Chapter 11 - General Linear Model (ANCOVA)

Abstract

The “model of the mean,” t-test, simple linear regression, and analysis of variance (ANOVA) are all just special cases of a very general and powerful statistical model, the general linear model. This model expresses a continuous response as a linear combination of the effects of discrete and/or continuous explanatory variables plus a single random contribution from a normal distribution, whose variance is estimated along with the coefficients of all discrete and continuous covariates and possible interactions. Models that contained both types of explanatory variables were usually treated as ANOVAs with typically a single continuous covariate to correct for preexisting variation among experimental units. These models were called analysis of covariance (ANCOVA) models. In WinBUGS, it is much easier to fit the means parameterization of the model, i.e., to specify three separate linear regressions for each mountain range. The effects are trivially easy to recover as derived parameters by just adding a few WinBUGS code lines. This allows for better comparison between input and output values.