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If I have a model y ~ A*B which is y ~ A+B+AB, is the interaction term AB considered as a covariate or not? I'm not sure whether I should say that there are three covariates or two covariates in this model. Thank you.

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I would argue that A and B are the covariates, not AB.

Consider your data as coming from a multivariate distribution. You have marginal variables A, B, and y. The dependence between them is such that the way A influences y depends on B, hence the interaction term, but I still say that there’s a trivariate distribution of A, B, and y.

The interaction term gets its own parameter in the regression equation, however.

EDIT

The terminology gets even worse. Let’s say that A is a binary variable denoting group membership, control vs treatment, and B is some other source of variability. If you’re interested in if the treatment has any impact and run ANCOVA with $\hat{y}=\beta_0+\beta_1A +\beta_2B$, I would call A the group variable and B a covariate. If you throw in the interaction term, then I would say there is a group variable, a covariate, and their interaction.

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    $\begingroup$ To add to the last point: when talking about a model's predictors, some divide them into factors (categorical) and covariates (integer or continuous). But I agree with @Dave's first point, too: each predictor (but not each term composed of predictor interactions) is typically called a covariate. $\endgroup$ – rolando2 Mar 7 '20 at 18:11

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