A general linear model is a flexible modeling framework for testing the effects of any combination of categorical and continuous predictor variables on a continuous response measure. The approach includes regression, ANOVA, t-tests and ANCOVA as special cases. The general linear model framework also serves as a starting point for expanding into more complex statistical models.

As with other statistical tests, general linear models have certain assumptions that must be satisfied if our inferences are going to be correct.

General linear models allow us to test whether the effects of predictors on a response variable are constant or whether these effects depend on the value of some other predictor. Linear models allow for any combination of interactions between categorical and continuous predictors.

For a case study including a hypothesis involving a statistical interaction, see the painted turtle nesting example.

General linear models assume that predictors are related to the response variable in a linear way, but in many cases biological relationships are non-linear. Luckily we can linearise non-linear relationships using transformations, quadratic terms or breakpoints.

1. Give three reasons that studies in biology sometimes have more than one explanatory variable. [Credit: Whitlock and Schluter, 2009]

2. Write an “R formula” for a linear model with two independent variables and one dependent variable- dog breed, brand of dog food, and the dog’s lifespan, respectively-, and include an interaction effect between the two dependent variables.

3. Which of the following methods could be categorized under “general linear models”?

   Binomial test

   Goodness-of-fit test

   Chi-squared test for independence

   t-test

   ANOVA

   Regression

   Multiple linear regression

4. When an interaction between two (or more) factors is present, what conclusions would you draw about the factors?