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Testing Unidimensionality in Polytomous Rasch Models
Psychometrika, 2002A fundamental assumption of most IRT models is that items measure the same unidimensional latent construct. For the polytomous Rasch model two ways of testing this assumption against specific multidimensional alternatives are discussed. One, a marginal approach assuming a multidimensional parametric latent variable distribution, and, two, a conditional
Christensen, Karl Bang +3 more
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Polytomous Rasch Models in Counseling Assessment
Measurement and Evaluation in Counseling and Development, 2017This article provides a brief introduction to the Rasch model. Motivation for using Rasch analyses is provided.
John T Willse
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Conditions for Rasch-Dichotomizability of the Unidimensional Polytomous Rasch Model
Psychometrika, 1989Jansen and Roskam (1986) discussed the compatibility of the unidimensional polytomous Rasch model with dichotomization of the response continuum. They derived a rather strict condition in which dichotomization of multicategory data that fit the unidimensional polytomous Rasch model, results in dichotomous data which fit the dichotomous Research model ...
Roskam, E.E., Jansen, Paul
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Residualanalysis in the Polytomous Rasch Model
Psychometrika, 1995Residuals for check of model fit in the polytomous Rasch model are examined. Comparisons are made between using counts for all response pattern and using item totals for score groups for the construction of the residuals. Comparisons are also, for the residuals based on score group totals, made between using as basis the item totals, or using the ...
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Psychometrika, 2003
A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data.
von Davier, Matthias, Molenaar, Ivo W.
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A normally distributed person-fit index is proposed for detecting aberrant response patterns in latent class models and mixture distribution IRT models for dichotomous and polytomous data.This article extends previous work on the null distribution of person-fit indices for the dichotomous Rasch model to a number of models for categorical data.
von Davier, Matthias, Molenaar, Ivo W.
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Quantifying Local, Response Dependence Between Two Polytomous Items Using the Rasch Model
Applied Psychological Measurement, 2012Models of modern test theory imply statistical independence among responses, generally referred to as local independence. One violation of local independence occurs when the response to one item governs the response to a subsequent item. Expanding on a formulation of this kind of violation as a process in the dichotomous Rasch model, this article ...
David Andrich +2 more
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Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model
Psychometrika, 2010Rasch models are characterised by sufficient statistics for all parameters. In the Rasch unidimensional model for two ordered categories, the parameterisation of the person and item is symmetrical and it is readily established that the total scores of a person and item are sufficient statistics for their respective parameters.
David Andrich
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2019
A category coefficient \( \kappa_{k} \) is the sum of the exceeded thresholds for response category k. The PRM can be rewritten in terms of principal components (Guttman) for the thresholds instead of the thresholds themselves. The principal component \( \lambda \) characterizes the spread of the responses, the principal component \( \eta ...
David Andrich, Ida Marais
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A category coefficient \( \kappa_{k} \) is the sum of the exceeded thresholds for response category k. The PRM can be rewritten in terms of principal components (Guttman) for the thresholds instead of the thresholds themselves. The principal component \( \lambda \) characterizes the spread of the responses, the principal component \( \eta ...
David Andrich, Ida Marais
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Modeling Household Food Insecurity with a Polytomous Rasch Model
2020The Household Food Security Survey Module (HFSSM) is an 18-item scale created and maintained by the US Department of Agriculture (USDA) that measures food insecurity in the United States. The HFSSM includes ten items that reference food hardships among adults in the household and eight items that reference food hardships among children.
Victoria T. Tanaka +2 more
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1995
In this chapter, the discrete mixture distribution framework is developed for Rasch models for items with a polytomous ordered response format. Four of these models will be considered, based on different restrictions regarding the so-called threshold distances (Section 20.2).
Matthias von Davier, Jürgen Rost
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In this chapter, the discrete mixture distribution framework is developed for Rasch models for items with a polytomous ordered response format. Four of these models will be considered, based on different restrictions regarding the so-called threshold distances (Section 20.2).
Matthias von Davier, Jürgen Rost
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