讨缺乏深入挖掘。本文将MPT模型与Cohen等人的研究范式对比,分析了该模型在事件性前瞻记忆研究中的优势。文章对模型的理论基础,模型的主要内容,模型的数据计算方法,模型的效度以及模型的应用等几个方面进行了介绍,同时对模型使用中需要注意的问题进行了讨论。