Coefficient change sign from negative to positive when control variables are added. Why?

[Kajsa Evertsson]

Hi!

I'm making multiple regression and has a variable namned RP as an independent/control variable. The RP variable is negative in two models, but in the last model when EDU is added, the coefficient change sign from negative to positve. Why? The table looks like in the table. I also checked for VIF statistics and found the following result.

Thanks in advance!
Best regards,
Kajsa

[Nick Cox]

Change of sign is not so fundamental when the predictors aren't significant at conventional levels any way, which is my reading of your table. The models are consistent at saying that RP has negligible effect with coefficient near zero in each model.

I doubt you need so many decimal places.

[Richard Williams]

I agree with Nick. I'll also add that you lost 29 cases, or about 18% of your sample, when you added EDU to the model. Across-model comparisons are problematic if the cases being analyzed are not the same. If you reran the earlier models restricting the cases to those that were in the final model, you might not even see the trivial changes that you did. For ways to keep the sample the same across all models, see p. 3 of

https://www3.nd.edu/~rwilliam/stats3/MD01.pdf

Because of suppressor effects, the signs of variables sometimes do change as you add more variables. For example, in a simple model, race might have a large effect on income. But, as you add more variables, e.g. education, the effect of race typically declines and may even switch sign.

A discussion of suppressor effects can be found at

https://www3.nd.edu/~rwilliam/stats2/l35.pdf

[Kajsa Evertsson]

Thank you very much for your responses!

[Kajsa Evertsson]

Hi again,

Sorry for bothering you, but since you've been so helpful I though that I maybe can ask you one more question.

As you can see in the table above, my second independent variable CORR (in my case CORR is a control variable, while WIP is my main independent variable) achieve as high significance as my main independent variable WIP. Does this suggest that the relationship between CORR and the dependent variable VB is as important as the relationship between WIP and VB? I ran the regression with Beta values and got higher values for CORR than WIP. Does this potentially imply a endogeneity problem?

Thanks in advance!

[Nick Cox]

Perhaps you should explain your distinction between control and independent variables, as the regression machinery knows nothing about it. My impression is that there is a fashion for naming them according to how you think about them in terms of your research project, but that has no implications for which looks important,

[Phil Bromiley]

Coming in late, let me try to address your last questions.
1. The statistical significance of a parameter estimate has no relation to how important that variable is. Statistical significance speaks to precision of estimation. You could have a very important variable but a high variance estimate of the parameter or vice versa. To talk about importance, you need to look at differences in predicted outcome for differences in values of the rhs variables (see the margins command). Some also look at explained variance, but I find that problematic in regression.
2. Betas vs conventional parameters have nothing whatsoever to do with endogeneity. Betas are essentially the parameters if you rescale all the variables to have standard deviation of one. Because they are essentially all in standard deviations as the scale, some use them to talk about importance - does a one standard deviation change in x1 result in a greater or smaller change in predicted dv than a one standard deviation change in x2?

[Bruce Weaver]

Hello Kajsa. One of the classic references about why signs of coefficients can change depending on what other variables are in the model is chapter 13 (Woes of Regression Coefficients) in the book by Mosteller & Tukey (1977). If your local library has a copy, take a look at it. HTH.