Title: Latent block distance-association model
Authors: J Fernando Vera - University of Granada (Spain) [presenting]
Abstract: Log-lineal models with a large number of parameter to be estimated results in tables with large number of cells. Distance association models have been proposed to reduce the number of parameters and also facilitate the interpretation. For tables involving profiles, the DA model can be estimated but the given results may be difficult to interpret because the presence of a large amount of modalities and/or zeros. Although collapsing rows is an advisable procedure this procedure may still fail in the representation of associations for tables having a large number of modalities in the response variable, and in particular for sparse tables as a profile by profile sparse contingency table. A latent block distance association model is formulated that aims the simultaneous partitioning of the rows and the columns of a contingency table, while the between blocks association is represented in a low dimensional space in terms of Euclidean distances. In the LBDA model, odds are defined in terms of the block-related main effects and of the distances, while odds ratio are defined only in terms of the squared distances.