Models for Categorical Response Variables

  • Helge Toutenburg
  • Shalabh
Part of the Springer Texts in Statistics book series (STS)


Generalized linear models (GLMs) are a generalization of the classical linear models of regression analysis and analysis of variance, which model the relationship between the expectation of a response variable and unknown predictor variables according to
$$\begin{array}{ll} {\rm E}(y_i) &= x_{i1}\beta_1 + \ldots + x_{ip}\beta_p\\ &= x^{\prime}_i \beta.\\ \end{array}$$
The parameters are estimated according to the principle of least squares and are optimal according to the minimum dispersion theory or, in the case of a normal distribution, are optimal according to the ML theory (cf. Chapter 3).


Contingency Table Saturated Model Binary Response Loglinear Model Independence Model 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Institut für StatistikLudwig-Maximilians-UniversitätMünchenGermany
  2. 2.Department of Mathematics & StatisticsIndian Institute of TechnologyKanpurIndia

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