How to interpret weird results? different sign of coefficient and correlation. The changing sign and significance in regreesion results

[SHIYI LI]

The correlation between fCOO and ROA &Q is positive, but in the fixed effects model, the coefficient is negative? Why the sign and significance of fCOO and NfemaleRe are chaning?
I use fixed effects.
The specific results and correlation are in the picture.

Mainly the interaction problem?

Thank you very much for helping!!!

[Joshua D Merfeld]

Hi Shiyi,

The correlations are bivariate correlations (I'm assuming). That is, they do not take into account any other variables when computing the correlation between the two variables (it is as if we are not controlling for any other variables). As such, when you run multivariate regressions--which DO take into account other variables--there is no reason to expect the correlation/coefficient to be similar nor even of the same sign.

Josh

[SHIYI LI]

Hi Shiyi,

The correlations are bivariate correlations (I'm assuming). That is, they do not take into account any other variables when computing the correlation between the two variables (it is as if we are not controlling for any other variables). As such, when you run multivariate regressions--which DO take into account other variables--there is no reason to expect the correlation/coefficient to be similar nor even of the same sign.

Josh

Hi Josh,

Thank you for answering! Yes, I think you are right. So I can simply write down that the sign of correlation is meaningless when we analyzing the regression results. It don't have reference value for analyzing. Is that right?

BTW, do you know why the sign and significance of coefficient of fCOO and NfemaleRe is changing? How to interpret interaction term? fCOO, fCEOduality and mCEOduality are dummy variables. Other is continuous variables. So interaction term have two kinds: dummy* continuous and continuous * continuous,

Thank you very much!

[Joshua D Merfeld]

Can you give an exact example of what kind of interpretation you mean? In the correlations or coefficients? An explicit example with numbers would be best.

[SHIYI LI]

Just like in Model 1, how can I explain the coefficient of fCOO? In model 1, there is an interaction term PfemalefCOO. This is the main problem.

[Carlo Lazzaro]

Shiyi:
as Joshua pointed out, please post what you typed and what Stata gave you back via code delimiters (take a look at the FAQ on how to do it).
Please consider that images are often unreadable and a very poor support to comment on.
Please skim through the literature in your research field and check which coefficients of your regression show a "weird" sign.
As an aside, that "weird" sign may depend on quasi-extreme multicollinearity as well.

[Phil Bromiley]

A couple of suggestions. 1. Use the factor notation for your interactions. If you do so, you can then use the margins command to generate predictions and total effects (main plus interaction at specific values of the interaction). 2. The parameter on the main effect when you have an interaction is the effect if the interacting variable equals zero. When you change interacting variables, the place where the interacting variable equals zero changes which gives your variation in parameters and significance. This is why you generally should not try to interpret the main effect without considering the interaction. Sometimes, zero is not even a feasible value in the interacting variable. Changing the zero on the interacting variable (e.g., adding or subtracting a constant from a continuous interacting variable) can also change the sign on the main effect. You might find Friedrich, "In Defense of Multiplicative Terms in Multiple Regression Equations" (American Journal of Political Science, 1982) helpful. Note that you do not need to do the calculations yourself - margins with the dydx option does them for you.

[SHIYI LI]

Hi:

I think problem might not be so complex. Is it necessary to use the margin command in master's dissertation?

I have thought how to interpret interaction for a few days by myself.

This is my new situation now:

Let me explain my research question first: I want to test whether the female directors who have relatives as officer in the firm would affect firm performance.
In my first regression equation, I have added independent variables about the percentage of female directors(A), the number of female directors who have relatives as officer(B), and some control variables. Dependent variable is Tobin's Q. It turns out that the number of female directors who have relatives as officer is significant.

However, when I add the interaction(AB) consists of the percentage of female directors and the number of female directors who have relatives as officer in second regression equation, other variables are the same as the first equation.
The number of female directors who have relatives become insignificant.

The joint significance test of AB and B, P- value of the test is 0. Therefore, the interaction cannot be deleted.

I use centering technique to deal with the second equation. I generate new independent variables which are A- mean of A; B- mean of B; C-mean of C. Dependent variable is still Tobin's Q. Then I use these variables to rerun the regression. It turns out that A- mean of A; B- mean of B; C-mean of C, all of these variables are not significant.

I look at my data again. I found that in my data, in the firm that have female directors who have relatives as officer is the only female directors on the board. Therefore, I think the possible reason for the change of significance of B (variable he number of female directors who have relatives as officer ) is because of the data overlap? I don't know the exact term to describe this situation.

Could any one can give me some suggestions?

Thank you very much!
Best, Shiyi Li