MIVA: An Alternative Method to Generalized Linear Models

Summary

The paper concernes an alternative method to that of generalized linear models. It uses mixed distributional classes to analyze association structures between both qualitative and quantitative characteristics observed in a study. In addition to tests of statistical significance the presented method yields unique systems of pairwise, partial, multiple and global mixed measures of association to describe practical relevance of discovered relations. Some of these coefficients are well-known ones supporting plausibility of the general concept, most of them are new ones. Between coefficients within a system exists a strict hierarchy and all measures may be generated from those ones of lower dimension. The corresponding information statistics (if independent) are additive. Interaction concepts may be applied. These measures may be used as an additional information to generalized linear model analysis, also autonomously in an exploratory model search or model selection sense but even for confirmatory statistical analyses.