Analysis of multinomial models under inequality constraints: Applications to measurement theory

Davis‐Stober, Clintin P.

doi:10.1016/j.jmp.2008.08.003

Cited by 70 publications

(78 citation statements)

References 63 publications

(74 reference statements)

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“…That method relied strongly upon an experimental setting that is perhaps not yet possible for educational assessments. This initial work was extended by Iverson and Falmagne (1985) and Davis-Stober (2009). Together, these articles offer a frequentist alternative that could be pursued, in theory, as an alternative to the Bayesian methodology employed here.…”

Section: Literature Reviewmentioning

confidence: 92%

Evaluating the Equal-Interval Hypothesis with Test Score Scales

Domingue

2013

Psychometrika

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DateThe final copy of this thesis has been examined by the signatories, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. In this dissertation, an improved version of Karabatsos's methodology is applied to simulated and empirical data to test whether such data are consistent with the axioms.It is first shown that the methodology behaves reasonably using data simulated to meet the cancellation axioms of ACM. It is then shown that the methodology is capable of distinguishing data simulated to meet the axioms from data that is not. In particular, it is demonstrated that the methodology is sensitive to item-side violations of the axioms. Empirical examples are then used to illustrate the fact that test score data may or may not conform to the ACM axioms. Empirical demonstration shows that an existing test scale thought to satisfy the ACM axioms using the Karabatsos (2001) approach does not do so using the modified approach here.Since not all data may meet the ACM axioms (and hence not warrant interval interpretations), this dissertation also examines whether scale distortions can lead to erroneous conclusions. At the score-level, an approach was developed using "difference matrices" to highlight the fact that when the Rasch (1960) model is applied to certain non-Rasch data, the estimates will be more compressed at lower abilities. This same phenomena was noted in two simulations meant to capture how educational assessment data is used-with respect to schools and educational interventionsiv although the effects of the distortions were small. DedicationDedicated to my family. And brevity.vi

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Section: Literature Reviewmentioning

confidence: 92%

Evaluating the Equal-Interval Hypothesis with Test Score Scales

Domingue

2013

Psychometrika

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“…To provide a proper statistical analysis of these models, we must employ orderconstrained statistical inference techniques. This necessity has been discussed at length in the decision literature (Davis-Stober, 2009;Iverson & Falmagne, 1985;Myung, Karabatsos, & Iverson, 2005;Tversky, 1969).…”

Section: Order-constrained Bayesian Inferencementioning

confidence: 99%

Individual differences in the algebraic structure of preferences

Davis‐Stober

Brown

Cavagnaro

2015

Journal of Mathematical Psychology

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“…We discuss these models informally here. Appendix B gives formal details and Davis-Stober (2009) provides the likelihood-based statistical inference framework for binary choice data that we build on. 6 …”

Section: The Geometry Of Binary Choicementioning

confidence: 99%

QTest: Quantitative testing of theories of binary choice.

et al. 2014

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The goal of this paper is to make modeling and quantitative testing accessible to behavioral decision researchers interested in substantive questions. We provide a novel, rigorous, yet very general, quantitative diagnostic framework for testing theories of binary choice. This permits the nontechnical scholar to proceed far beyond traditionally rather superficial methods of analysis, and it permits the quantitatively savvy scholar to triage theoretical proposals before investing effort into complex and specialized quantitative analyses. Our theoretical framework links static algebraic decision theory with observed variability in behavioral binary choice data. The paper is supplemented with a custom-designed public-domain statistical analysis package, the QTest software. We illustrate our approach with a quantitative analysis using published laboratory data, including tests of novel versions of “Random Cumulative Prospect Theory.” A major asset of the approach is the potential to distinguish decision makers who have a fixed preference and commit errors in observed choices from decision makers who waver in their preferences.

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Analysis of multinomial models under inequality constraints: Applications to measurement theory

Cited by 70 publications

References 63 publications

Evaluating the Equal-Interval Hypothesis with Test Score Scales

Evaluating the Equal-Interval Hypothesis with Test Score Scales

Individual differences in the algebraic structure of preferences

QTest: Quantitative testing of theories of binary choice.

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