Hello all,
I am coming towards the end of my PhD - as part of my analysis I used hierarchical regression (forwards). I selected this method because it was the one that was used in all the previous studies I found that investigated the topic I am studying. A friend has suggested that, during my viva, I should be prepared to defend why I didn't do backwards hierarchical regression. Apart from the reason I have just stated, are there advantages/disadvantages to each type (backwards v forwards hierarchical regression) that I should be aware of? I can find articles comparing stepwise regression to hierarchical regression but not forwards v backwards. One included backwards hierarchical regression as a type of stepwise regression? Is this correct? (I understand the limitations of stepwise regression). Thank you.
In my view, the forward approach is more useful if you are starting with a clear set of theoretical (and/or empirical) expectations about causal order of the IVs to one another and to the DV. In other words, when you have reasons to expect some of the IVs to be common causes of other IVS and of the DV, and therefore possible sources of spuriousness, and you also have expectations about which IVs mediate the relationships of other IVs to the DV, the forward approach is preferable.
In that application, you might enter a small subset of the IVs on the first step (those of primary theoretical interest in your field), control for likely common causes on the second step (to rule out spuriousness in the effects of primary interest), and enter likely mediators on the third step (to sort out direct effects vs. indirect effects for the IVs of primary interest). The second and third steps could be reversed, if that makes it easier to explain/interpret the results. If reversed (and assuming your cases are individual people), then you might divide the common causes into two bunches, entering non-demographic common causes on the third step and demographic IVs as a fourth and final step. (A demographic variable can virtually never mediate.)
None of these guidelines is set in stone, but if you have a clear causal model in mind, the forward approach can help you examine the theory or theories that led to the model. For example, if a particular IV goes from significant to non-significant with the addition of a particular set of controls, you don't just throw that IV out of the model. Rather you can interpret its non-significance as demonstrating that its effect is entirely indirect (or spurious, as the case may be).
The backward approach, on the other hand, is more useful if your main goal is to simultaneously maximize the predictive power of your final regression and minimize the number of variables used to do so. If you don't have, or don't want to examine, a clear theoretical structure of cause and effect, you can start with a big model that includes all the IVs you have measured, then discard the non-significant IVs from that initial model on the second step; rinse and repeat until you are down to a model that is, arguably, optimal for predictive purposes -- the highest (adjusted) R-square you can get with the smallest number of IVs you have to include.
And yes, in my view the backward approach would be more accurately categorized as a form of stepwise regression than as hierarchical, as the latter term is most often used. Even without knowing the specifics of your project, my guess is that forward hierarchical was the right choice.
I hope this is helpful; best wishes for the successful completion of your PhD.
Thank you Burke, that was very helpful indeed. Everything you have said confirms that I have made the right choice, and I now feel more confident about defending my reason for doing so. Best wishes.
If I was the opponent I would be critical to why you applied a stepwise regression approach, which is a criticized analytical approach.
Article Step away from stepwise
Why haven't you applied causal diagrams in choosing the IVs (Directed Acyclic Graph (DAG) http://www.dagitty.net/ ). A simple drawing of how variables are associated may be very helpful in choosing the most appropiate IVs, and not include intermediate variables. A regression model does not tell you how all variables are mutually associated, and inclusion of a certain variable may at the worst, lead to collider bias.
https://catalogofbias.org/biases/collider-bias/#:~:text=A%20distortion%20that%20modifies%20an,of%20the%20exposure%20and%20outcome
Just some food for discussion before you defense. I just want to help being prepared for these questions.
Good luck with the remaining of your PhD.
Thanks, Jesper. I have seen similar articles. Feeling confident about my choice!
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