I mean what should be the maximum number of control variables in a model.
Is there any limit?
OR
I can take as many as possible.
AND
How the number of control variables can affect the estimates?
It depends on the purpose. Therefore are methods that if you have hundreds of variables (or even thousands, including methods if you have many more predictors than cases, so called k >> n methods) that attempt to find a solution with fewer predictors (or covariates, or x variables, or independent variables, depending on your discipline). The lasso ( http://statweb.stanford.edu/~tibs/lasso.html ) is one of the most discussed of these procedures, and a good intro is https://web.stanford.edu/~hastie/ElemStatLearn//index.html (and they have a more intro version of this depending on your background). That said, it is usually better for YOU to choose how YOU expect different variables to relate with each other and with the outcome variable (or dependent variable or outcome variable or ...), rather than letting the computer decide. Methods for this have become fairly popular sometimes called graphical models (Pearl's 2009 is the classic text, but the approach is different enough it may require a few reads ... start with the appendix). Anyway, the short answer is "as many as you want, but how many do you want and which ones ... and this depends on your situation." Unfortunately is you were looking for an answer like 8 or 1 for every 20 cases these answers are not good.
Jaspreet,
I add on Daniel's answer. If your goal is to enhance/support the causal interpretation of your target effects, you have to include those controls that are involved in non-causal / spurious relationships between your IV's and DV's. By controlling (a better term would be adjusting or conditioning on) you block these problematic paths. For instance, the most apparent problem are confounders that affect your IV AND DV and, thus, create such a non-causal link. You can then block this path by either conditioning on the confounder itself or variables that lie on his path (e.g., mediators of the confounders-->DV-Effect.
At the same time, you MUST NOT adjust for variables that RECEIVE effects from the IV. These are either mediators in the IV-->DV path or "colliders" (variables which ARE affected by the IV and DV. Finally, you must not adjust for variables that are affected by the DV. Adjusting for mediators is called "overcontrol bias", as it kills the indirect effect and adjusting for colliders is collider bias. The latter is not always obvious. You create it, for instance, by stratifying on the DV (what happens if you analyse subgroups or have DV-related non-response bias). Here is a very interesting brief blog article by Julia Rohrer on an example. Once you have read it, you will have the antennas to observe it constantly :)))
http://www.the100.ci/2017/03/14/that-one-weird-third-variable-problem-nobody-ever-mentions-conditioning-on-a-collider/
Hence, the goal is to adjust for *theoretically appropriate" variables and to avoid controlling on the wrong ones. Of course you never be sure about these choices but at least you have a theoretical basis to select variables.
HTH
Holger
Here are some basic references about graphical models and adjustment. The last one is a nice practical example.
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.
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
Elwert, F., & Winship, C. (2014). Endogenous selection bias: The problem of conditioning on a collider variable. Annual Review of Sociology, 40, 31-53. doi:10.1146/annurev-soc-071913-043455
Vanderweele, T. J. (2019). Principles of confounder selection. European Journal of Epidemiology, 3, 211-219. doi:10.1007/s10654-019-00494-6
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.
Use your substance knowledge to identify which variables are important for your research question. Draw a DAG if it helps you to identify the relationship between the variables.
Hope this helps
Best wishes,
Sebastián
I think the control variable is related to the theoretical approach, and which a control variable can be used only as a conditional influence on dependent variable
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