Model: The hypothesised effect(s) on a response, which can be tested with ANOVA for evidence of pattern in the data. An ANOVA model contains one or more terms, each having an effect on the response that is tested against unmeasured error or residual variation. A model with a single factor (whether categorical or covariate) is written: Y = A + ε, and the ANOVA tests the term A against the residual ε. A fully-replicated model with two crossed factors is written: Y = A + B + B*A + ε, and the two-way ANOVA tests each main effect A and B, and the interaction B*A, against the residual ε.
Models with multiple factors require care with declaring all terms in a statistical package. For example, the cross factored with nesting model: Y = C|B'(A) + ε is analysed by declaring the terms: C|A + C|B(A). The two-factor randomised block model: Y = S'|B|A is analysed by declaring the terms: S|B|A - S*B*A for a Model-1 analysis, or the terms: S + B|A for a Model-2 analysis.
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.