General Linear Model:
General (or generalized) linear models (GLM), in contrast to linear models, allow you to describe both additive and nonadditive relationship between a dependent variable and N independent variables. The independent variables in GLM may be continuous as well as discrete. (The dependent variable is often named "response", independent variables  "factors" and "covariates", depending on whether they are controlled or not).
Consider a clinical trial investigating the effect of two drugs on survival time. Each drug is tested at three levels  "not used", "low dose", "high dose", and all the 9 (=3x3) combinations of the three levels of the two drugs are tested. The following general linear model might have been used:

where Y is survival time (response), i and j correspond to the three levels of drug I and drug II respectively, X is age, C_{i} are additive effects (called "main effects") of each level of drug I, D_{j} are main effects of drug II, R_{ij} are nonadditive effects (called interaction effects or simply "interactions") of drugs I and II, N is random deviation.
We have here three independent variables: two discrete factors  "drug I" and "drug II" with three levels each, and a continuous covariate "age".
In this particular case, because each of the two factors (drugs) has a zero level i,j=1 ("not used"), main effects C_{1}, B_{1}, and interactions R_{1j}, j=1,2,3; R_{i1}, i=1,2,3 are zeros. The remaining unknown coefficients  A, B, C_{i}, D_{j}, R_{ij}  are estimated from the data. The main effects C_{i}, D_{j} of the two drugs and their interaction effects R_{ij} are of primary interest. For example, their positive values would indicate a positive effect  longer survival time due to use of the drug(s).
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