Bayesian inference for psychometric functions

Kuß, Malte; Jäkel, Frank; Wichmann, Felix A.

doi:10.1167/5.5.8

Cited by 145 publications

(151 citation statements)

References 33 publications

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“…Although time-accuracy curves were the primary focus here, similar issues arise in other domains as well. Some of these domains include forgetting or retention curves (Rubin & Wenzel, 1996), learning curves (Heathcote, Brown, & Mewhort, 2000), psychometric functions (Kuss et al, 2005), and multinomial processing models (Batchelder & Riefer, 1990).…”

Section: Discussionmentioning

confidence: 99%

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Comparing time-accuracy curves: Beyond goodness-of-fit measures

Liu

Smith

2009

Psychonomic Bulletin & Review

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The speed-accuracy trade-off (SAT) is a ubiquitous phenomResponse time (RT) and response accuracy are the two most common dependent variables in experimental psychology. These two variables are often measured together to assess the possibility of a speed-accuracy trade-off (SAT): That is, at a given level of sensitivity, faster responses tend to produce more errors. The SAT phenomenon is often unrelated to the underlying mental processes of interest and, therefore, has been regarded as a nuisance variable in most studies.One strategy for controlling SAT is to formulate a quantitative model for the decision process. For example, sequential sampling models of decision making account for SAT with a criterion parameter, which determines the amount of information accumulated by the participant before he or she responds (

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Section: Discussionmentioning

confidence: 99%

“…Below, we will report estimates that are based on 10,000 samples. A detailed discussion of these methods is beyond the scope of this article; introductions for experimental psychologists are presented in Kuss, Jäkel, and Wichmann (2005), Lee (2008), and . Here, we used the plotted as a point.…”

Section: Interval Estimates: Bayesianmentioning

confidence: 99%

Comparing time-accuracy curves: Beyond goodness-of-fit measures

Liu

Smith

2009

Psychonomic Bulletin & Review

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“…IRT models specify the performance of a participant to an item in terms of such factors as item difficulty and item discriminability, and these parameters function very much as the threshold and discriminability parameters, respectively, of psychometric functions (e.g., Klein, 2001;Kuss, Jäkel, & Wichmann, 2005). Suppose a model postulates a latent cognitive event that either does or does not occur during the manifest response to an item-for example, recognizing by familiarity or recollection, clustering related items, or guessing Category A instead of Category B.…”

Section: Modeling Inhomogeneities In the Data The Case Of Heterogeneimentioning

confidence: 99%

Assessing individual differences in categorical data

Smith

Batchelder

2008

Psychonomic Bulletin & Review

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This article develops statistical methods to detect individual differences in cognitive data in the form of categorical observations from a set of participants, each of whom responds to the same set of item events-for example, memory items, item serial positions, or repeated choice trials. The purpose of these methods is to determine whether there is heterogeneity in either participants or item events that might make it inappropriate to aggregate the data, respectively, over participants or item events. These determinations are especially important in the case where the data will be analyzed with a cognitive model. If heterogeneity in participants or item events is detected, several recent developments in computational statistics make it feasible to augment a parametric model with a hierarchical level that models random effects on the parameters. On the other hand, a model that includes random effects assumptions on the parameters is clearly more complex (e.g., Myung & Pitt, 1997) and capable of accounting for more data than the same model is, assuming that all effects are equal; so the decision of whether or not to include random effects in a model analysis is a crucial one. Our methods for informing this decision, because they are based on the sampling assumptions of the basic data structure itself, are completely agnostic as to the appropriate cognitive model underlying the data. Before developing the methods, it is useful to review the way that most cognitive models have been employed in the past and how researchers have tried to deal with parametric heterogeneity.Parametric stochastic models of cognition are usually assessed with data taken from one or more experimental conditions consisting of a group of participants, each of whom provides responses to the same set of item events (hereafter, items). Within a given experimental condition, subsets of these observations are usually pooled (aggregated) and treated as if they are a sample from the cognitive model. In the terminology of mathematical statistics, the assumption that a sequence of observations constitutes a sample from a parametric model means that the observations arise from a sequence of independent and identically distributed (i.i.d.) random variables, whose common distribution is determined through the model equations by some fixed but unknown set of model parameters (e.g., Hogg, McKean, & Craig, 2005;Lehmann & Romano, 2005). One particular form of this assumption is when data on a particular item are aggregated over participants and analyzed on the assumption of no individual differences-that is, the assumption of participant homogeneity. Another form of the assumption is when the data from each particular participant are treated as a sample over items. It is not uncommon in list-memory experiments (e.g., the middle items of free recall, old or new items in recognition memory) to aggregate the data over both participants and items, thereby treating all the observations in some experimental condition as a sample from the model.Most examples in ...

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“…The Bayesian statistical framework is becoming increasingly important and popular for implementing and evaluating psychological models, including models of psychophysical functions (Kuss, Jäkel & Wichmann, 2005), stimulus representations (Lee, 2008), category learning (Lee & Vanpaemel, 2008;Vanpaemel & Storms, 2010), signal detection , response times (Rouder, Lu, Speckman, Sun & Jiang, 2005) and decision making (Wetzels, Grasman & Wagenmakers, 2010). It is widely recognized in statistics (Gelman, Carlin, Stern & Rubin, 2004;Jaynes, 2003) and, increasingly, in psychology (Dienes, 2011;Kruschke, 2010Kruschke, , 2011Lee & Wagenmakers, 2005) that the Bayesian approach offers a complete and coherent framework for making inferences using models and data.…”

Section: Introductionmentioning

confidence: 99%

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

Vanpaemel

Lee

2012

Psychon Bull Rev

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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 underused 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.

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Bayesian inference for psychometric functions

Cited by 145 publications

References 33 publications

Comparing time-accuracy curves: Beyond goodness-of-fit measures

Comparing time-accuracy curves: Beyond goodness-of-fit measures

Assessing individual differences in categorical data

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

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