How do we treat control variables in structural equation modeling, do they have any part to play in structural model
Hi
In SEM, there is actually no concept of control variables. However, the model should be structured in such a way that all relevant variables are contained. "Relevant variables" are those that create "non-causal" links between an independent variable and a dependent variable (i.e., omitted variables and their descendents, as well as confounders and their descendents). However, if you have instrumental variables, you can omit covariates or confounders of downstream variabes (mediators and outcomes) and solve the confounding problem by correlated the error covariances between the mediators and outcomes.
You will learn much more about these essential things by googeling about "DAGs". Felix Ewert has a nice chapter about it:
http://www.ssc.wisc.edu/soc/faculty/pages/docs/elwert/Elwert 2013.pdf
Also learning/googling about the "path tracing rules" gives you a basic understanding what exactly SEM does and which variables have to be incorporated. This a kind of knowledge you will fruitfully also be able to apply to regression analysis (where the same rules work).
HTH
Hogler
Thanks Sir Hogler, in fact the reply is so clear and concise that it solved my problem, thanks again
Dear Razia,
Please find the attached file for control variable. Thank you
Dear Wan,
the powerpoint-presentation misses one essential thing. In order to be relevant as a control variable, a variable does NOT ONLY has to be related to the DV but also to the IV of interest. Otherwise, there is no link between the IV and the "control variable" and omission of the control variable would do no harm (i.e., would not bias the IV's effect). Otherwise we would have to incorporate ALL causes of the DV which implies that our models are always bias.
Best,
Holger
Thanks Sir Holger, and Sir Wan Mohamad Asyraf, but if I don't include control variables in my model using SEM, the model will be incomplete or what???????
I think I already gave an answer (and provided references). If a variable Z correlates with your IV and the DV it creates a link - thus, creating correlation between the IV and the DV. Hence, you need to control for it in order to avoid bias of the IV --> DV effect.
The only exception to the above is when Z is an outcome of the IV (hence, a mediator).
Best,
Holger
Hi Holdger,
Kindly share with me some literature the conditions for incorporating control variable in a model. Thank you
Hi Kabiru,
you can take a look into this thread in which I recommended some literature.
https://www.researchgate.net/post/What_is_the_role_of_control_variables_in_multiple_moderation_regression
The main issue is that your IV and your DV are influenced by confounders. Confounders create what Pearl describes as "backdoor paths" which add to the covariance between IV and DV. If you adjust for a confounder or a variable that mediates its effects you block or disrupt the backdoor path. This is a quite mechanistic issue. Of course you never know which confounder actually exist--this is where causal assumptions come into play (on which the selection of control variables rest). Your estimates and causal conclusions always rests on the correctness of the causal assumptions, there's no hideaway (even in experiments).
Graph theory (Pearl) also gives you some theoretical basis which control variables NOT to simply adjust
a) Mediators that lie in the IV --> DV path
b) Colliders (common effects of the IV and DV)
c) Descendents of the DV (i.e., variables that are caused by the DV)
d) Instruments (causes of the IV) as these cause "z-bias" which is the amplification of existing confounding bias (Ding et al., 2017).
Ding, P., VanderWeele, T., & Robins, J. (2017). Instrumental variables as bias amplifiers with general outcome and confounding. Biometrika, 104(2), 291-302. doi:10.1093/biomet/asx009
In these papers, you find a practical approach that I found interesting
Shrier, I., & Platt, R. W. (2008). Reducing bias through directed acyclic graphs. BMC Medical Research Methodology, 8(1), 70.
Vahratian, A., Siega-Riz, A. M., Savitz, D. A., & Zhang, J. (2005). Maternal pre-pregnancy overweight and obesity and the risk of cesarean delivery in nulliparous women. Annals of Epidemiology, 15(7), 467-474. doi:10.1016/j.annepidem.2005.02.005
Having said that, be aware that research fields (and thus reviewers) have expectations which controls to include. Consider that or your paper dies a unnessesary death.
Best,
Holger
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