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A Gibbs Sampler for the (Extended) Marginal Rasch Model.

Maris G, Bechger T, San Martin E - Psychometrika (2015)

Bottom Line: In their seminal work on characterizing the manifest probabilities of latent trait models, Cressie and Holland give a theoretically important characterization of the marginal Rasch model.Such an approach would be highly efficient as its computational cost does not depend on the number of respondents, which makes it suitable for large-scale educational measurement.In this paper, such an approach will be developed and its operating characteristics illustrated with simulated data.

View Article: PubMed Central - PubMed

ABSTRACT
In their seminal work on characterizing the manifest probabilities of latent trait models, Cressie and Holland give a theoretically important characterization of the marginal Rasch model. Because their representation of the marginal Rasch model does not involve any latent trait, nor any specific distribution of a latent trait, it opens up the possibility for constructing a Markov chain - Monte Carlo method for Bayesian inference for the marginal Rasch model that does not rely on data augmentation. Such an approach would be highly efficient as its computational cost does not depend on the number of respondents, which makes it suitable for large-scale educational measurement. In this paper, such an approach will be developed and its operating characteristics illustrated with simulated data.

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Autocorrelation for lag 0 to 50, after a burnin of 49 iterations, for  based on 5000 replications of the Gibbs sampler.
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Fig2: Autocorrelation for lag 0 to 50, after a burnin of 49 iterations, for based on 5000 replications of the Gibbs sampler.

Mentions: Figure 2 gives the autocorrelation for lag 0 to 50, after discarding the first 49 iterations. It is clear from Figure 2 that except for the lag 1 autocorrelation, autocorrelation is negligible.Fig. 2


A Gibbs Sampler for the (Extended) Marginal Rasch Model.

Maris G, Bechger T, San Martin E - Psychometrika (2015)

Autocorrelation for lag 0 to 50, after a burnin of 49 iterations, for  based on 5000 replications of the Gibbs sampler.
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4644215&req=5

Fig2: Autocorrelation for lag 0 to 50, after a burnin of 49 iterations, for based on 5000 replications of the Gibbs sampler.
Mentions: Figure 2 gives the autocorrelation for lag 0 to 50, after discarding the first 49 iterations. It is clear from Figure 2 that except for the lag 1 autocorrelation, autocorrelation is negligible.Fig. 2

Bottom Line: In their seminal work on characterizing the manifest probabilities of latent trait models, Cressie and Holland give a theoretically important characterization of the marginal Rasch model.Such an approach would be highly efficient as its computational cost does not depend on the number of respondents, which makes it suitable for large-scale educational measurement.In this paper, such an approach will be developed and its operating characteristics illustrated with simulated data.

View Article: PubMed Central - PubMed

ABSTRACT
In their seminal work on characterizing the manifest probabilities of latent trait models, Cressie and Holland give a theoretically important characterization of the marginal Rasch model. Because their representation of the marginal Rasch model does not involve any latent trait, nor any specific distribution of a latent trait, it opens up the possibility for constructing a Markov chain - Monte Carlo method for Bayesian inference for the marginal Rasch model that does not rely on data augmentation. Such an approach would be highly efficient as its computational cost does not depend on the number of respondents, which makes it suitable for large-scale educational measurement. In this paper, such an approach will be developed and its operating characteristics illustrated with simulated data.

Show MeSH