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Title: A fused lasso penalization for the nominal response model Authors:  Michela Battauz - University of Udine (Italy) [presenting]
Abstract: The nominal response model, which can be used to analyze the categorical responses to a set of items, does not assume a predetermined order for the response categories. Due to this feature, the model is particularly suitable to group the response categories, which is pursued through a fused lasso penalization. Besides forcing the slope parameters towards a common value, the penalty adopted shrinks these coefficients towards zero. This is particularly interesting in the multidimensional nominal response model, since it is able to perform the selection of the latent variables related to each item. Hence, the proposal tends to reduce the large number of parameters of this model either by grouping the slope parameters of the response categories, or by setting all the slope parameters of one latent variable to zero. Simulation studies show that the resulting estimator not only presents a lower root mean square error, but also has a lower bias in small samples than the maximum likelihood estimator.