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Chapter 4: Introduction to Linear Models

Chapter 4: Introduction to Linear Models

pp. 45-61

Authors

, Deakin University, Victoria, , University of Melbourne
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Extract

There is a daunting array of statistical “methods” out there – regression, ANOVA, loglinear models, GLMMS, ANCOVA, etc. They often are treated as different data analysis approaches. We take a more holistic view. Most methods biologists use are variations on a central theme of generalized linear models – relating a biological response to a linear combination of predictor variables. We show how several common “named” methods are related, based on classifying biological response and predictor variables as continuous or categorical. We use simple regression, single-factor ANOVA, logistic regression, and two-dimensional contingency tables to show how these methods all represent generalized linear models with a single predictor. We describe how we fit these models and outline their assumptions.

Keywords

  • linear model
  • ordinary least squares
  • maximum likelihood
  • exponential distribution
  • link function
  • generalized linear model
  • analysis of variance
  • deviance
  • assumptions

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