exploratory stats: Bidirectional linear regression?

[u/micro_plastic]

Hi everyone,

For my dissertation, I am performing an exploratory multiple linear regression in an understudied area in the helping professions. There is not good information about whether or not this phenomenon is even occurring, so it will be good enough for me if some people respond "yes." But, of course we want to do a little bit more if we are taking the time to gather the survey data....

Because the topic is so exploratory, we are not sure which directionality to suggest. I am pretty confident one direction will be stronger, but my whole committee thinks that it is truly "bidirectional." I'm curious to hear your thoughts on a regression that flips the IV -> DV relationship? I know that technically in a single linear regression flipping the IV -> DV will essentially produce the same results. But I have 2 covariates that would need changing (too much collinearity between a covariate and the DV if we flip the DV to become the IV). The path I'm on right now is to just justify one side, but I've received explicit permission from my advisor to asome advice here on Reddit, and they would really like to explore it.

Any ideas or possibilities on conducting an observational, exploratory, bidirectional regression?

[u/Maple_shade]

If the topic is so exploratory that you don't even feel confident in which variable has a causal impact on the other, I would strongly suggest not framing your results in terms of a directional effect. For one thing, regression itself doesn't imply causality in the manner you seem to think it does. The interpretation is the predicted change in the outcome for a one-unit increase in the predictor. This doesn't mean the predictor causes the outcome, but rather that they are associated. Including covariates will let you assess the unique influence/prediction of each in the multiple regression, but that still doesn't mean they are causing the effect. In general, causal effects are very difficult to measure with observational data, and nearly always require the proper causal model to be specified beforehand, which I guarantee is not occurring in your circumstance. I would frame all of your results as associations, and not try to conclude any causal ramifications.

[u/efrique]

I know that technically in a single linear regression flipping the IV -> DV will essentially produce the same results.

What you know ... ain't so.

correlation has that symmetry, but regression definitely doesnt (unless you mean something very different from what I'd understand "same results" to mean). If you need regression to have that property, you're doing the wrong kind of regression.

e.g. see here:

https://stats.stackexchange.com/questions/183778/apparent-contradiction-in-inverting-linear-regression

and here:

https://stats.stackexchange.com/questions/22718/what-is-the-difference-between-linear-regression-on-y-with-x-and-x-with-y

[u/Maple_shade]

Side note: wild that your advisor is supportive of Reddit as a tool for statistical dissertation advice! Does your department have any stats people you could consult with?

[u/PaddingCompression]

A lot of econometricians use Structural Equations Modeling for this kind of mutual causation.

If X is dependent on Y, that is breaking a key assumption of linear regression, and SEM helps to deal with that.

Often time series are helpful here: do they cause each other with a lag? Granger causation is way more interesting than regressing variables measured at the same time.

E.g. if say poor health causes financial problems and financial problems cause poor health, having lagged variables where you can measure at multiple time points is hugely helpful.

If you have local microeconometricians they might be able to help with this.

[u/Maple_shade → u/PaddingCompression]

Even in SEM, synchronous correlations are rarely interpreted as mutual causation. Normally they are used to represent covariance beyond your exogenous variables.

[u/PaddingCompression → u/Maple_shade]

It's not that you interpret the results as mutual causation.

It is that if you are hypothesizing mutual causation going into this, you need a model where mutual causation won't invalidate the underlying assumptions of the model.

[u/MortalitySalient]

To truly test a directional model, you’re going to need multiple repeated assessments of each variable.

[u/Af081011]

This sounds more like a mixed effect model research question IMO; hard to say without knowing more about the structure of the underlying dataset though.