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I have three predictor variables: one is measured, two were manipulated (2x2). The dependent variable is measured.

My main hypothesis is that the continuous predictor would lower the effect of the interaction of the manipulated predictors on the dependent variable.

Should I use hierarchical linear regression? In Step 1, I would add all predictors. In Step 2 I would add the interaction of the manipulated predictors. And in Step 3, the interaction of all three predictors. Or should I use ANCOVA?

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It sounds like your hypothesis is about a 3-way interaction term in a linear model (of which ANCOVA is one variety). I don't see an obvious hierarchy in your design.

I would be careful, though. Quantifying high-dimensional interactions is challenging and needs a large amount of data to estimate robustly. You may also need to think carefully about whether linear terms alone are sufficient to describe the effects of the individual predictors.

EDIT: I just learnt that the term 'hierarchical regression' refers to a model selection procedure and is distinct from hierarchical modelling. This would be an appropriate modelling selection approach. However, the approach you describe is not an appropriate implementation because you are adding terms in groups (first all main effects, then all two-way interactions..) Instead, you should add/remove terms one at a time; starting with the full model and removing one at a time might be best.

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