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Generalized Linear Models

In: Statistical Modeling and Computation

Author

Listed:
  • Dirk P. Kroese

    (The University of Queensland, School of Mathematics and Physics)

  • Joshua C. C. Chan

    (Australian National University, Department of Economics)

Abstract

The linear models introduced in Chap. 4 deal with continuous response variables—such as height and crop yield—and continuous or discrete explanatory variables. For example, under a normal linear model, the responses $$\{Y _{i}\}$$ are independent of each other, and each has a normal distribution with mean $$\mu _{i} = \mathbf{x}_{i}^{\top }\boldsymbol{\beta }$$ , where $$\mathbf{x}_{i}^{\top }$$ is the ith row of the design matrix X. However, these continuous models are obviously not suitable for data that take on discrete values. For example, we might want to analyze women’s labor market participation decision (whether to work or not), voters’ opinion of the government (rating on the government performance on a scale of five), or the choice among a few cereal brands, as a function of one or more explanatory variables. In this chapter we discuss models that are suitable for analyzing these discrete response variables. We will first introduce the flexible framework of generalized linear models.

Suggested Citation

  • Dirk P. Kroese & Joshua C. C. Chan, 2014. "Generalized Linear Models," Springer Books, in: Statistical Modeling and Computation, edition 127, chapter 0, pages 265-286, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-8775-3_9
    DOI: 10.1007/978-1-4614-8775-3_9
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