Models for Multicategorical Responses: Multivariate Extensions of Generalized Linear Models

  • Ludwig Fahrmeir
  • Gerhard Tutz
Part of the Springer Series in Statistics book series (SSS)

Abstract

In this chapter the concept of generalized linear models is extended to the case of a vector-valued response variable. Consider Example 2.1, where we were interested in the effect of risk factors and antibiotics on infection following birth by caesarian section. In this example the response was binary, distinguishing only between occurrence and nonoccurrence of infection, and thereby ignoring that the data originally provided information on the type of infection (type I or II) as well. It is possible, however, to use this information by introducing a response variable with three categories (no infection, infection type I, infection type II). Naturally, these categories cannot be treated as a unidimensional response. We have to introduce a (dummy) variable for each category, thus obtaining a multivariate response variable. Therefore, link and response functions for the influence term will be vector-valued functions in this chapter. The focus is on multicategorical response variables and multinomial models. Variables of this type are often called polychotomous, the possible values are called categories. Extension to other multivariate exponential family densities is possible but not considered in this text.

Keywords

Generalize Linear Model Generalize Estimate Equation Infection Type Canopy Density Correlate Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Ludwig Fahrmeir
    • 1
  • Gerhard Tutz
    • 2
  1. 1.Department of StatisticsUniversity of MunichMünchenGermany
  2. 2.Department of StatisticsUniversity of MunichMünchenGermany

Personalised recommendations