Advances and Applications in Statistics
Volume 18, Issue 2, Pages 109 - 126
(October 2010)
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DISTRIBUTION-FREE ITEM RESPONSE MODEL BASED ON MARGINAL MAXIMUM LIKELIHOOD ESTIMATION
M. E. Ferrão, P. Costa and J. M. R. Gama
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Abstract: Two-parameter logistic item response model is a latent variable model which is widely used both in educational and psychological data analysis. In this paper, we propose an extension of the marginal maximum likelihood estimation using a wavelet density estimator for the latent variable instead of assuming a normal distribution. The approach can be straightforward applied to the Rasch model and to the three parameter logistic model. Illustrations with simulated and real data are given. Several statistics such as mean absolute error, mean square error, integrated squared error and chi-square goodness-of-fit test, are used to compare the results obtained. |
Keywords and phrases: item response model, non-parametric estimation, marginal maximum likelihood estimation, wavelet density estimator, educational performance. |
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