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I am interested in understanding if two predictors variables are associated with treatment outcome (DV). I included two covariates that 1) differed across my levels of IV (age) and 2) another that is strongly associated with the DV (baseline functioning). I ran a simultaneous multiple regression with the covariates and both IVs entered into the same time to estimate the unique relationships between the IVs with the DV.

A reviewer implied that hierarchical regression was needed (enter covariates into step 1 and IVs into step 2. My understanding is this would be asking a different question and that it is totally appropriate to include covariates in a single step in simultaneous regression.

Another reviewer suggested that only ANCOVA was appropriate to address this question. I'm pretty confident that this is a consequence of the reviewer being trained in ANOVA but not regression models, and is a misunderstanding.

Welcoming feedback and any academic citations to support the statistical approach.

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    $\begingroup$ Welcome to Cross Validated? Is an IV an instrumental variable in this case? $\endgroup$ Commented Feb 29, 2024 at 15:33

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Why not do the first reviewer the favor and run the regression with just the covariates in Step 1, then add the substantive predictors in Step 2? From my perspective, I don't see how it could hurt anything. Or, put differently, it makes the reviewer happy and (probably) does not make you unhappy ;-)

ANCOVA would be equivalent to linear regression (both fall under the general linear model) and you would get the exact same results, so that other reviewer's point is unclear to me.

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First, it is entirely appropriate to enter both variables at once. This is what the multiple in multiple regression means. It is not necessary to do this in a hierarchical way.

However, second, I don't see how it could hurt to do a hierarchical regression (although you'll have to choose some order for the hierarchy). The first step does add some information. But be careful not to use the first step as a screening method.

Third, ANOVA, ANCOVA and multiple regression are the same model. All are, in matrix terms $Y = XB + e$. ANOVA is used when the independent variables are categorical, but regression can handle this. ANCOVA is for some continuous variables, but regression can handle this, as well. The output will look different but the meaning will be the same.

(ANOVA and regression developed separately, and some people still haven't caught on to the equivalence.)

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