Independent random utility representations

Suck, Reinhard

doi:10.1016/s0165-4896(02)00020-3

Cited by 17 publications

(14 citation statements)

References 9 publications

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“…In this section, we discuss a direct test of this assumption and establish an additional predictive test based on the relationships between forced choice, ranking, and yes-no judgments that follow from latent-variable independence. 14 Sattath and Tversky (1976) formally showed that the assumption of latent-variable independence implies a number of multiplicative inequalities at the level of choice probabilities (see also Shaw, 1980;Suck, 2002;Suppes et al, 1989). Let A, B ⊆ T be option subsets including alternative a (i.e., a ∈ A ∩ B).…”

Section: Resultsmentioning

confidence: 99%

“…This means that the tests conducted by both Wixted (1992) and Hintzmann et al (1995) did not include an exhaustive evaluation of all of the constraints implied by a random-scale representation. They also did not directly test whether latent-variable independence is violated (Suck, 2002;see also McCausland & Marley, 2013. Until recently, a reanalysis of these previously-published data would have been unfeasible -but recent algorithmic developments have made the challenge much more tractable (see Smeulders, Davis-Stober, Regenwetter, & Spieksma, 2019).…”

Section: Testing Sdt In More Complex Designsmentioning

confidence: 99%

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Testing the Foundations of Signal Detection Theory in Recognition Memory

Kellen¹,

Winiger²,

Dunn³

et al. 2018

Preprint

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Signal Detection Theory (SDT) plays a central role in the characterization of human judgments in a wide range of domains, most prominently in recognition memory. But despite its success, many of its fundamental assumptions are often misunderstood, especially when its comes to its testability. The present work examines five main assumptions that are characteristic of existing SDT models -- the existence of a random scale representation, independent sampling, monotonic likelihood, Receiver Operating Characteristic (ROC) asymmetry, and a continuous (non-threshold) representation. In each case, we derive a testable consequence and test it against data collected in the appropriately designed recognition memory experiment. We also discuss the connection between yes-no, forced-choice, and ranking judgments. This connection introduces additional behavioral constraints and yields an alternative method of reconstructing yes-no ROC functions. Overall, the reported results provide a strong empirical foundation for SDT modeling in recognition memory.

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Section: Resultsmentioning

confidence: 99%

Section: Testing Sdt In More Complex Designsmentioning

confidence: 99%

Testing the Foundations of Signal Detection Theory in Recognition Memory

Kellen¹,

Winiger²,

Dunn³

et al. 2018

Preprint

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show abstract

“…For example, when considering all possible pairs X ≠ Y among up to five choice options, the choice probabilities P XY are known to satisfy the model in Equation if and only if the following collection of constraints holds:

\begin{matrix} right \\ P_{italicKL} + P_{italicLM} - P_{italicKM} \leq 1, for any distinct K, L, M . \end{matrix}

In its general form of Equation , the model allows the utility random variables to be interdependent across stimuli and across multiple observations. Very little is known about the special case where the random utilities are independent across choice options (within a pairwise choice) but unconstrained otherwise (Suck, ). For our discussion here, note that the general random utility model per se does not state whether repeated observations are iid or not (as we will see in more detail below).…”

Section: The General (Distribution‐free) Random Utility Modelmentioning

confidence: 99%

The Role of Independence and Stationarity in Probabilistic Models of Binary Choice

Regenwetter

Davis‐Stober

2017

Behavioral Decision Making

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After more then 50 years of probabilistic choice modeling in economics, marketing, political science, psychology, and related disciplines, theoretical and computational advances give scholars access to a sophisticated array of modeling and inference resources. We review some important, but perhaps often overlooked, properties of major classes of probabilistic choice models. For within-respondent applications, we discuss which models require repeated choices by an individual to be independent and response probabilities to be stationary. We show how some model classes, but not others, are invariant over variable preferences, variable utilities, or variable choice probabilities. These models, but not others, accommodate pooling of responses or averaging of choice proportions within participant when underlying parameters vary across observations. These, but not others, permit pooling/averaging across respondents in the presence of individual differences. We also review the role of independence and stationarity in statistical inference, including for probabilistic choice models that, themselves, do not require those properties. Copyright © 2017 John Wiley & Sons, Ltd.Additional Supporting Information may be found online in the supporting information tab for this article.key words probabilistic choice models; iid assumptions; modeling heterogeneity; statistical testingWhen selecting a probabilistic choice model to use in their work, scholars may want to consider which model class makes what assumptions and which model class warrants or precludes what types of data manipulations. In this conceptual and theoretical synthesis, we summarize, for several prominent probabilistic choice models, whether or not they assume mutually independent (in the sense of probability theory) responses and/or stationary response probabilities. 1 We also unpack whether various models are invariant under varying preferences, varying utility functions, or varying response probabilities, either because of individual differences or because of within-subject heterogeneity in behavior. We discuss what it means to average or pool binary choice data across respondents and/or across time points. To that end, we spell out, for some prominent statistical tests of probabilistic choice models, whether they, in turn, make additional independence and/or stationarity assumptions even when the models themselves do not require such properties to hold. We concentrate on those models, statistical tests, and data-generating processes whose basic observational unit-one observation-is one person's selection of one choice alternative among two, at one moment in time. Knowing a model's interconnected assumptions helps the applied scholar better understand their role in empirical evaluations. In particular, when a model performs or replicates poorly, knowing all assumptions is crucial for revising the theory in question. Motivation and backgroundConsider the following two questions posed in an experiment. We use these questions for various illustrations thr...

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“…For MI, see Sattath and Tversky (1976), Colonius (1983) and Suck (2002). For the remaining conditions, see Luce and Suppes (1965).…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference and model comparison for random choice structures

McCausland

Marley

2014

Journal of Mathematical Psychology

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Le Centre interuniversitaire de recherche en économie quantitative (CIREQ) regroupe des chercheurs dans les domaines de l'économétrie, la théorie de la décision, la macroéconomie et les marchés financiers, la microéconomie appliquée et l'économie expérimentale ainsi que l'économie de l'environnement et des ressources naturelles. Ils proviennent principalement des universités de Montréal, McGill et Concordia. Le CIREQ offre un milieu dynamique de recherche en économie quantitative grâce au grand nombre d'activités qu'il organise (séminaires, ateliers, colloques) et de collaborateurs qu'il reçoit chaque année.

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Independent random utility representations

Cited by 17 publications

References 9 publications

Testing the Foundations of Signal Detection Theory in Recognition Memory

Testing the Foundations of Signal Detection Theory in Recognition Memory

The Role of Independence and Stationarity in Probabilistic Models of Binary Choice

Bayesian inference and model comparison for random choice structures

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