Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables
The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Foundation for Open Access Statistics
2007-02-01
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| Series: | Journal of Statistical Software |
| Subjects: | |
| Online Access: | http://www.jstatsoft.org/v20/i06/paper |
| _version_ | 1811267182941700096 |
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| author | Carolyn J. Anderson Zhushan Li Jeroen K. Vermunt |
| author_facet | Carolyn J. Anderson Zhushan Li Jeroen K. Vermunt |
| author_sort | Carolyn J. Anderson |
| collection | DOAJ |
| description | The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent. |
| first_indexed | 2024-04-12T20:56:46Z |
| format | Article |
| id | doaj.art-47a0da425ee04db0a78208718ff1db41 |
| institution | Directory Open Access Journal |
| issn | 1548-7660 |
| language | English |
| last_indexed | 2024-04-12T20:56:46Z |
| publishDate | 2007-02-01 |
| publisher | Foundation for Open Access Statistics |
| record_format | Article |
| series | Journal of Statistical Software |
| spelling | doaj.art-47a0da425ee04db0a78208718ff1db412022-12-22T03:16:57ZengFoundation for Open Access StatisticsJournal of Statistical Software1548-76602007-02-01206Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent VariablesCarolyn J. AndersonZhushan LiJeroen K. VermuntThe Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.http://www.jstatsoft.org/v20/i06/paperpseudo-likelihood estimationlog-linear-by-linear association modelslogistic regressionmultinomial logistic regressionconditionally specified modelsR |
| spellingShingle | Carolyn J. Anderson Zhushan Li Jeroen K. Vermunt Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables Journal of Statistical Software pseudo-likelihood estimation log-linear-by-linear association models logistic regression multinomial logistic regression conditionally specified models R |
| title | Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables |
| title_full | Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables |
| title_fullStr | Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables |
| title_full_unstemmed | Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables |
| title_short | Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables |
| title_sort | estimation of models in a rasch family for polytomous items and multiple latent variables |
| topic | pseudo-likelihood estimation log-linear-by-linear association models logistic regression multinomial logistic regression conditionally specified models R |
| url | http://www.jstatsoft.org/v20/i06/paper |
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