General Linear Model (GLM): A linear model is a statistical model with linear (additive) combinations of parameter constants describing effect sizes and variance components. Linear models can describe non-linear trends in covariates, for example by transformation of the data or fitting a polynomial model. GLM is a generic term for parametric analyses of variance that can accommodate combinations of factors and covariates, and unbalanced and non-orthogonal designs. GLMs generally use an unrestricted model for analysing combinations of fixed and random factors.
Significant effects are tested with the F statistic, which is constructed from sums of squared deviations of observations from means, adjusted for any non-orthogonality. This statistic assumes random sampling of independent replicates, homogeneous within-sample variances, a normal distribution of the residual error variation around sample means, and a linear response to any covariate. Transformations may be necessary to the response and/or covariate to meet these assumptions. A further generalization of GLM, the Generalized Linear Model (GLIM), accommodates non-normally distributed response variables, and partitions the components of variation using maximum likelihood rather than sums of squares.
Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.