Why do the signs of coefficients change when moving from OLS regression to Fixed Effect Regression? my theory stands on the assumption that PS would be positive and significant, the same as in the OLS result, but the fixed effect changes that. What's the solution?
The reason for this is obvious and is related to the removal of the fixed effect or the same intercept in the Fixed Effect model. According to your description, I think Model OLS is better.
Hello Rand,
I can't tell whether the two models include all of the same IVs and whether both include an intercept.
If model 1 includes only an intercept and the PS variable, whereas model 2 includes 5 IVs and an intercept, then the reason for the apparent difference in regression coefficient for PS is most likely attributable to some degree of IV overlap/redundancy/collinearity.
If both model 1 and model 2 are identical _except_ for the inclusion of an intercept (as suggested by Abolfazi), then the no-intercept model forces the regression line through the origin ("X"=0, Y=0). The interpretation of individual regression coefficients isn't apples-to-apples across the two methods.
Good luck with your work.
Thank you so much for your answer, the problem is as you suggested is a problem of collinearity. How can I solve it?
Hello again Rand,
If you are concerned about excessive collinearity among IVs, you can:
1. Choose to drop one or more of the offending variables (the thinking being, if the variance associated with one variable can still be captured by retaining the others, you lose little in the explanatory power of the overall model);
2. Combine two or more of the IVs (showing the greatest overlap) into a new, composite variable. Methods such as principal components analysis or factor analysis (choice depends on your assumptions and specific goals) are common for this.
3. Use non-traditional methods, such as ridge regression, which inserts noise into the data set in exchange for less biased estimates of regression coefficients.
4. Try a different technique for selecting among a candidate set of IVs to explain/account for differences in some DV. The data mining literature has many such options.
5. And, of course, you can accept the collinearity, and explain that the regression coefficients will not necessarily track the zero order (bivariate: one IV with the DV) correlations (but present both, so as not to speak inappropriately about the strength or direction of relationship of a given IV with the DV).
Good luck with your work.
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