Multinomial Processing Tree Models Research Articles

Model selection by minimum description length: Lower-bound sample sizes for the Fisher information approximation

The Fisher information approximation (FIA) is an implementation of the minimum description length principle for model selection. Unlike information criteria such as AIC or BIC, it has the advantage of taking the functional form of a model into account. Unfortunately, FIA can be misleading in finite samples, resulting in an inversion of the correct rank order of complexity terms for competing models in the worst case. As a remedy, we propose a lower-bound N′ for the sample size that suffices to preclude such errors. We illustrate the approach using three examples from the family of multinomial processing tree models.

Analyzing stochastic dependence of cognitive processes in multidimensional source recognition.

Stochastic dependence among cognitive processes can be modeled in different ways, and the family of multinomial processing tree models provides a flexible framework for analyzing stochastic dependence among discrete cognitive states. This article presents a multinomial model of multidimensional source recognition that specifies stochastic dependence by a parameter for the joint retrieval of multiple source attributes together with parameters for stochastically independent retrieval. The new model is equivalent to a previous multinomial model of multidimensional source memory for a subset of the parameter space. An empirical application illustrates the advantages of the new multinomial model of joint source recognition. The new model allows for a direct comparison of joint source retrieval across conditions, it avoids statistical problems due to inflated confidence intervals and does not imply a conceptual imbalance between source dimensions. Model selection criteria that take model complexity into account corroborate the new model of joint source recognition.

The impact of subjective recognition experiences on recognition heuristic use: A multinomial processing tree approach

The recognition heuristic (RH) theory states that, in comparative judgments (e.g., Which of two cities has more inhabitants?), individuals infer that recognized objects score higher on the criterion (e.g., population) than unrecognized objects. Indeed, it has often been shown that recognized options are judged to outscore unrecognized ones (e.g., recognized cities are judged as larger than unrecognized ones), although different accounts of this general finding have been proposed. According to the RH theory, this pattern occurs because the binary recognition judgment determines the inference and no other information will reverse this. An alternative account posits that recognized objects are chosen because knowledge beyond mere recognition typically points to the recognized object. A third account can be derived from the memory-state heuristic framework. According to this framework, underlying memory states of objects (rather than recognition judgments) determine the extent of RH use: When two objects are compared, the one associated with a “higher” memory state is preferred, and reliance on recognition increases with the “distance” between their memory states. The three accounts make different predictions about the impact of subjective recognition experiences—whether an object is merely recognized or recognized with further knowledge—on RH use. We estimated RH use for different recognition experiences across 16 published data sets, using a multinomial processing tree model. Results supported the memory-state heuristic in showing that RH use increases when recognition is accompanied by further knowledge.Electronic supplementary materialThe online version of this article (doi:10.3758/s13423-014-0587-4) contains supplementary material, which is available to authorized users.

Bayesian Estimation of Multinomial Processing Tree Models with Heterogeneity in Participants and Items

Multinomial processing tree (MPT) models are theoretically motivated stochastic models for the analysis of categorical data. Here we focus on a crossed-random effects extension of the Bayesian latent-trait pair-clustering MPT model. Our approach assumes that participant and item effects combine additively on the probit scale and postulates (multivariate) normal distributions for the random effects. We provide a WinBUGS implementation of the crossed-random effects pair-clustering model and an application to novel experimental data. The present approach may be adapted to handle other MPT models.

The Class Stereotype-Driven False Memories in a Source Monitoring Framework

Class stereotypes are simplistic generalizations about attributes, differences of the social class, and about roles of individuals and/or groups. Stereotypes provide perceives a basis to generate inferences about unseen orunobserved aspects of a stereotypic schema, enabling them to make conjectures beyond the information given. Multinomial Processing Tree Models(MPT) are theories about the decision processes that were involved in source monitoring and can provide separate parameters for source discrimination, item detection, and response biases. It has been suggested by stereotype studies in a framework of source monitoring that stereotypes provided after encoding and before test, might produce a response bias in favor of the stereotype. This bias can distort memory representations of earlier events, resulting in false memories. Previous studies suggested that participants may resort to guess based on their stereotypes knowledge in situations when they cannot remember the source in a source-monitoring task(Bayen, Nakamura, Dupuis, Yang, 2000). According to this guessing hypothesis, if stereotypes are activated during retrieval in an explicit way, participants are prone to consciously make use of stereotypes knowledge and to guess the source in a stereotype consistent manner, particularly when they fail to remember the actual source. However, recent research has provided mixed evidence. By controlling the guessing, other researchers still found that participants create illusory recollections when stereotypes are activated during retrieval in an explicit way(Dodson, Darragh, Williams, 2008). So an intriguing question is: If guessing plays a critical role in creating false memories, what other factors should be responsible for false memories after controlling guessing? In this study, MPT were used for the measurement of cognitive processes in two source monitoring experiments. Sixty-six college students of normal vision, twenty-six in Experiment 1 and forty in Experiment 2, were enrolled to participate. The purpose of Experiment 1 was to determine how stereotypes influence source-monitoring decision processes when the class stereotypes are subliminally primed during retrieval. The results showed that when the subliminally primed class stereotype is provided during retrieval, participants' memory performance was distorted in a stereotype consistent manner, presumably through guessing responses. Particularly, the automatically activated class stereotypes affect source guessing process, thus producing false memories. In Experiment 2, explicit warning was provided to reduce false memory. We aimed to investigate how stereotypes influence decision processes of source monitoring, when the class stereotypes are explicitly primed during retrieval. Our results demonstrated that participants showed similar stereotype-induced false memories even after the stereotypes guessing at conscious level was controlled. Although it was difficult to fully control the stereotypes guessing at unconscious level, the explicit warning could lower the rate of false recall. Thus, the unconscious stereotypes guessing and illusory recollections might be the basis for false memories in a stereotype consistent manner. To sum up, the present study indicated that class stereotypes can affect source memory under different conditions in a flexible way. The activation of class stereotypes, in a source monitoring framework, affects not only guessing processes but also illusory recollections, both of which provide a potential basis for erroneous source attributions.

Reformulating Markovian processes for learning and memory from a hazard function framework

With the development of stimulus sampling theory (SST), William K. Estes demonstrated the importance of Markov chains for capturing many important features of learning. In this paper, learning and memory retention are reexamined from a hazard function framework and linked to the stochastic transition matrices of a Markov model. The probabilities in the transition matrix are shown to be discrete hazard values. In order for the stochastic matrix to be a homogeneous Markov chain, there is a requirement that the transition matrix values remain constant. Yet for some learning and memory retention applications, there is evidence that the transition matrix probabilities are dynamically changing. For list learning, the change in hazard is attributed in part to differences in the learning rate of individual items within the list. Even on an individual basis, any variability in item difficulty whatsoever is enough to induce a change in hazard with training. Another analysis was done to delineate the hazard function for memory loss. Evidence is again provided that the hazard associated with the loss of memory is systematically changing. A Markov chain is not a suitable model when there are dynamic changes in the hazard. However, for both the learning and memory applications, a general Markovian model can be used, where transition probabilities are a function of trial number or interpolated event number. Finally, a more complex, four-state application is considered. This application is based on the Chechile, Sloboda, and Chamberland (2012) multinomial processing tree model called the IES model. The IES model obtains probability estimates for the representation of target information in memory in terms of four possible states—explicit memory, implicit memory, fractional memory, and non-storage. Stochastic matrices for the IES model are provided and are shown to yield new insights about implicit memory.

The Development of Episodic Memory

Episodic memory involves the formation of relational structures that bind information about the stimuli people experience to the contexts in which they experience them. The ability to form and retain such structures may be at the core of the development of episodic memory. In the first experiment reported here, 4- and 7-year-olds were presented with paired-associate learning tasks requiring memory structures of different complexity. A multinomial-processing tree model was applied to estimate the use of different structures in the two age groups. The use of two-way list-context-to-target structures and three-way structures was found to increase between the ages of 4 and 7. Experiment 2 demonstrated that the ability to form increasingly complex relational memory structures develops between the ages of 4 and 7 years and that this development extends well into adulthood. These results have important implications for theories of memory development.

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.

Effort reduction after self-control depletion: The role of cognitive resources in use of simple heuristics

Heuristics have been described as decision strategies that save time and effort. Given this advantageous property, heuristics should be more often used when cognitive resources are scarce. We tested this general view with respect to the fast and frugal recognition heuristic which assumes one-reason decision making based on recognition alone whenever one object in a paired comparison is recognised and the other is not. In an experiment, we manipulated cognitive resources through an executive control procedure previously used in ego-depletion research. From the choice frequencies, the probability of using the recognition heuristic was estimated by means of a multinomial processing tree model. Results confirmed that use of the recognition heuristic was indeed more likely under depleted resources and thus limited cognitive capacity. These findings corroborate the general notion that a need for effort reduction fosters use of simple decision heuristics.

Contingency Table Automatic Data Mining Based on Multinomial Model

This paper presented an automatic data mining method of multinomial model list to solve the problem of losing the information of tabular data in data mining. On the basis of the location of the vantage point in the original table, the introduction of MPT model and the structure of the algorithm, this paper proceeded an automatic tree model fitting and clustering grouping to the original data, then used some correlation theory about multinomial processing tree model to generate a set of hypothesized relationships to be elected , and finally completed the estimation of parameter and the goodness-of-fit test. The example showed that the algorithm is more effective and accurate in extracting the missing information and specific rules of tabular data mining.

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/ .

Inferring the biggest and best: A measurement model for applying recognition to evoke consideration sets and judge between multiple alternatives

It has long been supposed that preference judgments between sets of to-be-considered possibilities are made by means of initially winnowing down the most promising-looking alternatives to form smaller “consideration sets” (Howard, 1963; Wright & Barbour, 1977). In preference choices with >2 options, it is standard to assume that a “consideration set”, based upon some simple criterion, is established to reduce the options available. Inferential judgments, in contrast, have more frequently been investigated in situations in which only two possibilities need to be considered (e.g., which of these two cities is the larger?) Proponents of the “fast and frugal” approach to decision-making suggest that such judgments are also made on the basis of limited, simple criteria. For example, if only one of two cities is recognized and the task is to judge which city has the larger population, the recognition heuristic states that the recognized city should be selected. A multinomial processing tree model is outlined which provides the basis for estimating the extent to which recognition is used as a criterion in establishing a consideration set for inferential judgments between three possible options.

Discrete-state models: Comment on Pazzaglia, Dube, and Rotello (2013).

Pazzaglia, Dube, and Rotello (2013) have provided a lengthy critique of threshold and continuous models of recognition memory. Although the early pages of their article focus mostly on the problems they see with 3 vintage threshold models compared with models from signal detection theory (SDT), it becomes clear rather quickly that Pazzaglia et al. are concerned more generally with problems they see with multinomial processing tree (MPT) models. First, we focus on Pazzaglia et al.'s discussion of the evidence concerning receiver operating characteristics (ROCs) in simple recognition memory, then we consider problems they raise with a subclass of MPT models for more complex recognition memory paradigms, and finally we discuss the difference between scientific models and measurement models in the context of MPT and SDT models in general. We argue that Pazzaglia et al. have not adequately considered the evidence relevant to the viability of the simple threshold models and that they have not adequately represented the issues concerning validating a cognitive measurement model. We further argue that selective influence studies and model flexibility studies are as important as studies showing that a model can fit behavioral data. In particular, we note that despite over a half century of effort, no generally accepted scientific theory of recognition memory has emerged and that it is unlikely to ever emerge with studies using standard behavioral measures. Instead, we assert that useful measurement models of both the SDT and the MPT type have been and should continue to be developed.

Estimating the contributions of associations and recoding in the Implicit Association Test: The ReAL model for the IAT.

We introduce the ReAL model for the Implicit Association Test (IAT), a multinomial processing tree model that allows one to mathematically separate the contributions of attitude-based evaluative associations and recoding processes in a specific IAT. The ReAL model explains the observed pattern of erroneous and correct responses in the IAT via 3 underlying processes: recoding of target and attribute categories into a binary representation in the compatible block (Re), evaluative associations of the target categories (A), and label-based identification of the response that is assigned to the respective nominal category (L). In 7 validation studies, using an adaptive response deadline procedure in order to increase the amount of erroneous responses in the IAT, we demonstrated that the ReAL model fits IAT data and that the model parameters vary independently in response to corresponding experimental manipulations. Further studies yielded evidence for the specific predictive validity of the model parameters in the domain of consumer behavior. The ReAL model allows one to disentangle different sources of IAT effects where global effect measures based on response times lead to equivocal interpretations. Possible applications and implications for future IAT research are discussed.

A critical comparison of discrete-state and continuous models of recognition memory: Implications for recognition and beyond.

Multinomial processing tree (MPT) models such as the single high-threshold, double high-threshold, and low-threshold models are discrete-state decision models that map internal cognitive events onto overt responses. The apparent benefit of these models is that they provide independent measures of accuracy and response bias, a claim that has motivated their frequent application in many areas of psychological science including perception, item and source memory, social cognition, reasoning, educational testing, eyewitness testimony, and psychopathology. Before appropriate conclusions about a given analysis can be drawn, however, one must first confirm that the model's assumptions about the underlying structure of the data are valid. The current review outlines the assumptions of several popular MPT models and assesses their validity using multiple sources of evidence, including receiver operating characteristics, direct model fits, and experimental tests of qualitative predictions. We argue that the majority of the evidence is inconsistent with these models and that, instead, the evidence supports continuous models such as those based on signal detection theory (SDT). Hybrid models that incorporate both SDT and MPT processes are also explored, and we conclude that these models retain the limitations associated with their threshold model predecessors. The potentially severe consequences associated with using an invalid model to interpret data are discussed, and a simple tutorial and model-fitting tool is provided to allow implementation of the empirically supported SDT model.

The statistical accuracy and theoretical status of discrete-state MPT models: Reply to Batchelder and Alexander (2013).

In "A Critical Comparison of Discrete-State and Continuous Models of Recognition Memory: Implications for Recognition and Beyond," Pazzaglia, Dube, and Rotello (2013) explored the threshold multinomial processing tree (MPT) framework as applied to several domains of experimental psychology. Pazzaglia et al. concluded that threshold MPT analyses require assumptions at the representation and measurement levels that are contradicted by existing data in several domains. Furthermore, they showed that this flaw in the threshold MPT framework produces systematic errors in data interpretation. Pazzaglia et al. suggested measures derived from the empirically validated unequal-variance signal detection theory framework as a viable alternative and provided a simple tutorial for implementing such measures in an Excel spreadsheet. In their reply, Batchelder and Alexander (2013) disputed the conclusions advanced by Pazzaglia et al. Their arguments consisted of a small number of strong assertions, some of which were accompanied by references and/or data. In this reply, we demonstrate that both types of assertions--those with and without supporting references and/or data--are, at best, contradicted by several existing studies (many of which were already discussed in Pazzaglia et al., 2013) and, at worst, patently false. We conclude that the conclusions of Pazzaglia et al. are valid.

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.

Beyond ROC curvature: Strength effects and response time data support continuous-evidence models of recognition memory

A classic question in the recognition memory literature is whether retrieval is best described as a continuous-evidence process consistent with signal detection theory (SDT), or a threshold process consistent with many multinomial processing tree (MPT) models. Because receiver operating characteristics (ROCs) based on confidence ratings are typically curved as predicted by SDT, this model has been preferred in many studies of recognition memory (Wixted, 2007). Recently, Bröder and Schütz (2009) argued that curvature in ratings ROCs may be produced by variability in scale usage; therefore, ratings ROCs are not diagnostic in deciding between the two approaches. From this standpoint, only ROCs constructed via experimental manipulations of response bias (‘binary’ ROCs) are predicted to be linear by threshold MPT models. The authors claimed that binary ROCs are linear, consistent with the assumptions of threshold MPT models. We compared SDT and the double high-threshold MPT model using binary ROCs differing in target strength. Results showed that the SDT model provided a superior account of both the ROC curvature and the effect of strength compared to the MPT model. Moreover, the bias manipulation produced differences in RT distributions that were well described by the diffusion model (Ratcliff, 1978), a dynamic version of SDT.

Differential Patterns of Planning Impairments in Parkinson's Disease and Sub-Clinical Signs of Dementia? A Latent-Class Model-Based Approach

Planning impairments mark a well-documented consequence of neurodegenerative diseases such as Parkinson's disease (PD). Recently, using the Tower of London task we demonstrated that, rather than being generally impaired, PD patients selectively fail when planning requires flexible in-breadth search strategies. For a better understanding of the interindividual patterns underlying specific planning impairments, here we performed an explorative re-analysis of the original data using a latent-class model-based approach. Data-driven classification according to subjects' performance was based on a multinomial processing tree (MPT) model accommodating the impact of increased breadth versus depth of looking ahead during planning. In order to assess interindividual variability in coping with these different task demands, an extension of MPT models was used in which sample-immanent heterogeneity is accounted for by identifying different latent classes of individuals. Two latent classes were identified that differed considerably in performance for problems placing high demands on the depth of anticipatory search processes. In addition, these impairments were independent of PD diagnosis. However, latent-class mediated search depth-related deficits in planning performance were associated with poorer outcomes in dementia screenings, albeit sub-clinical. PD patients exhibited additional deficits related to the breadth of searching ahead. Taken together, results revealed dissociable impairments in specific planning processes within a single task of visuospatial problem solving. Present analyses put forward the hypothesis that cognitive sequelae of PD and sub-clinical signs of dementia may be related to differential patterns of planning impairments.

Prospective memory after moderate-to-severe traumatic brain injury: a multinomial modeling approach.

Prospective memory (PM), which can be understood as the processes involved in realizing a delayed intention, is consistently found to be impaired after a traumatic brain injury (TBI). Although PM can be empirically dissociated from retrospective memory, it inherently involves both a prospective component (i.e., remembering that an action needs to be carried out) and retrospective components (i.e., remembering what action needs to be executed and when). This study utilized a multinomial processing tree model to disentangle the prospective (that) and retrospective recognition (when) components underlying PM after moderate-to-severe TBI. Seventeen participants with moderate to severe TBI and 17 age- and education-matched control participants completed an event-based PM task that was embedded within an ongoing computer-based color-matching task. The multinomial processing tree modeling approach revealed a significant group difference in the prospective component, indicating that the control participants allocated greater preparatory attentional resources to the PM task compared to the TBI participants. Participants in the TBI group were also found to be significantly more impaired than controls in the when aspect of the retrospective component. These findings indicated that the TBI participants had greater difficulty allocating the necessary preparatory attentional resources to the PM task and greater difficulty discriminating between PM targets and nontargets during task execution, despite demonstrating intact posttest recall and/or recognition of the PM tasks and targets.