- Isn't bi-directional effect/causality difficult to demonstrate?
- Could it be simply demonstrated by examining correlation, regression or any other metric to measure the goodness of fit?
- How can one find out about the directionality (whether A has an effect on B or B has an effect on A) using LR?
According to your theoretical framework or previous studies, the correlation does not imply causality unlike the regression, there are a lot of tutorials in youtube that can be used to perform these analyses according to the statistical program you use the most.
Tarushi Tanwar , my epistemological two cents: mainstream scientific approach agree that claims causality can only be obtained with experimental studies, and hence causality cannot be claimed with estimates based on observational data. So, it does not depend on your statistical model, but rather on your study design (observational vs. experimental).
Having say that, it is possible to approximate causality with observational data, using quasi-experimental methods, as e.g. a regression discontinuity design or AIPW.
Also, it depends on what you mean with "causality". There exist the concept for example of "Granger causality", which is based on linear regression, it can be easily estimated, and provides you also with evidence about the directionality of the Granger-causality (A to B, B to A, or both).
Adding to what Cristian Ramos-Vera properly said, correlation does not imply causation, but causation implies correlation. Linear regression models (estimated with observational data) are just a little bit more sophisticated way of finding the (conditional) correlation between two variables (conditional on other factors that may affect the relationship).
Yes, asserting any causal relationship requires an appropriate experimental design. You must control the assumed stimulus and record the assumed response (at some later time points than the stimulus is given). Its further important that giving the stimulus is independent of any feature of property of your study subject/object. Then and only then a correlation implies causation (as you ruled out any other possible reason for this correlation ["fluke" as a possible reason is controlled by tests of statistical significance]). If there are further potentially influencial variables (aka confounders), the interesting correlation might become clearer in the data when either experimentally or statistically controlling for these confounders, what can be done with regression model.
And this should answer your questions about bi-directionality, too. To demonstrate that A is a cause of B and that B is a cause of A, you need two experiments, in one controlling A and measuering B, and in the other the other way around.
"Granger causality", to my understanding, is something different and not that kind of "cause-effect causality" as we understand in normal life (it's a hypothesis test of the correlation of time series).
Jochen Wilhelm , you are right, "Granger causality" is not the traditional view of causality, it is a different concept, more precisely related to the ability of A to have information to predict B, and vice versa. Born in time-series analysis, the concept has extended to longitudinal studies.
My point was just that what Tarushi Tanwar needs, depends on what "causality" is in the first place, which is at the end an epistemological issue rather than a statistical one (nothing again statistics, I am statistician myself and I loved it).
Dear: The theoretical and logical aspect is what determines the direction of the phenomenon, i.e. defines the independent variable and the dependent variable
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