Jochen, hierarchical regression is used in several different ways in different fields or by different authors. Nicola's description is one (fairly common) use in social science and psychology. It describes a strategy of blocking variables and testing in stages. For example, one can have all demographic factors added as a block and then a second block to add in main effects of predictors that are of theoretical interest.

Nicola: the answer is that the final model treats all predictors equivalently - there is no priority to predictors entered earlier (though there are ways to force this e.g., by using Type I sums of squares etc.). The purpose of blocking is to provide a combined test of the variables in each block and reduce the reliance of multiple testing. You also get a test of the differences in the two models. The tests of individual predictors in the final model would be identical to the simultaneously adding all predictors. Bear in mind though that these tests of individual predictors test the unique effect of a predictor (excluding variance shared with other predictors). This means that collinearity between predictors can reduce power of the individual tests quite considerably (e.g., all predictors could be significant in terms of their simple correlation with Y, the overall model could be highly significant and yet no individual predictor have a significant effect in the regression).

There is a further complication with interaction effects - but that's an extra layer of complexity.

I think you are not talking about hierarchical regression but about multiple regression.

Hierarchical regression would mean that a coefficient in your regression model won't be given a fixed value but itself be described by a probability distribution. This coefficient is called a "random effect" (in contrasts to the "fixed effects" as coefficient that are estimated by a fixed value). This is particularily useful when your data consists of repeated (correlated) measures, so that the random effect can account for the correlation structure.

In a multiple regression, several predictors (like age, gender, income) are used to model/predict a response (the DV). The model doe not care about the "order" of the predictors. A model with age, gender and income will predict the DV depending on income "adjusted for age and gender", as it will predict the DV depending on age "adjusted for gender and income", or predict the DV depending on income "adjusted for age and gender". There are simply differen perspectived on the very same model.

Tests on the predictors (e.g. ANOVAs) can be performed to show the contribution of a predictor (to reduce the residual SS or the deviance) when no, some or all other predictore are already considered. For instance, to see if income reduces the residual SS when age and gender are already considered (to explain the variance), then one would carry out an ANOVA comparing a model with all three predictors to a model with age and gender as predictors. Some software calculate ANOVAs by subsequently adding predictors to the model and testing each model with the previous (the first one is the "null model" or "intercept-only model" fitting only the grand mean). Here, the order of adding the predictors is (well, can be) relevant.

Jochen, hierarchical regression is used in several different ways in different fields or by different authors. Nicola's description is one (fairly common) use in social science and psychology. It describes a strategy of blocking variables and testing in stages. For example, one can have all demographic factors added as a block and then a second block to add in main effects of predictors that are of theoretical interest.

Nicola: the answer is that the final model treats all predictors equivalently - there is no priority to predictors entered earlier (though there are ways to force this e.g., by using Type I sums of squares etc.). The purpose of blocking is to provide a combined test of the variables in each block and reduce the reliance of multiple testing. You also get a test of the differences in the two models. The tests of individual predictors in the final model would be identical to the simultaneously adding all predictors. Bear in mind though that these tests of individual predictors test the unique effect of a predictor (excluding variance shared with other predictors). This means that collinearity between predictors can reduce power of the individual tests quite considerably (e.g., all predictors could be significant in terms of their simple correlation with Y, the overall model could be highly significant and yet no individual predictor have a significant effect in the regression).

There is a further complication with interaction effects - but that's an extra layer of complexity.

@ Manuel: I don't know. I have no experience with partial regression.

@ Thom: thank you for clarification. That's actually nice about RG that the different disciplines start taking to (with) each other. This may probably promote some unification of the terms and languages, making inter-disziplinary communication easier.

Thank-you so much Jochen Wilhelm, Manuel Weinkauf and Thom Baguley! I always know when I post questions on ResearchGate that I'll get excellent answers! Jochen, you explanation of how each IV in the regression predicting the DV is adjusted for the other variables in the model made so much sense. Manuel, I'll have to research partial regression as I've not heard of it before, but thanks for the suggestion. And Thom and Jochen, i agree one of the great things about social media platforms like researchgate is that it gives researchers from different disciplines the opportunity to discuss/share their different perspectives on research methods

Dear Nicola

In hierarchical regression analysis, it is more accurate to enter variables into steps according to certain theoretical bases. A good solution would be to enter the control variables into the equation by the "stepwise" regression technique in the first step and enter the main variables of the research into the equation by "enter" regression method in the continuing steps by considering a theoretical basis.

Best.

Mithat