Multinomial Processing Tree Models Research Articles

Parameter validation in hierarchical MPT models by functional dissociation with continuous covariates: An application to contingency inference

In traditional multinomial processing tree (MPT) models for aggregate frequency data, parameters have usually been validated by means of experimental manipulations, thereby testing selective effects of discrete independent variables on specific model parameters. More recently, hierarchical MPT models which account for parameter heterogeneity between participants have been introduced. These models offer a new possibility of parameter validation by analyzing selective covariations of interindividual differences in MPT model parameters with continuous covariates. The new approach enables researchers to test parameter validity in terms of functional dissociations, including convergent validity and discriminant validity in a nomological network. Here, we apply the novel approach to a multidimensional source-monitoring model in the domain of stereotype formation based on pseudocontingency inference. Using hierarchical Bayesian MPT models, we test the validity of source-guessing parameters as indicators of specific source evaluations on the individual level. First, analyzing experimental data on stereotype formation (N=130), we replicated earlier findings of biased source-guessing parameters while taking parameter heterogeneity across participants into account. Second, we investigated the specificity of covariations between conditional guessing parameters and continuous direct measures of source evaluations. Interindividual differences in direct evaluations predicted interindividual differences in specific source-guessing parameters, thus validating their substantive interpretation. Third, in an exploratory analysis, we examined relations of memory parameters and guessing parameters with cognitive performance measures from a standardized cognitive assessment battery.

A comparison of correlation and regression approaches for multinomial processing tree models

Multinomial processing tree (MPT) models are a class of stochastic models for categorical data that have recently been extended to account for heterogeneity in individuals by assuming separate parameters per participant. These extensions enable the estimation of correlations among model parameters and correlations between model parameters and external covariates. The present study compares different approaches regarding their ability to estimate both types of correlations. For parameter–parameter correlations, we considered two Bayesian hierarchical MPT models – the beta-MPT approach and the latent-trait approach – and two frequentist approaches that fit the data of each participant separately, either involving a correction for attenuation or not (corrected and uncorrected individual-model approach). Regarding parameter-covariate correlations, we additionally considered the latent-trait regression. Recovery performance was determined via a Monte Carlo simulation varying sample size, number of items, extent of heterogeneity, and magnitude of the true correlation. The results indicate the smallest bias regarding parameter–parameter​ correlations for the latent-trait approach and the corrected individual-model approach and the smallest bias regarding parameter-covariate correlations for the latent-trait regression and the corrected individual-model approach. However, adequately recovering correlations of MPT parameters generally requires a sufficiently large number of observations and sufficient heterogeneity.

Hierarchical multinomial modeling to explain individual differences in children’s clustering in free recall

The measurement of individual differences in cognitive processes and the advancement of multinomial processing tree (MPT) models were two of William H. Batchelder’s major research interests. Inspired by his work, we investigated developmental differences between 7-year-old children, 10-year-old children, and young adults, in free recall with the pair-clustering model by Batchelder and Riefer (1980, 1986). Specifically, we examined individual differences (in initial levels and in change across multiple study–test trials) in cluster encoding, retrieval, and covariation with three basic cognitive abilities: semantic verbal understanding, short-term memory capacity, information-processing speed. Data from two developmental studies in which 228 participants freely recalled clusterable words in four study–test cycles were used for reanalysis. We combined two model extensions not linked so far (Klauer, 2010; Knapp & Batchelder, 2004). This novel combination of modeling methods made it possible to analyze the relation between individual cognitive abilities and changes in cluster encoding and retrieval across study–test cycles. Inspired by William H. Batchelder, this work illustrates how MPT modeling can contribute to the understanding of cognitive development.

Rtmpt: An R package for fitting response-time extended multinomial processing tree models.

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.

Extending RT-MPTs to enable equal process times

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.

Representing probabilistic models of knowledge space theory by multinomial processing tree models

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.

An application of multinomial processing tree models and Bayesian methods to understanding memory impairment

We model word-list learning over sequences of immediate and delayed free recall tasks to study the impact of memory impairment on episodic memory. We use a previously developed Multinomial Processing Tree (MPT) model of encoding, retrieval, and learning (Alexander et al., 2016), and apply it to behavioral data from thousands of patients tested tens of thousands of times in a cognitive disorders clinic. The patients were independently diagnosed, using the Functional Assessment Staging Test (FAST), into six stages of impairment. We apply hierarchical and latent-mixture versions of the MPT model to patients in each FAST stage, exploring individual differences among people and item-position effects across the word lists. Our results show clear and theoretically interpretable regularities in how model parameters change over item positions, corresponding to standard primacy and recency effects in free recall. Accordingly, we develop an extended model that directly incorporates theoretical assumptions about serial position. Inferences from this model allow us to reach conclusions about how learning, encoding, and retrieval processes change as memory impairment progresses.

Sequential hypothesis tests for multinomial processing tree models

Stimulated by William H. Batchelder’s seminal contributions in the 1980s and 1990s, multinomial processing tree (MPT) modeling has become a powerful and frequently used method in various research fields, most prominently in cognitive psychology and social cognition research. MPT models allow for estimation of, and statistical tests on, parameters that represent psychological processes underlying responses to cognitive tasks. Therefore, their use has also been proposed repeatedly for purposes of psychological assessment, for example, in clinical settings to identify specific cognitive deficits in individuals. However, a considerable drawback of individual MPT analyses emerges from the limited number of data points per individual, resulting in estimation bias, large standard errors, and low power of statistical tests. Classical test procedures such as Neyman–Pearson tests often require very large sample sizes to ensure sufficiently low Type 1 and Type 2 error probabilities. Herein, we propose sequential probability ratio tests (SPRTs) as an efficient alternative. Unlike Neyman–Pearson tests, sequential tests continuously monitor the data and terminate when a predefined criterion is met. As a consequence, SPRTs typically require only about half of the Neyman–Pearson sample size without compromising error probability control. We illustrate the SPRT approach to statistical inference for simple hypotheses in single-parameter MPT models. Moreover, a large-sample approximation, based on ML theory, is presented for typical MPT models with more than one unknown parameter. We evaluate the properties of the proposed test procedures by means of simulations. Finally, we discuss benefits and limitations of sequential MPT analysis.

Benefits of response time-extended multinomial processing tree models: A reply to Starns (2018).

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.

Are subjective sleepiness and sleep quality related to prospective memory?

Event-based prospective memory (PM) involves carrying out intentions when specific events occur and is ubiquitous in everyday life. It consists of a prospective component (remembering that something must be done) and a retrospective component (remembering what must be done and when). Subjective sleep-related variables may be related to PM performance and an attention-demanding prospective component. In two studies, the relationship of subjective sleepiness and subjective sleep quality with both PM components was investigated with a laboratory PM task and separation of its components via Bayesian multinomial processing tree modeling. In Study 1, neither component of PM was related to naturally occurring subjective sleepiness or sleep quality. In Study 2, sleepiness was experimentally increased by placing some participants in a supine body posture. Testing participants in upright vs. supine posture affected neither PM component. However, body posture moderated the relationship between subjective sleep quality and the prospective component: In supine posture, subjective sleep quality tended to be more positively related to the prospective component. Overall, neither subjective sleepiness nor subjective sleep quality alone was related to PM.

Is knowledge reliance in source guessing a cognitive trait? Examining stability across time and domain.

When people need to infer the source of information in the absence of memory, they may rely on general knowledge (e.g., stereotypes) to guess the source. Prior research documented task-related determinants and individual differences of stereotype reliance in source guessing, but little is known about the underling nature of this process. In two experiments, we tested whether a cognitive trait could account for the knowledge reliance in source guessing. Participants performed two distinct study-test cycles of a classical source-monitoring paradigm in which two person sources present stereotypical information that in a later test phase had to be attributed to its origin. In Experiment 1, both tasks used item material from the same knowledge domain (age stereotypes) and were either separated by 10 minutes or 7 days. In Experiment 2, we used item material from two different knowledge domains (Task 1: age stereotypes; Task 2: gender stereotypes). Although cross-task correlations of source-guessing parameters from Bayesian-hierarchical multinomial processing tree model analyses showed only weak positive correlations, absolute source guessing remained fairly stable within individuals across time (Experiment 1) and knowledge domains (Experiment 2). Considering statistical challenges of the assessment of relative stability via correlations, we suggest based on the stricter absolute stability criterion that source guessing rather encompasses trait-like features. We discuss implications regarding the generalizability and nature of source guessing in comparison to other cognitive processes involved in source attribution, which were highly stable in both experiments.

Revisiting the divide between deontology and utilitarianism in moral dilemma judgment: A multinomial modeling approach.

We investigate the psychological bases underlying moral dilemma judgment with the help of multinomial processing tree modeling, and consider how determinants of dilemma judgment should best be conceptualized. We argue that, for conceptual as well as empirical reasons, norms and consequences should be considered as more intimately linked with one another than their systematic juxtaposition in dilemma research may suggest, and propose that norm-endorsement should be viewed through a consequentialist lens as well. Investigating this proposal, we introduce a variant of the CNI model of moral dilemma judgment, which focuses on the use of proscriptive norms only. In five experiments, we validate this proCNI model and assess the parameters' sensitivity to different types of consequences and personal involvement. Our findings suggest that the parameter representing "norms" is sensitive to consequences as well, such that norms do not guide moral judgment unless they are expected to produce tangible consequences. Thus, present research suggests that the split between norms and "consequences" (or "deontology" and "utilitarianism") as determinants of judgment is artificial. We suggest that, ultimately, viewing dilemma judgments through a consequentialist lens may be a useful approach for advancing theoretical development in the field of dilemma research. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Testing Interactions in Multinomial Processing Tree Models.

Multinomial processing tree (MPT) models allow testing hypotheses on latent psychological processes that underlie human behavior. However, past applications of this model class have mainly been restricted to the analysis of main effects. In this paper, we adopt the interaction concept as defined in log-linear models and show why it is appropriate for MPT models. We then explain how to implement and test ordinal and disordinal two-way interaction hypotheses in MPT models. We also show how our method generalizes to higher-order interactions involving three or more factors. An empirical example from source memory and aging demonstrates the applicability of this method and allows for directly testing the associative deficit theory that age differences are larger in associative (e.g., source) memory as opposed to item memory. Throughout the paper, we explain how most analytic steps can be easily implemented in the freely available software multiTree.

A hybrid model of source monitoring in paired-associates learning.

Three source-monitoring models were tested using the data of Bellezza, Elek, and Zhang (2016), who presented word pairs with each word in 1 of 4 locations. Given 1 word as a cue, participants had to remember the other word as well as the 2 corresponding locations. Results included (a) locations of the cue and target words were identified equally well; (b) source identification of unrecalled words was above chance; (c) the correct identification of the cue word was positively correlated with that of the target word; and (d) the location of the cue word was frequently confused with the location of the target. Three multinomial processing-tree models were tested to explain these results: a word-code model, an event-code model, and a hybrid model. The hybrid model was able to fit the data from the 5 experimental conditions of Bellezza et al. data. The model also fit data both from an experiment using four background colors as the source attributes and from a validation experiment manipulating visual-imagery instructions. The parameter values of the hybrid model suggested that source performance using locations was based predominantly on a memory code labeled an event code that included a source axis describing the locations of the 2 words, whereas performance using color relied more on word codes that associated each word with its color. It appears that different source attributes draw upon different combinations of cognitive processes, but each process occurs within the framework of the hybrid model. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Are there two independent evaluative conditioning effects in relational paradigms? Dissociating the effects of CS-US pairings and their meaning

ABSTRACTRecent research into evaluative conditioning (EC) shows that information about the relationship between the conditioned and unconditioned stimuli can exert strong effects on the size and direction of the EC effect. Additionally, the co-occurrence of these stimuli seems to exert an orthogonal effect on evaluations. This finding has been interpreted as support for two independent types of EC effects. However, previous research devoted to this question relied on aggregated evaluative measures, allowing for alternative interpretations. In four experiments, we developed and validated a multinomial processing tree model that distinguishes effects of the pairings from effects of the meaning of the pairings. Our findings suggest that two independent EC effects contribute to overall evaluative change in a relational EC paradigm. The model that we developed offers a helpful method for future research in that it allows for an assessment of the effects of manipulations on processes rather than overall performance on an evaluative measure.

Adaptive memory: enhanced source memory for animate entities

ABSTRACTThe animacy effect refers to enhanced memory for animate over inanimate items. In two studies, we examined whether this memory advantage generalises to source memory. A multinomial processing tree model was used to disentangle item recognition, source memory, and guessing processes. In Study 1, animate and inanimate words were presented at different spatial locations on the screen. Animacy was associated with enhanced source memory for the spatial locations of the items. In Study 2, pseudowords were associated with animate and inanimate properties. Replicating previous results, the pseudowords were better remembered when they were associated with animate properties than when they were associated with inanimate properties. What is more, participants had enhanced source memory for the association between the pseudowords and the animate properties. The results strengthen the idea that animate items are associated with richer mnemonic representations than inanimate items.

False Memory for Orthographically Related Words: Research in the Simplified Conjoint Recognition Paradigm

Abstract The aim of this study was to define the processes underlying false recognition memory for orthographically related words by using the simplified conjoint recognition paradigm (Stahl & Klauer, 2009), which is grounded in the fuzzy trace theory. We considered 2 accounts. The first assumes that false memory stems from the perceptual feature overlap between targets and distractors represented in the gist memory parameter. The second account assumes that false memory for orthographically related distractors results from the misattribution of verbatim information, which is reflected in the phantom recollection parameter. Data from two experiments were analyzed with multinomial processing tree modeling to estimate the contribution of latent processes to performance in recognition memory tests. These analyses supported the feature overlap account, suggesting that gist trace encodes both semantic and orthographic patterns. We also showed that a boost in false memories due to the adding of semantic associates to a list of orthographically related words stems from an increase in phantom recollection. We discussed further directions in theoretical and empirical research on the gist and verbatim traces’ contribution to false recognition of perceptually related stimuli.

Age differences in hindsight bias: A meta-analysis.

After people have learned a fact or the outcome of an event, they often overestimate their ability to have known the correct answer beforehand. This hindsight bias has two sources: an impairment in direct recall of the original (i.e., uninformed) judgment after presentation of the correct answer (recollection bias) and a reconstruction of the original judgment that is biased toward the correct answer (reconstruction bias). Research on how cognitive aging affects these two sources of hindsight bias has produced mixed results. To synthesize the available findings, we conducted a meta-analysis of nine studies (N = 366 young, N = 368 older adults). We isolated the probabilities of recollection, recollection bias, and reconstruction bias with a Bayesian, three-level hierarchical implementation of the multinomial processing tree model of hindsight bias (Erdfelder & Buchner, 1998). Additionally, we quantified the magnitude of bias in the reconstructed judgment. Overall, older adults were less likely to recollect their original judgment than young adults, and thus had to reconstruct it more frequently. Importantly, whereas outcome knowledge impaired recollection of the original judgment (i.e., recollection bias) to a similar extent in both age groups, outcome knowledge was more likely to distort reconstruction of the original judgment (i.e., reconstruction bias) in older adults. In addition, the magnitude of bias in the reconstructed judgments was slightly larger in older than in young adults. Our results provide the basis for a targeted investigation of the mechanisms driving these age differences. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Adaptive memory: Source memory is positively associated with adaptive social decision making

The key insight behind the adaptive memory framework is that the primary function of remembering is not to help us to relive the past but to inform adaptive behavior in the future. However, the beneficial effects of memory on the individual’s fitness are often difficult to study empirically. In the case of social cooperation, it is comparatively easy to derive testable predictions about the relationship between specific types of memory (e.g., source memory) and specific types of adaptive decision making (e.g., direct reciprocity). In the present study, we examined both the participants’ behaviors in a Prisoner’s Dilemma game and their memory performance in a source-monitoring test. Participants showed evidence of adaptive decision making. Their willingness to cooperate was strongly determined by their partners’ behaviors in previous rounds. Individual parameter estimates of old-new recognition, source memory, and guessing were obtained via hierarchical multinomial processing tree modeling. Source memory was positively associated with adaptive decisions in the Prisoner’s Dilemma game. The better participants’ source memory, the more often they cooperated with cooperators and the less often they cooperated with cheaters. Guessing in the memory test, by contrast, was unrelated to cooperation. The results underline the importance of source memory in adaptive decision making.

Can self-referential information improve directed forgetting? Evidence from a multinomial processing tree model.

A large body of research has shown that self-referential processing can enhance an individual’s memory of information. However, there are many arguments about how self-referential processing affects directed forgetting (DF). In this study, two experiments were designed to investigate the DF effect and its internal psychological mechanism under explicit and implicit referential conditions using the item-method DF paradigm combined with the storage-retrieval MPT model. We compare the difference in the DF effect between self-referential and other-referential conditions and explain the reasons for the difference. Our results suggest that the item-method DF effect is the result of a selective rehearsal mechanism and a retrieval inhibition mechanism working together. Both self-reference and other-reference can cause DF in explicit referential processing or implicit referential processing, although the DF effect is stronger under the self-referential condition. Furthermore, the memory advantage effect of implicit self-referential processing is stronger than that of explicit self-referential processing.