A general latent assignment approach for modeling psychological contaminants

Data from psychological experiments are rife with ‘contaminants’, which can generally be defined as data generated by psychological processes different from those intended as the object of study. Contaminant data can interfere with the testing of substantive psychological models and their parameters, so it is important to have methods for their identification and removal. After noting that current practices in cognitive modeling for dealing with contaminants are not completely satisfactory, we argue for a general latent mixture approach to the problem. We demonstrate the tractability and effectiveness of the approach concretely, through a series of four applications. These applications involve a simple choice problem, a diffusion model of a response time and accuracy in decision-making, a hierarchical signal detection model of recognition memory, and a reinforcement learning model of decision-making on bandit problems. We conclude that developing models of contaminant processes requires the same sort of creative effort that is needed to model substantive psychological processes, but that it is a necessary endeavour that can be coherently and usefully pursued within the latent mixture modeling approach.     

Kognitive Lernermodellierung

Different types of learner models and their usefulness for tutoring have been discussed widely since the beginning of intelligent tutoring systems. In this paper we compare pragmatic and cognitive approaches of learner modeling. Pragmatic approaches consider relevant learner features for adaptive methods in learning environments and adapt different aspects of instruction to a restricted model representing these features. Cognitive approaches aim for a psychologically adequate modeling of human problem solving. We introduce the case-based learner model ELM as an example of a cognitive approach to learner modeling. The learning environments ELM-PE and ELM-ART use ELM for adaptional methods on conceptual, plan, and episodic levels and provide individual help and learning support. Especially in the case of integrated learning environments like ELM-ART which support a variety of learning activities, a combination of pragmatic and cognitive learner models is proposed to be a necessary and useful solution.     

A dynamical approach to speech categorization: Two routes to learning

Learning to perceive a non-native speech sound reliably is a specific instance of the more general issue of category learning. Here we take a dynamical approach that provides a theoretically motivated way to understand individual differences in the process of learning to perceive new speech sounds. Fundamental to this approach is the focus on the initial categorization and discrimination abilities of individual perceivers and how these structure the form of learning over time. Two distinct patterns of learning were observed that were predictable based on initial perceptual abilities. In one pattern, subjects became more attuned to small acoustic distinctions between stimuli and could use that sensitivity to label tokens reliably. In the second pattern, subjects became less attuned to within-category acoustic distinctions, suggesting cognitive restructuring. Finally, we present a dynamical model that incorporates both modes of category learning, and also allows for failure to learn.     

Individual differences in learning and memory: A unitary information processing approach

Recent research in the area of individual differences in learning and memory is reviewed from a cognitive perspective. Using the two-state model of memory as a framework, individual variations in attentional, short-term store, and long-term store processes are discussed. The focus is on using individual differences to evaluate nomothetic cognitive models, as well as on using cognitive models in guiding research on individual differences. Both within-individual and between-individual differences in basic processes are examined. In so doing, the importance of strategy choice is stressed using the concept of cognitive flexibility. Several promising directions, both methodological and theoretical, are noted and the value of using specific information processing models in the study of individual differences is emphasized.     

多项式加工树模型在再认启发式中的应用

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

Abstraction and model evaluation in category learning

Thirty previously published data sets, from seminal category learning tasks, are reanalyzed using the varying abstraction model (VAM). Unlike a prototype-versus-exemplar analysis, which focuses on extreme levels of abstraction only, a VAM analysis also considers the possibility of partial abstraction. Whereas most data sets support no abstraction when only the extreme possibilities are considered, we show that evidence for abstraction can be provided using the broader view on abstraction provided by the VAM. The present results generalize earlier demonstrations of partial abstraction (Vanpaemel & Storms, 2008), in which only a small number of data sets was analyzed. Following the dominant modus operandi in category learning research, Vanpaemel and Storms evaluated the models on their best fit, a practice known to ignore the complexity of the models under consideration. In the present study, in contrast, model evaluation not only relies on the maximal likelihood, but also on the marginal likelihood, which is sensitive to model complexity. Finally, using a large recovery study, it is demonstrated that, across the 30 data sets, complexity differences between the models in the VAM family are small. This indicates that a (computationally challenging) complexity-sensitive model evaluation method is uncalled for, and that the use of a (computationally straightforward) complexity-insensitive model evaluation method is justified.     

Three case studies in the Bayesian analysis of cognitive models

Bayesian statistical inference offers a principled and comprehensive approach for relating psychological models to data. This article presents Bayesian analyses of three influential psychological models: multidimensional scaling models of stimulus representation, the generalized context model of category learning, and a signal detection theory model of decision making. In each case, the model is recast as a probabilistic graphical model and is evaluated in relation to a previously considered data set. In each case, it is shown that Bayesian inference is able to provide answers to important theoretical and empirical questions easily and coherently. The generality of the Bayesian approach and its potential for the understanding of models and data in psychology are discussed.     

How cognitive modeling can benefit from hierarchical Bayesian models

Hierarchical Bayesian modeling provides a flexible and interpretable way of extending simple models of cognitive processes. To introduce this special issue, we discuss four of the most important potential hierarchical Bayesian contributions. The first involves the development of more complete theories, including accounting for variation coming from sources like individual differences in cognition. The second involves the capability to account for observed behavior in terms of the combination of multiple different cognitive processes. The third involves using a few key psychological variables to explain behavior on a wide range of cognitive tasks. The fourth involves the conceptual unification and integration of disparate cognitive models. For all of these potential contributions, we outline an appropriate general hierarchical Bayesian modeling structure. We also highlight current models that already use the hierarchical Bayesian approach, as well as identifying research areas that could benefit from its adoption.     

Modeling individual differences using Dirichlet processes

We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explains the variation between individuals, but rather as representatives of a latent, arbitrarily rich structure. As more people are seen, and more details about the individual differences are revealed, the number of inferred groups is allowed to grow. We use the Dirichlet process—a distribution widely used in nonparametric Bayesian statistics—to define a prior for the model, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model. As an initial demonstration of the approach, we present three applications that analyze the individual differences in category learning, choice of publication outlets, and web-browsing behavior.     

Are there representational shifts during category learning?

Early theories of categorization assumed that either rules, or prototypes, or exemplars were exclusively used to mentally represent categories of objects. More recently, hybrid theories of categorization have been proposed that variously combine these different forms of category representation. Our research addressed the question of whether there are representational shifts during category learning. We report a series of experiments that tracked how individual subjects generalized their acquired category knowledge to classifying new critical transfer items as a function of learning. Individual differences were observed in the generalization patterns exhibited by subjects, and those generalizations changed systematically with experience. Early in learning, subjects generalized on the basis of single diagnostic dimensions, consistent with the use of simple categorization rules. Later in learning, subjects generalized in a manner consistent with the use of similarity-based exemplar retrieval, attending to multiple stimulus dimensions. Theoretical modeling was used to formally corroborate these empirical observations by comparing fits of rule, prototype, and exemplar models to the observed categorization data. Although we provide strong evidence for shifts in the kind of information used to classify objects as a function of categorization experience, interpreting these results in terms of shifts in representational systems underlying perceptual categorization is a far thornier issue. We provide a discussion of the challenges of making claims about category representation, making reference to a wide body of literature suggesting different kinds of representational systems in perceptual categorization and related domains of human cognition.     

Modeling Noisy Data with Differential Equations Using Observed and Expected Matrices

Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.     

Using priors to formalize theory: Optimal attention and the generalized context model

Formal models in psychology are used to make theoretical ideas precise and allow them to be evaluated quantitatively against data. We focus on one important??but under-used and incorrectly maligned??method for building theoretical assumptions into formal models, offered by the Bayesian statistical approach. This method involves capturing theoretical assumptions about the psychological variables in models by placing informative prior distributions on the parameters representing those variables. We demonstrate this approach of casting basic theoretical assumptions in an informative prior by considering a case study that involves the generalized context model (GCM) of category learning. We capture existing theorizing about the optimal allocation of attention in an informative prior distribution to yield a model that is higher in psychological content and lower in complexity than the standard implementation. We also highlight that formalizing psychological theory within an informative prior distribution allows standard Bayesian model selection methods to be applied without concerns about the sensitivity of results to the prior. We then use Bayesian model selection to test the theoretical assumptions about optimal allocation formalized in the prior. We argue that the general approach of using psychological theory to guide the specification of informative prior distributions is widely applicable and should be routinely used in psychological modeling.     

Unpacking buyer-seller differences in valuation from experience: A cognitive modeling approach

People often indicate a higher price for an object when they own it (i.e., as sellers) than when they do not (i.e., as buyers)—a phenomenon known as the endowment effect. We develop a cognitive modeling approach to formalize, disentangle, and compare alternative psychological accounts (e.g., loss aversion, loss attention, strategic misrepresentation) of such buyer-seller differences in pricing decisions of monetary lotteries. To also be able to test possible buyer-seller differences in memory and learning, we study pricing decisions from experience, obtained with the sampling paradigm, where people learn about a lottery’s payoff distribution from sequential sampling. We first formalize different accounts as models within three computational frameworks (reinforcement learning, instance-based learning theory, and cumulative prospect theory), and then fit the models to empirical selling and buying prices. In Study 1 (a reanalysis of published data with hypothetical decisions), models assuming buyer-seller differences in response bias (implementing a strategic-misrepresentation account) performed best; models assuming buyer-seller differences in choice sensitivity or memory (implementing a loss-attention account) generally fared worst. In a new experiment involving incentivized decisions (Study 2), models assuming buyer-seller differences in both outcome sensitivity (as proposed by a loss-aversion account) and response bias performed best. In both Study 1 and 2, the models implemented in cumulative prospect theory performed best. Model recovery studies validated our cognitive modeling approach, showing that the models can be distinguished rather well. In summary, our analysis supports a loss-aversion account of the endowment effect, but also reveals a substantial contribution of simple response bias.     

Working memory capacity and categorization: individual differences and modeling

Working memory is crucial for many higher-level cognitive functions, ranging from mental arithmetic to reasoning and problem solving. Likewise, the ability to learn and categorize novel concepts forms an indispensable part of human cognition. However, very little is known about the relationship between working memory and categorization, and modeling in category learning has thus far been largely uninformed by knowledge about people's memory processes. This article reports a large study (N = 113) that related people's working memory capacity (WMC) to their category-learning performance using the 6 problem types of Shepard, Hovland, and Jenkins (1961). Structural equation modeling revealed a strong relationship between WMC and category learning, with a single latent variable accommodating performance on all 6 problems. A model of categorization (the Attention Learning COVEring map, ALCOVE; Kruschke, 1992) was fit to the individual data and a single latent variable was sufficient to capture the variation among associative learning parameters across all problems. The data and modeling suggest that working memory mediates category learning across a broad range of tasks.     

Why Higher Working Memory Capacity May Help You Learn: Sampling,Search, and Degrees of Approximation

Algorithms for approximate Bayesian inference, such as those based on sampling (i.e., Monte Carlo methods), provide a natural source of models of how people may deal with uncertainty with limited cognitive resources. Here, we consider the idea that individual differences in working memory capacity (WMC) may be usefully modeled in terms of the number of samples, or “particles,” available to perform inference. To test this idea, we focus on two recent experiments that report positive associations between WMC and two distinct aspects of categorization performance: the ability to learn novel categories, and the ability to switch between different categorization strategies (“knowledge restructuring”). In favor of the idea of modeling WMC as a number of particles, we show that a single model can reproduce both experimental results by varying the number of particles—increasing the number of particles leads to both faster category learning and improved strategy‐switching. Furthermore, when we fit the model to individual participants, we found a positive association between WMC and best‐fit number of particles for strategy switching. However, no association between WMC and best‐fit number of particles was found for category learning. These results are discussed in the context of the general challenge of disentangling the contributions of different potential sources of behavioral variability.     

Expanding the search for a linear separability constraint on category learning

Formal models of categorization make different predictions about the theoretical importance of linear separability. Prior research, most of which has failed to find support for a linear separability constraint on category learning, has been conducted using tasks that involve learning two categories with a small number of members. The present experiment used four categories with three or nine patterns per category that were either linearly separable or not linearly separable. With overall category structure equivalent across category types, the linearly separable categories were found to be easier to learn than the not linearly separable categories. An analysis of individual participants' data showed that there were more participants operating under a linear separability constraint when learning large categories than when learning small ones. Formal modeling showed that an exemplar model could not account for many of these data. These results are taken to support the existence of multiple processes in categorization.     

A hierarchical bayesian model of human decision-making on an optimal stopping problem

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally.     

Modelling individual difference in visual categorization

Recent years has seen growing interest in understanding, characterizing, and explaining individual differences in visual cognition. We focus here on individual differences in visual categorization. Categorization is the fundamental visual ability to group different objects together as the same kind of thing. Research on visual categorization and category learning has been significantly informed by computational modelling, so our review will focus both on how formal models of visual categorization have captured individual differences and how individual difference have informed the development of formal models. We first examine the potential sources of individual differences in leading models of visual categorization, providing a brief review of a range of different models. We then describe several examples of how computational models have captured individual differences in visual categorization. This review also provides a bit of an historical perspective, starting with models that predicted no individual differences, to those that captured group differences, to those that predict true individual differences, and to more recent hierarchical approaches that can simultaneously capture both group and individual differences in visual categorization. Via this selective review, we see how considerations of individual differences can lead to important theoretical insights into how people visually categorize objects in the world around them. We also consider new directions for work examining individual differences in visual categorization.     

Sampling assumptions in inductive generalization

Inductive generalization, where people go beyond the data provided, is a basic cognitive capability, and it underpins theoretical accounts of learning, categorization, and decision making. To complete the inductive leap needed for generalization, people must make a key 'sampling' assumption about how the available data were generated. Previous models have considered two extreme possibilities, known as strong and weak sampling. In strong sampling, data are assumed to have been deliberately generated as positive examples of a concept, whereas in weak sampling, data are assumed to have been generated without any restrictions. We develop a more general account of sampling that allows for an intermediate mixture of these two extremes, and we test its usefulness. In two experiments, we show that most people complete simple one-dimensional generalization tasks in a way that is consistent with their believing in some mixture of strong and weak sampling, but that there are large individual differences in the relative emphasis different people give to each type of sampling. We also show experimentally that the relative emphasis of the mixture is influenced by the structure of the available information. We discuss the psychological meaning of mixing strong and weak sampling, and possible extensions of our modeling approach to richer problems of inductive generalization.