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on Discrete Choice Models |
| By: | ALBERTO MAYDEU (Instituto de Empresa) |
| Abstract: | We introduce a multidimensional latent trait model for binary data with non-monotone item response functions. We assume that the conditional probability of endorsing an item is a normal probability density function, and that the latent traits are normally distributed. The model yields closed form expressions for the moments of the multivariate Bernoulli (MVB) distribution. As a result, cell probabilities can be computed also in closed form, regardless of the dimensionality of the latent traits. The model is an ideal point model in the sense that a respondent -precisely at the ideal point (the mode of the item response function)- endorses the item with probability one. |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:emp:wpaper:wp05-11&r=dcm |
| By: | ALBERTO MAYDEU (Instituto de Empresa) |
| Abstract: | We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables of arbitrary dimensions. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any consistent and asymptotically normal estimator. We show that when r is small (r = 2) the proposed statistics have more accurate empirical Type I errors and are more powerful than Pearson´s X2 for a widely used item response model. Also, we show that the proposed statistics are asymptotically chi-squared under the null hypothesis when applied to subtables. |
| Date: | 2005–02 |
| URL: | http://d.repec.org/n?u=RePEc:emp:wpaper:wp05-12&r=dcm |