Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer‐adaptive practice

@article{Brinkhuis2019DynamicEI,
  title={Dynamic estimation in the extended marginal Rasch model with an application to mathematical computer‐adaptive practice},
  author={Matthieu J. S. Brinkhuis and Gunter K. J. Maris},
  journal={The British Journal of Mathematical and Statistical Psychology},
  year={2019},
  volume={73},
  pages={72 - 87}
}
We introduce a general response model that allows for several simple restrictions, resulting in other models such as the extended Rasch model. For the extended Rasch model, a dynamic Bayesian estimation procedure is provided, which is able to deal with data sets that change over time, and possibly include many missing values. To ensure comparability over time, a data augmentation method is used, which provides an augmented person‐by‐item data matrix and reproduces the sufficient statistics of… 

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References

SHOWING 1-10 OF 54 REFERENCES
A Gibbs Sampler for the (Extended) Marginal Rasch Model
TLDR
An approach for constructing a Markov chain - Monte Carlo method for Bayesian inference for the marginal Rasch model that does not rely on data augmentation is developed and its operating characteristics illustrated with simulated data.
Turning Simulation into Estimation: Generalized Exchange Algorithms for Exponential Family Models
TLDR
This work frames the Exchange algorithm as a mixture of Metropolis transition kernels and proposes strategies that automatically select the more efficient transition kernels, achieving significant improvements in convergence rate and autocorrelation of the Markov chain.
Fitting and Testing Conditional Multinormal Partial Credit Models
A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland in Psychometrika
The calculation of posterior distributions by data augmentation
TLDR
If data augmentation can be used in the calculation of the maximum likelihood estimate, then in the same cases one ought to be able to use it in the computation of the posterior distribution of parameters of interest.
A Connection between Rasch's Item Analysis Model and a Multiplicative Poisson Model
Introduction of random row effects in Rasch's item analysis model (or the two-way logit-additive model for binary data), followed by a (not very controversial) extension of this model leads to a
A goodness of fit test for the rasch model
The Rasch model is an item analysis model with logistic item characteristic curves of equal slope,i.e. with constant item discriminating powers. The proposed goodness of fit test is based on a
The Dutch Identity: A New Tool for the Study of Item Response Models.
The Dutch Identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions (IRFs) and the latent trait
Computing Elementary Symmetric Functions and Their Derivatives: A Didactic
TLDR
How various recursion formulas work and how they are used to compute elementary symmetric functions and their derivatives are described to promote a more thorough understanding of item parameter estimation in the Rasch model among both measurement specialists and practitioners.
Filtering Data for Detecting Differential Development
TLDR
This work proposes the use of simple data filters to obtain a reduced set of relevant data, which allows for simple checks on the relative development of persons, items, or both.
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