An essay on inequalities and order-restricted inference

Iverson, Geoffrey

doi:10.1016/j.jmp.2006.01.007

Cited by 19 publications

(12 citation statements)

References 10 publications

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“…To test psychological theories, it is important that statistical models reflect a theory's core predictions without requiring strong and often arbitrary auxiliary assumptions. Multinomial models with inequality constraints provide an ideal framework for this purpose and allow to test both formal theories assuming deterministic axioms (Iverson, 2006) as well as verbal theories predicting multiple choice patterns (Regenwetter and Robinson, 2017). Given the implementation of Bayesian inference for this model class in the R package multinomineq (Heck and Davis-Stober, 2019), it will thus become easier for researchers to test psychological theories.…”

Section: Resultsmentioning

confidence: 99%

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Heck

Davis‐Stober

2019

Journal of Mathematical Psychology

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Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices).For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq, which provides an easily-accessible interface to a computationally efficient implementation of these techniques.

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Section: Resultsmentioning

confidence: 99%

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Heck

Davis‐Stober

2019

Journal of Mathematical Psychology

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“…Inequality-restricted models are infrequently used in the social sciences (Iverson, 2006). Aside from a lack of awareness, two major complications when evaluating these models using frequentist methodology contribute to their relatively rare use.…”

Section: Introductionmentioning

confidence: 99%

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

Davis‐Stober

2009

Journal of Mathematical Psychology

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“…The same cannot be said of the higher-order interactions that would bedevil linear-model analyses of the same data. Also, because these methods can be applied to the predictions of a theory as whole, they often provide high-powered tests (e.g., Iverson, 2006;Regenwetter & Davis-Stober, 2012).…”

Section: What Can Be Done?mentioning

confidence: 99%

The Problem of Coordination and the Pursuit of Structural Constraints in Psychology

Kellen¹,

Davis‐Stober²,

Dunn³

et al. 2020

Preprint

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Paul Meehl's famous critique laid out in detail many of the pathological practices and conceptual confusions that stand in the way of meaningful theoretical progress in psychological science. Integrating some of Meehl's points, we argue that one of the reasons for the slow progress in psychology is the failure to acknowledge the problem of coordination. This problem arises whenever we attempt to measure quantities that are not directly observable, but can be inferred from observable variables. The solution to this problem is far from trivial, as demonstrated by a historical analysis of thermometry. Also, it is not a problem that can be solved by empirical means. At its center is the need for a clear understanding of the functional relations between theoretical concepts and observations. In the case of psychology, the problem of coordination has dramatic implications in the sense that it severely limits our ability to make meaningful theoretical claims. We discuss several examples and lay out some of the solutions that are currently available.

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An essay on inequalities and order-restricted inference

Cited by 19 publications

References 10 publications

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

Multinomial models with linear inequality constraints: Overview and improvements of computational methods for Bayesian inference

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

The Problem of Coordination and the Pursuit of Structural Constraints in Psychology

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