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, Yina M. Quique
Seminars in Speech and Language, Volume 42, pp 240-255; https://doi.org/10.1055/s-0041-1727251

Abstract:
People with aphasia demonstrate language impairments evident in both performance accuracy and processing speed, but the direct relationship between accuracy and speed requires further consideration. This article describes two recent attempts to make quantitative progress in this domain using response time modeling: the diffusion model (Ratcliff, 1978) applied to two-choice tasks and a multinomial ex-Gaussian model applied to picture naming. The diffusion model may be used to characterize core linguistic processing efficiency and speed–accuracy tradeoffs independently, and research suggests that maladaptive speed–accuracy tradeoffs lead to performance impairments in at least some people with aphasia. The multinomial ex-Gaussian response time model of picture naming provides a simple and straightforward way to estimate the optimal response time cutoffs for individual people with aphasia (i.e., the cutoff where additional time is unlikely to lead to a correct response). While response time modeling applied to aphasia research is at an early stage of development, both the diffusion model and multinomial ex-Gaussian response time model of picture naming show promise and should be further developed in future work. This article also provides preliminary recommendations for clinicians regarding how to conceptualize, identify, and potentially address maladaptive speed–accuracy tradeoffs for people with aphasia.
Published: 21 February 2021
Abstract:
Recent results have challenged the widespread assumption of dual process models of belief bias that sound reasoning relies on slow, careful reflection, whereas biased reasoning is based on fast intuition. Instead, parallel process models of reasoning suggest that rule- and belief-based problem features are processed in parallel and that reasoning problems that elicit a conflict between rule- and belief-based problem features may also elicit more than one Type 1 response. This has important implications for individual-differences research on reasoning, because rule-based responses by certain individuals may reflect that these individuals were either more likely to give a rule-based default response or that they successfully inhibited and overrode a belief-based default response. In two studies, we used the diffusion model to describe decision making in a transitive reasoning task. In Study 1, 41 participants were asked to evaluate conclusions based on their validity. In Study 2, 133 participants evaluated conclusions based on their validity or believability. We tested which diffusion model parameters reflected conflict resolution and related those model parameters to individual differences in cognitive abilities and thinking styles. Individual differences in need for cognition predicted successful conflict resolution under logic instruction, which suggests that a disposition to engage in reflective thinking facilitates the inhibition and override of Type 1 responses. Intelligence, however, was negatively related to successful conflict resolution under belief instruction, which suggests that individuals with high cognitive abilities quickly generated a higher-level logical response that interfered with their ability to evaluate lower-level intrinsic problem features. Taken together, this double dissociation indicates that cognitive abilities and thinking styles affect the processing of conflict information through different mechanisms and at different stages: Greater cognitive abilities facilitate the efficient creation of decoupled problem representations, whereas a greater disposition to engage in critical thinking facilitates the detection and override of Type 1 responses.
Marco Perugini, Birk Hagemeyer, Cornelia Wrzus, Mitja D. Back
The Handbook of Personality Dynamics and Processes pp 551-577; https://doi.org/10.1016/b978-0-12-813995-0.00020-0

Abstract:
During the last decades, dual process models concerning reflective and impulsive pathways to behavior have been applied in many psychological domains, including personality psychology. In this chapter, we review the literature on dual processes approaches and models for the conceptualization and assessment of two broad domains of personality, self-concepts and motives. We first distinguish explicit and implicit constructs as assessed with direct and indirect measures, respectively. We then focus on measures to assess implicit representations of self-concepts and motives, with special attention to reliability and validity. Some advanced issues will also be examined, specifically novel assessment methods and scoring systems for indirect measures, developmental aspects of implicit personality characteristics, and interpersonal extensions of dual process approaches to personality. To conclude, we share some reflections on controversial issues in dual-process personality research, that is the convergence (or lack thereof) among indirect measures and between indirect and direct measures and the debate on unitary versus dualistic theories.
Jimmy Calanchini
Published: 1 November 2020
Social Cognition, Volume 38; https://doi.org/10.1521/soco.2020.38.supp.s165

Abstract:
Implicit measures were developed to provide relatively pure estimates of attitudes and stereotypes, free from the influence of processes that constrain true and accurate reporting. However, implicit measures are not pure estimates of attitudes or stereotypes but, instead, reflect the joint contribution of multiple processes. The fact that responses on implicit measures reflect multiple cognitive processes complicates both their interpretation and application. In this article, I highlight contributions made to research using implicit measures by multinomial processing trees (MPTs), an analytic method that quantifies the joint contributions of multiple cognitive processes to observed responses. I provide examples of how MPTs have helped resolve mysteries that have arisen over the years, examples of findings that were initially taken at face value but were later reinterpreted by MPTs, and look to the future for ways in which MPTs seem poised to further advance research using implicit measures.
Brian A. O'shea, Reinout W. Wiers
Published: 1 November 2020
Social Cognition, Volume 38; https://doi.org/10.1521/soco.2020.38.supp.s187

Abstract:
A relative assessment of implicit biases is limited because it produces a combined summary evaluation of two attitudinal beliefs while concealing the biases driving this evaluation. Similar limitations occur for relative explicit measures. Here, we will discuss the benefits and weaknesses of using relative versus absolute (individual/separate) assessments of implicit and explicit attitudes. The Implicit Association Test (IAT) will be the focal implicit measure discussed, and we will present a new perspective challenging the evidence that the IAT can only be utilized to measure relative, not absolute, implicit attitudes. Modeling techniques (i.e., Quad models) that can determine the separate biases behind the relative summary evaluation will also be considered. Accurately utilizing absolute implicit bias scores will enable academia and industry to answer more complex research questions. For implicit social cognition to maintain and expand its usefulness, we encourage researchers to further test and refine the measurement of absolute implicit biases.
, Pritha Dhir, Xiaofang Zheng, Marie Poirier
Published: 14 August 2020
Journal of Mathematical Psychology, Volume 98; https://doi.org/10.1016/j.jmp.2020.102433

Abstract:
Use of Multinomial Processing Tree (MPT) models is illustrated by fitting one to data of Dhir (2017). Her experiment examined age and association type in a paired-associate recall task. Age and Pair-Type had interactive effects on probability of a correct response. A natural interpretation of the interaction would be that both factors impact the same mental process. However, fitting an MPT leads to the conclusion that Age and Pair-Type selectively influence two separate processes, one following the other. A possible interpretation of these is as attempts at specific (verbatim) retrieval and knowledge supported (gist) processing, selectively influenced by Age and Pair-Type, respectively. The order of these processes is not determined by the response probabilities. In a further section of the paper, we show that if response times or other measures had also been available, they could have resolved the process order, but might have left it undetermined. We give necessary and sufficient conditions for two factors to selectively influence two ordered vertices in an MPT, with either order of the vertices accounting for both response probability and response time. They do so if and only if the MPT is equivalent to a special processing tree, not necessarily an MPT itself.
, Lea Johannsen, Karl Christoph Klauer
Published: 6 May 2020
Behavior Research Methods, Volume 52, pp 1313-1338; https://doi.org/10.3758/s13428-019-01318-x

Abstract:
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.
, Karl Christoph Klauer
Journal of Mathematical Psychology, Volume 96; https://doi.org/10.1016/j.jmp.2020.102340

Abstract:
The response-time extended multinomial processing tree (RT-MPT; Klauer and Kellen, 2018) model class and its implementation (rtmpt; Hartmann et al., in press) in the programming language R enable one to estimate process-completion times and encoding plus motor-execution times along with the process probabilities of traditional multinomial processing tree (MPT) models via an MCMC algorithm in a hierarchical Bayesian framework. This implementation is, however, restricted to RT-MPT models without process repetition in any of the model’s processing paths, implying that models such as the pair-clustering model (Batchelder and Riefer, 1980, 1986) cannot be fitted. Here, we develop a new MCMC algorithm that overcomes this restriction. Furthermore, we validate the algorithm, and demonstrate its usefulness on a dataset from recognition-memory research.
Journal of Mathematical Psychology, Volume 96; https://doi.org/10.1016/j.jmp.2020.102329

Abstract:
Knowledge Space Theory (KST) aims at modeling the hierarchical relations between items or skills in a learning process. For example, when studying mathematics in school, students first need to master the rules of summation before being able to learn multiplication. In KST, the knowledge states of individuals are represented by means of partially ordered latent classes. In probabilistic KST models, conditional probability parameters are introduced to model transitions from latent knowledge states to observed response patterns. Since these models account for discrete data by assuming a finite number of latent states, they can be represented by Multinomial Processing Tree (MPT) models (i.e., binary decision trees with parameters referring to the conditional probabilities of entering different states). We prove that standard probabilistic models of KST such as the Basic Local Independence Model (BLIM) and the Simple Learning Model (SLM) can be represented as specific instances of MPT models. Given this close link, MPT methods may be applied to address theoretical and practical issues in KST. By highlighting the MPT–KST link and its implications for modeling violations of local stochastic independence in Item Response Theory (IRT), we hope to facilitate an exchange of theoretical results, statistical methods, and software across these different domains of mathematical psychology and psychometrics.
William S. Evans, William D. Hula, Yina Quique, Jeffrey J. Starns
Journal of Speech, Language, and Hearing Research, Volume 63, pp 599-614; https://doi.org/10.1044/2019_jslhr-19-00255

Abstract:
Purpose Aphasia is a language disorder caused by acquired brain injury, which generally involves difficulty naming objects. Naming ability is assessed by measuring picture naming, and models of naming performance have mostly focused on accuracy and excluded valuable response time (RT) information. Previous approaches have therefore ignored the issue of processing efficiency, defined here in terms of optimal RT cutoff, that is, the shortest deadline at which individual people with aphasia produce their best possible naming accuracy performance. The goals of this study were therefore to (a) develop a novel model of aphasia picture naming that could accurately account for RT distributions across response types; (b) use this model to estimate the optimal RT cutoff for individual people with aphasia; and (c) explore the relationships between optimal RT cutoff, accuracy, naming ability, and aphasia severity. Method A total of 4,021 naming trials across 10 people with aphasia were scored for accuracy and RT onset. Data were fit using a novel ex-Gaussian multinomial RT model, which was then used to characterize individual optimal RT cutoffs. Results Overall, the model fitted the empirical data well and provided reliable individual estimates of optimal RT cutoff in picture naming. Optimal cutoffs ranged between approximately 5 and 10 s, which has important implications for assessment and treatment. There was no direct relationship between aphasia severity, naming RT, and optimal RT cutoff. Conclusion The multinomial ex-Gaussian modeling approach appears to be a promising and straightforward way to estimate optimal RT cutoffs in picture naming in aphasia. Limitations and future directions are discussed.
Published: 12 February 2020
Psychonomic Bulletin & Review, Volume 27, pp 571-580; https://doi.org/10.3758/s13423-019-01663-0

Abstract:
In his comment on Heck and Erdfelder (2016, Psychonomic Bulletin & Review, 23, 1440-1465), Starns (2018, Psychonomic Bulletin & Review, 25, 2406-2416) focuses on the response time-extended two-high-threshold (2HT-RT) model for yes-no recognition tasks, a specific example for the general class of response time-extended multinomial processing tree models (MPT-RTs) we proposed. He argues that the 2HT-RT model cannot accommodate the speed-accuracy trade-off, a key mechanism in speeded recognition tasks. As a remedy, he proposes a specific discrete-state model for recognition memory that assumes a race mechanism for detection and guessing. In this reply, we clarify our motivation for using the 2HT-RT model as an example and highlight the importance and benefits of MPT-RTs as a flexible class of general-purpose, simple-to-use models. By binning RTs into discrete categories, the MPT-RT approach facilitates the joint modeling of discrete responses and response times in a variety of psychological paradigms. In fact, many paradigms either lack a clear-cut accuracy criterion or show performance levels at ceiling, making corrections for incautious responding redundant. Moreover, we show that some forms of speed-accuracy trade-off can in fact not only be accommodated but also be measured by appropriately designed MPT-RTs.
, K. Nakamura, Y.A. Murtaza
Published: 9 February 2020
Journal of Memory and Language, Volume 112; https://doi.org/10.1016/j.jml.2020.104105

Abstract:
Complementarity is a paradoxical phenomenon in which memory for incompatible reality states (e.g., old vs. new) violates basic logical constraints: Subjects remember certain groups of items as belonging to both of two incompatible states at reliable levels. The theoretical principle that predicts this phenomenon, non-compensatory gist memory, also predicts a more stringent form in which individual items are successively remembered as belonging to each of two incompatible states. In the present experiments, we investigated this within-item form of complementarity and evaluated an alternative theoretical explanation that relies on a selective retrieval principle. The experiments provided evidence of robust within-item complementarity, for both old items and new items that were semantically related to old ones. Logical incompatibility constrained memory for different reality states to only a limited degree. Our experiments provided no support for the selective retrieval explanation of complementarity. That account predicts several effects, some for judgment probabilities and others for latencies, none of which was observed. Thus, non-compensatory gist memory proved to be the more satisfactory of the two explanations.
, Sophie Scharf
Journal of Experimental Social Psychology, Volume 87; https://doi.org/10.1016/j.jesp.2019.103917

Abstract:
The goal of this study was to understand the cognitive dynamics of stereotype influences on source monitoring employing mouse tracking. By continuously recording cursor movements, we examined how stereotypical knowledge influences decision uncertainty when processing and later remembering stereotype-consistent and -inconsistent exemplars of the age categories of “young” and “old”. In a source-monitoring task, participants (N = 60) learned age-stereotype consistent or -inconsistent statements from two different-aged sources (young vs. old person) that they attributed to their original sources via mouse clicks in a later memory test. Our results showed that individuals experienced cognitive conflict during source attributions depending on both the correctness of the source response and whether the original source was (in)consistent with the stereotype of the respective age group reflected in the statement. This pattern of results was supplemented by the analysis of prototypical mouse-trajectory clusters. Modeling individual source-monitoring processes revealed that individuals' experienced conflict was less pronounced when they remembered the source and was unrelated to guessing resulting from memory failure. These results highlight the benefits of combining cognitive modeling and process-tracing techniques to unpack the mechanisms behind social influences on source monitoring. The methodology of mouse tracking illuminated the role of stereotypes in the underlying cognitive processes during source attributions that is not evident from discrete categorical responses. For designed counter-stereotypical interventions, process-tracing methods may also be used to test their effectiveness on cognitive processes involved in source monitoring.
, Laura Anne Grigutsch, Nicolas Koranyi, Florian Müller, Klaus Rothermund
Published: 8 November 2019
Frontiers in Psychology, Volume 10; https://doi.org/10.3389/fpsyg.2019.02483

Abstract:
Two decades ago, the introduction of the Implicit Association Test (IAT) sparked enthusiastic reactions. With implicit measures like the IAT, researchers hoped to finally be able to bridge the gap between self-reported attitudes on one hand and behavior on the other. Twenty years of research and several meta-analyses later, however, we have to conclude that neither the IAT nor its derivatives have fulfilled these expectations. Their predictive value for behavioral criteria is weak and their incremental validity over and above self-report measures is negligible. In our review, we present an overview of explanations for these unsatisfactory findings and delineate promising ways forward. Over the years, several reasons for the IAT’s weak predictive validity have been proposed. They point to four potentially problematic features: First, the IAT is by no means a pure measure of individual differences in associations but suffers from extraneous influences like recoding. Hence, the predictive validity of IAT-scores should not be confused with the predictive validity of associations. Second, with the IAT, we usually aim to measure evaluation (“liking”) instead of motivation (“wanting”). Yet, behavior might be determined much more often by the latter than the former. Third, the IAT focuses on measuring associations instead of propositional beliefs and thus taps into a construct that might be too unspecific to account for behavior. Finally, studies on predictive validity are often characterized by a mismatch between predictor and criterion (e.g., while behavior is highly context-specific, the IAT usually takes into account neither the situation nor the domain). Recent research, however, also revealed advances addressing each of these problems, namely (1) procedural and analytical advances to control for recoding in the IAT, (2) measurement procedures to assess implicit wanting, (3) measurement procedures to assess implicit beliefs, and (4) approaches to increase the fit between implicit measures and behavioral criteria (e.g., by incorporating contextual information). Implicit measures like the IAT hold an enormous potential. In order to allow them to fulfill this potential, however, we have to refine our understanding of these measures, and we should incorporate recent conceptual and methodological advancements. This review provides specific recommendations on how to do so.
Published: 18 October 2019
Journal of Mathematical Psychology, Volume 93; https://doi.org/10.1016/j.jmp.2019.102281

Abstract:
If the survival function of a random variable X lies to the right of the survival function of a random variable Y, then X is said to stochastically dominate Y. Inferring stochastic dominance is particularly complicated because comparing survival functions raises four possible hypotheses: identical survival functions, dominance of X over Y, dominance of Y over X, or crossing survival functions. In this paper, we suggest four-decision tests for stochastic dominance suitable for paired samples. The tests are permutation-based and do not rely on distributional assumptions. One-sided Cramér–von Mises and Kolmogorov–Smirnov statistics are employed but the general idea may be utilized with other test statistics. The power to detect dominance and the different types of wrong decisions are investigated in an extensive simulation study. The proposed tests are applied to data from an experiment concerning the individual’s willingness to pay for a given environmental improvement.
, Xiaofang Zheng
Journal of Mathematical Psychology, Volume 91, pp 51-69; https://doi.org/10.1016/j.jmp.2019.02.004

Abstract:
Multinomial Processing Trees are widely used in Psychology to model probabilities of responses in classes such as correct and incorrect. Some models include an additional measure such as response time, but predictions can become complex. Here we develop testable predictions using a method traditional for response times: manipulating experimental factors that selectively influence processes. In a Multinomial Processing Tree, each vertex represents a process, such as memory retrieval. An arc descending from a vertex represents a possible process outcome; for example, success or failure. Each arc has associated with it the probability the outcome it represents will occur. We assume that also associated with each arc is the time required for the outcome to occur. A factor that changes parameter values on arcs descending from a single vertex selectively influences that vertex. Suppose each of two factors selectively influences a different vertex in a Multinomial Processing Tree. There are only two ways the two vertices can be arranged. Either there is a path from one vertex to the other, and parameters on some arc on this path are changed by a factor, or there is not. Here we consider two Multinomial Processing Trees, important representatives of the two vertex arrangements. For each we develop testable necessary and sufficient conditions. Parameter values in the Multinomial Processing Trees may not be unique. If two sets of parameter values both lead to the same predictions, the values are related by admissible transformations, which we derive along with degrees of freedom.
, Xiaofang Zheng
Journal of Mathematical Psychology, Volume 92; https://doi.org/10.1016/j.jmp.2019.02.005

Abstract:
In many experiments a person performs a task, such as identifying a letter, and an experimental factor, such as brightness, is manipulated. Empirically, changing the level of a factor often produces a relation, stochastic dominance, on the response time cumulative distribution functions. Specifically, for levels 1 and 2 of the factor, let H1(t) and H2(t) be the cumulative distribution functions of the correct response time. Then one often finds that for all times t, H1(t) > H2(t). We consider a Multinomial Processing Tree in which arcs have a probability of being selected and require time to be selected. It is natural to consider the effect of a factor on products of probability and time. At levels 1 and 2 of the factor, let π(1) and π(2) be the probability of a correct response. The factor produces weighted stochastic dominance if π(1)H1(t) > π(2)H2(t) for all times t. An experimental factor selectively influences a vertex in a Multinomial Processing Tree if changing the level of the factor changes parameters at a single vertex, leaving all else invariant. We consider conditions under which a factor selectively influencing a vertex in a Multinomial Processing Tree produces weighted stochastic dominance. Our assumptions allow parameters in a Multinomial Processing Tree to vary from trial to trial, and to be correlated through dependence on a common random variable. Further, the same Multinomial Processing Tree need not be used on every trial, there may be a mixture of Multinomial Processing Trees. We demonstrate results of theorems with a simulation.
, Xiaofang Zheng
Published: 27 December 2018
Journal of Mathematical Psychology, Volume 88, pp 58-77; https://doi.org/10.1016/j.jmp.2018.12.001

Abstract:
Multinomial Processing Trees are widely used to model response probability and sometimes to model response time and other measures. Information about the structure of a Multinomial Processing Tree can be discovered by manipulating experimental factors that selectively influence its vertices. A factor selectively influences a vertex if changing the level of the factor changes values of parameters associated with arcs descending from that vertex, leaving all else invariant. If two factors, each with a finite number of levels, selectively influence two different vertices in a Multinomial Processing Tree, an infinite number of Multinomial Processing Trees can be constructed that account for the response probability and response time. Under relatively unrestrictive assumptions, we show that all are equivalent, for these two factors, to one of two relatively simple Multinomial Processing Trees. We also show that if response probabilities and response times are produced by averaging over a mixture of different trees, the mixture is equivalent to one of the two relatively simple trees.
, Eric-Jan Wagenmakers, , Dora Matzke
Published: 27 November 2018
Psychometrika, Volume 84, pp 261-284; https://doi.org/10.1007/s11336-018-9648-3

Abstract:
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.
Published: 12 November 2018
Psychology of Learning and Motivation pp 39-65; https://doi.org/10.1016/bs.plm.2018.09.002

Abstract:
Cognitive and social psychologists have long investigated dual-process theories of automaticity and control. These theories seek to explain and predict the conditions under which people can intentionally control their judgments and behavior in the face of impulses produced by biasing and distracting incidental stimuli. Based on this dual-process perspective, cognitive and social psychologists have developed tasks that create conditions under which impulses act in parallel or in opposition to control-oriented processes—commonly referred to as response conflict tasks. Though the response conflict tasks used by cognitive and social psychologists are often structurally similar, researchers from the two disciplines often interpret performance on such tasks in very different ways: Cognitive psychologists tend to focus on the contributions of control-oriented processes, whereas social psychologists generally focus on the contributions of activated mental associations. Both of these interpretations rest on assumptions of process purity: that a response conflict task reflects either control-oriented processes or mental associations. However, this assumption is untenable. Both types of mental processes jointly influence behavioral responses on most response conflict tasks. Multinomial processing tree models are well suited to assess the contributions of multiple cognitive processes to response conflict tasks commonly used in cognitive and social psychology. In this chapter, we review the applications of multinomial processing trees to response conflict tasks, and highlight their utility in bridging interpretive divides that separate cognitive and social psychologists.
Published: 23 October 2018
Journal of Memory and Language, Volume 104, pp 83-107; https://doi.org/10.1016/j.jml.2018.09.001

Abstract:
The question of whether recognition performance should be analyzed assuming continuous memory strength or discrete memory states has been bothering researchers for decades. Continuous-strength models (signal-detection theory) assume that memory strength varies according to Gaussian distributions, leading to graded memory-strength values. In contrast, discrete-state models (threshold theory) are formally equivalent to continuous-strength models with rectangular distributions, giving rise to detection and guessing states. Despite these different core properties, the models fits to empirical data are often highly positively correlated, and the form of empirical receiver-operating characteristics (ROCs) supports neither of the rival models conclusively. In an attempt to reconcile opposing model properties and inconclusive empirical findings, we propose that memory distributions may be Gaussian but sometimes deviate more or less in the direction of rectangular distributions. In a series of three experiments, the shape of memory distributions in individual recognition data is explored using a signal-detection model with Tukey-lambda distributions. This family of distributions contains Gaussian and rectangular shapes as special cases, and the Tukey-lambda model—as a formal measurement tool without a psychological interpretation—allows pitting the special cases against each other. The results show that empirical memory distributions are predominantly bell-shaped or rectangular, though hybrid shapes exist. Implications for the continuous–discrete modeling debate and for the future of ROC research are discussed.
, Xiaofang Zheng
Published: 20 August 2018
Journal of Mathematical Psychology, Volume 86, pp 10-29; https://doi.org/10.1016/j.jmp.2018.07.001

Abstract:
Multinomial Processing Trees are successful models of response probabilities for many phenomena. Empirical validation is often based on manipulating an experimental factor intended to selectively influence a process represented in a Multinomial Processing Tree, to see whether the factor indeed has an effect on and only on a parameter associated with that process. Response times are rarely included, but have great potential for increasing resolution. We consider Multinomial Processing Trees in which outcomes of processes represented by vertices occur with probabilities (as usual), and also take time. For response time itself, the method of selectively influencing processes is well developed. Established tests are based on response time means and distribution functions. We modify well established tests so they can be applied to Multinomial Processing Trees in which responses fall into two classes, say, correct and incorrect. The new tests are based on response time means and distribution functions, each multiplied by response probability. If two experimental factors selectively influence two different vertices in a two class Multinomial Processing Tree, the tree is equivalent to one of two simple trees. Patterns in response probabilities and times will indicate which of the two trees accounts for the data. In one of the two trees, the selectively influenced vertices are executed in order, in the other they are not. If there are more than two response classes, each class can be tested separately. If the patterns do not occur, no Multinomial Processing Tree exists in which the two experimental factors selectively influence two different vertices. We demonstrate the method with simulated data from a two factor experiment.
Published: 24 May 2018
Psychometrika, Volume 83, pp 893-918; https://doi.org/10.1007/s11336-018-9622-0

Abstract:
Multinomial processing tree models assume that discrete cognitive states determine observed response frequencies. Generalized processing tree (GPT) models extend this conceptual framework to continuous variables such as response times, process-tracing measures, or neurophysiological variables. GPT models assume finite-mixture distributions, with weights determined by a processing tree structure, and continuous components modeled by parameterized distributions such as Gaussians with separate or shared parameters across states. We discuss identifiability, parameter estimation, model testing, a modeling syntax, and the improved precision of GPT estimates. Finally, a GPT version of the feature comparison model of semantic categorization is applied to computer-mouse trajectories.
, Chad Dubé, Matthew E. Frelinger
Published: 1 May 2018
Cognitive Psychology, Volume 102, pp 21-40; https://doi.org/10.1016/j.cogpsych.2018.01.001

Abstract:
In this report, we evaluate single-item and forced-choice recognition memory for the same items and use the resulting accuracy and reaction time data to test the predictions of discrete-state and continuous models. For the single-item trials, participants saw a word and indicated whether or not it was studied on a previous list. The forced-choice trials had one studied and one non-studied word that both appeared in the earlier single-item trials and both received the same response. Thus, forced-choice trials always had one word with a previous correct response and one with a previous error. Participants were asked to select the studied word regardless of whether they previously called both words "studied" or "not studied." The diffusion model predicts that forced-choice accuracy should be lower when the word with a previous error had a fast versus a slow single-item RT, because fast errors are associated with more compelling misleading memory retrieval. The two-high-threshold (2HT) model does not share this prediction because all errors are guesses, so error RT is not related to memory strength. A low-threshold version of the discrete state approach predicts an effect similar to the diffusion model, because errors are a mixture of responses based on misleading retrieval and guesses, and the guesses should tend to be slower. Results showed that faster single-trial errors were associated with lower forced-choice accuracy, as predicted by the diffusion and low-threshold models.
Journal of Behavioral Decision Making, Volume 31, pp 181-198; https://doi.org/10.1002/bdm.2075

Abstract:
Organisms must be capable of adapting to environmental task demands. Which cognitive processes best model the ways in which adaptation is achieved? People can behave adaptively, so many frameworks assume, because they can draw from a repertoire of decision strategies, with each strategy particularly fitting to certain environmental demands. In contrast to that multi-mechanism assumption, competing approaches posit a single decision mechanism. The juxtaposition of such single-mechanism and multi-mechanism approaches has fuelled not only much theory-building, empirical research, and methodological developments, but also many controversies. This special issue on “Strategy Selection: A Theoretical and Methodological Challenge” sheds a spotlight on those developments. The contribution of this introductory article is twofold. First, we offer a documentation of the controversy, including an outline of competing approaches. Second, this special issue and this introductory article represent adversarial collaborations among the three of us: we have modeled adaptive decision making in different ways in the past. Together, we now work on resolving the controversy and point to five guiding principles that might help to improve our models for predicting adaptive behavior. Copyright © 2018 John Wiley & Sons, Ltd.
Comment
Published: 12 March 2018
Psychonomic Bulletin & Review, Volume 25, pp 2406-2416; https://doi.org/10.3758/s13423-018-1456-3

Abstract:
Heck and Erdfelder (2016) developed a model that extends discrete-state multinomial processing tree models to response time (RT) data. Their model is an important advance, but it does not have a mechanism to produce the speed–accuracy trade-off, the bedrock empirical observation that rushed decisions are less accurate. I present a similar model, the “discrete-race” model, with a simple mechanism for the speed–accuracy trade-off. In the model, information that supports detection of the stimulus type is available for some proportion of items and unavailable for others. Both the amount of time needed for detection to succeed and the amount of time that the decision maker waits before guessing are variable from trial to trial. Responses are based on detection when it is available and has a finishing time before the guess time for that trial. In other words, the decision maker sometimes loses opportunities to respond correctly on the basis of detection by first making a guess. These lost opportunities are more common when the guess-time distribution tends to have low wait times, which decreases accuracy. I report simulations showing that the model can accurately recover parameter values and is strongly constrained by the speed–accuracy trade-offs across conditions with different levels of response caution.
Published: 1 February 2018
Journal of Mathematical Psychology, Volume 82, pp 111-130; https://doi.org/10.1016/j.jmp.2017.12.003

Abstract:
Multinomial processing tree models have been widely used for characterizing categorical responses in terms of a finite set of discrete latent states, and a number of processes arranged serially in a processing tree. We extend the scope of this model class by proposing a method for incorporating response times. This extension enables the estimation of the completion times of each process and the testing of alternative process orderings. In line with previous developments, the proposed method is hierarchical and implemented using Bayesian methods. We apply our method to the two-high-threshold model of recognition memory, using previously published data. The results provide interesting insights into the ordering of memory-retrieval and guessing processes and show that the model performs at least as well as established benchmarks such as the diffusion model.
, Nina R. Arnold,
Published: 3 April 2017
Behavior Research Methods, Volume 50, pp 264-284; https://doi.org/10.3758/s13428-017-0869-7

Abstract:
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.
, Eric-Jan Wagenmakers
Journal of Mathematical Psychology, Volume 73, pp 110-116; https://doi.org/10.1016/j.jmp.2016.05.004

Abstract:
Many psychological theories that are instantiated as statistical models imply order constraints on the model parameters. To fit and test such restrictions, order constraints of the form θi≤θj can be reparameterized with auxiliary parameters η∈[0,1] to replace the original parameters by θi=η⋅θj. This approach is especially common in multinomial processing tree (MPT) modeling because the reparameterized, less complex model also belongs to the MPT class. Here, we discuss the importance of adjusting the prior distributions for the auxiliary parameters of a reparameterized model. This adjustment is important for computing the Bayes factor, a model selection criterion that measures the evidence in favor of an order constraint by trading off model fit and complexity. We show that uniform priors for the auxiliary parameters result in a Bayes factor that differs from the one that is obtained using a multivariate uniform prior on the order-constrained original parameters. As a remedy, we derive the adjusted priors for the auxiliary parameters of the reparameterized model. The practical relevance of the problem is underscored with a concrete example using the multi-trial pair-clustering model.
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