Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

Anderson, Carolyn J.; Li, Zhushan; Vermunt, Jeroen K.

doi:10.18637/jss.v020.i06

Cited by 25 publications

(20 citation statements)

References 37 publications

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“…From a psychometric perspective, it is clear that the relations in Figure 5 also correspond to a model with a single latent variable. From this perspective, it is interesting to observe that the Curie-Weiss model is closely related to the extended-Rasch model (E-RM; Cressie & Holland, 1983;Tjur, 1982), a particular item response model originating from educational and psychological measurement (Anderson, Li, & Vermunt, 2007;Hessen, 2011;Maris, Bechger, & San Martin, 2015). In the E-RM, the distribution of n binary variables x-typically the scores of items on a test-is given by…”

Section: The Curie-weiss and Rasch Modelsmentioning

confidence: 99%

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

Marsman

Borsboom

Kruis

et al. 2017

Multivariate Behavioral Research

208

175

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In recent years, network models have been proposed as an alternative representation of psychometric constructs such as depression. In such models, the covariance between observables (e.g., symptoms like depressed mood, feelings of worthlessness, and guilt) is explained in terms of a pattern of causal interactions between these observables, which contrasts with classical interpretations in which the observables are conceptualized as the effects of a reflective latent variable. However, few investigations have been directed at the question how these different models relate to each other. To shed light on this issue, the current paper explores the relation between one of the most important network models-the Ising model from physics-and one of the most important latent variable models-the Item Response Theory (IRT) model from psychometrics. The Ising model describes the interaction between states of particles that are connected in a network, whereas the IRT model describes the probability distribution associated with item responses in a psychometric test as a function of a latent variable. Despite the divergent backgrounds of the models, we show a broad equivalence between them and also illustrate several opportunities that arise from this connection.

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Section: The Curie-weiss and Rasch Modelsmentioning

confidence: 99%

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

Marsman

Borsboom

Kruis

et al. 2017

Multivariate Behavioral Research

208

175

View full text Add to dashboard Cite

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“…This estimation is analogous to that of pairwise conditional estimation of item parameters already well established in the literature (Anderson, Li, & Vermunt, 2007;Andrich & Luo, 2003;Choppin, 1968;Zwinderman, 1995).…”

Section: Conditional Probability Of the Responses Of Two Persons To Omentioning

confidence: 58%

Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model

Andrich

2010

Psychometrika

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“…The plRasch package (Anderson et al 2007) using maximum likelihood and pseudolikelihood estimation for loglinear formulations of the Rasch family of models for response patterns of binary and polytomous items and a single or multiple latent traits.…”

Section: Two Packages For Rasch Families Of Modelsmentioning

confidence: 99%

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

Boeck¹,

Bakker²,

Zwitser³

et al. 2011

J. Stat. Soft.

257

254

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In this paper we elaborate on the potential of the lmer function from the lme4 package in R for item response (IRT) modeling. In line with the package, an IRT framework is described based on generalized linear mixed modeling. The aspects of the framework refer to (a) the kind of covariates -their mode (person, item, person-by-item), and their being external vs. internal to responses, and (b) the kind of effects the covariates have -fixed vs. random, and if random, the mode across which the effects are random (persons, items). Based on this framework, three broad categories of models are described: Item covariate models, person covariate models, and person-by-item covariate models, and within each category three types of more specific models are discussed. The models in question are explained and the associated lmer code is given. Examples of models are the linear logistic test model with an error term, differential item functioning models, and local item dependency models. Because the lme4 package is for univariate generalized linear mixed models, neither the two-parameter, and three-parameter models, nor the item response models for polytomous response data, can be estimated with the lmer function.

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Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

Cited by 25 publications

References 37 publications

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model

The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR

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Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

Cited by 25 publications

References 37 publications

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

An Introduction to Network Psychometrics: Relating Ising Network Models to Item Response Theory Models

Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model

The Estimation of Item Response Models with thelmerFunction from thelme4Package inR

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Product

Resources

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The Estimation of Item Response Models with the`lmer`Function from thelme4Package inR