I need to know the diffrence between the covariance line and the regression one while using structural equation modeling.
Thank you all in advance.
Hi Mohammed
> I need to know the diffrence between the covariance line and the regression one while using structural equation modeling.
I suppose that in one way there is no difference between them, as they are just both parts of a latent variable model. So the software does not treat them as being 'different', they are both just parameters that need to be estimated.
In another way, they are very different, in terms of the hypotheses that they represent. The straight line hypotheses a directional effect, with one variable acting as a predictor (base of the arrow) and the other variables as an outcome variable (at the head of the arrow). So the hypothesis the straight line represents is directional. The curvey double-headed arrow is a hypothesis that two variables just covary or correlate; there is no 'causal' inference.
Best wishes
Mark
Double header curved arrows are meant for covariance between variables while single header straight arrow is meant for relationship.
Hi all,
when I started to get acquainted with the graph theoretical approach to SEM (i.e., drawing DAGs) I was first confused but then became convinced by the much more specific meaning of a bidirectional path in graph theory: While traditional SEM would (as my Mark and Imran have pointed out) understand a bidirectional arrow/path as a mere covariance (stemming from unknown or not specified reasons), graph theory is more specific and interprets it as omitted confounding. In this regard, a bidirectional arrow connecting two predictors would express the researchers assumption that both share an omitted common cause. In the years, I found much value in this approach as it forces you as researcher to think about potential reasons for covariances between predictors. By doing so, you reduce the danger to unintentionally control for mediators (which happens often!).
I cannot tell how often researchers throw in a bunch of predictors into a SEM or regression model without reflecting the causal structure *among* the predictors and whether perhaps one predictors mediates the effect of one predictor on the outcome. In the worst case, you have a full mediation effect and controlling for the (unrecognized) mediators leaves you with the impression that your predictor is completely irrelevant. The traditional SEM perspective on covariances IMHO increases such dangers.
My 2 c
--Holger
Rohrer, J. M. (2018). Thinking clearly about correlations and causation: Graphical causal models for observational data. Advances in Methods and Practices in Psychological Science, 1(1), 27-42. doi:10.1177/2515245917745629
Keele, L., Stevenson, R. T., & Elwert, F. (2019). The causal interpretation of estimated associations in regression models. Political Science Research and Methods, 1-13. doi:doi:10.1017/psrm.2019.31
Elwert, F. (2013). Graphical causal models. In S. L. Morgan (Ed.), Handbook of causal analysis for social research. (pp. 245-273). Dordrecht Heidelberg New York London: Springer.
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