hierarchical regression with different DV for each block?

vtmft

New Member
#1
Greetings.

I'm trying to figure out how to do a hierarchical regression whereby the DV regressed on block 1 becomes the IV in block 2, which then has a different DV. That DV then becomes the IV in block 3, at which point the final DV is in place.

It'd look something like this:
Block 1: y1 regressed on x1 x2 x3 x4 x5
Block 2: y2 regressed on "y1"
Block 3: y3 regressed on "y2"

Y3 is my final outcome variable of most interest.

I'm told that this can be accomplished in STATA (perhaps using the nestreg command). I imagine R could handle it as well.

Can anyone help me out with syntax/steps to achieve this, preferably using STATA (or R)?

Thank you so much!
GH
 
#2
How do you know there is nesting and hierarchy in your design? Please explain more about your research, sample sizes in each group, variables in each group, the groups themselves, etc. Is each "Block" supposed to be a nesting level? Please explain much more.
 

Dason

Ambassador to the humans
#3
I agree - could you elaborate a little more on what you're actually interested in doing by describing your actual situation? It sounds like you just need some sort of hierarchical model.
 

vtmft

New Member
#4
Thank you for the responses. I'm using survey data, so I'm not exactly comparing specific groups (e.g., not testing moderation). And I'm using hierarchical regression in the theoretically-ordered blocks of variables sense, as opposed to the hierarchical linear modeling nested variables sense, so there are no nested variables per se (e.g., no students, in classrooms, in schools, in districts, etc.). Basically, I'm testing a family stress model. I was originally creating a structural equation model, but had to abandon this due to difficulties I was having with creating a composite variable of five indicators of stress (these five indicators would now constitute the first block of variables in my hierarchical regression model). So, in order to test the mechanism that I was essentially testing with SEM, I was thinking I could run this modified hierarchical regression in which the dependent variable for Block 1 becomes the IV of Block 2 and so forth. Each additional block then does not represent a nesting level but another (endogenous) variable in my analysis. Thus, Block 1 contains five stress variables that need to be controlled, and Blocks 2 and 3 contain "mediating" variables (i.e., two different constructs that family stress theory suggests are pathways for the transmission of stress), if you will (I don't necessarily intend to test for mediation though). The effects of variables in Blocks 2 and 3 are the ones I'm particularly interested in on the final outcome variable (in this case, it is a measure of family functioning).

I could do a simple hierarchical regression, which would let me know the effect of my main variables of interest above and beyond those control variables on a single outcome variable. However, after being alerted to a different type of analysis, I really like the idea of this modified hierarchical approach in which subsequent DVs are incorporated into blocks. It seems I get much more valuable information out of the latter option, and a better test of the mechanism of family stress.

I attached a screenshot from the article that prompted my interest in this kind of modified hierarchical regression. Above each column of data is, for example, "Step 1: Mastery" with Mastery being the dependent variable for that block. You can then see that Mastery was entered into Block 2, with Burden regressed upon the blocks, and so forth.

Please let me know if you need more information. Thank you again for the help!
 
#5
It'd look something like this:
Block 1: y1 regressed on x1 x2 x3 x4 x5
Block 2: y2 regressed on "y1"
Block 3: y3 regressed on "y2"

Y3 is my final outcome variable of most interest.
Such a model structure is called Wold's causal chain. It can (surprisingly) be estimated with ordinary least squares. Otherwise one might believe that it should be estimated with a system approach (as in structural equations) like for example two stage least squares (2sls).
 
#6
I could do a simple hierarchical regression, which would let me know the effect of my main variables of interest above and beyond those control variables on a single outcome variable. However, after being alerted to a different type of analysis, I really like the idea of this modified hierarchical approach in which subsequent DVs are incorporated into blocks. It seems I get much more valuable information out of the latter option, and a better test of the mechanism of family stress.
I can't see yet how you can relate this design to a hierarchical regression in which the sub-DVs are being treated like nested data, because they apparently are not nested. I doubted that this design is hierarchical in the first place, since I could not see any signs of nesting or random effects in the steps explained. Now with Greta's interesting answer, I feel somehow more confident that the design is not really hierarchical, but still not fully sure. Please explain why you thought this is hierarchical? :)
 

vtmft

New Member
#7
It is hierarchical in terms of the ordered, logical input of variables at each step in the regression model as opposed to stepwise regression where variables are all considered at one time for statistical significance and then empirically chosen (i.e., without prior theory ordering at which step they enter the model). The data are not "nested" in the sense of hierarchical linear modeling.

Greta - thank you for naming what I'm attempting to do. Of course, now I need help in executing it. Any idea on how to do such a thing in R or STATA?

Incidentally, I had tried estimating the model using structural equation modeling but ran into problems trying to create a composite variable out of the five indicators that would make up my first block of variables. Basically, they're control variables, and I would have simply made them covariates in my SEM but this dropped my degrees of freedom and given my already somewhat small sample size, I couldn't afford to lose any more power.

Thank you for any help you can offer regarding how I could actually perform this analysis.
 
#8
I could do a simple hierarchical regression, which would let me know the effect of my main variables of interest above and beyond those control variables on a single outcome variable.
It is hierarchical in terms of the ordered, logical input of variables at each step in the regression model as opposed to stepwise regression where variables are all considered at one time for statistical significance and then empirically chosen (i.e., without prior theory ordering at which step they enter the model). The data are not "nested" in the sense of hierarchical linear modeling.
Well I doubt that counts as "hierarchical" model then, and that you can run a hierarchical regression for it, in the first place.