I have dependent variable of "rational decision making" with two independent variables of Leadership and "Self efficacy". When i use only one independent variable of leadership, it shows positive relation with rational decision making which is consistent with the theory. However, when I added variable of self efficacy as another independent variable then the leadership showed negative relation with rational decision making which is inconsistent with the theory. Why it happen?
Umar, your second independet variable (x2) is collelated with the first and primary one (x1) in some way AND x2 also affects y. You should look at the magnitude and direction of the correlation between x1 and x2 :-)
Dear Umar, there are essentially several possibilities for this phenomenon (from your description, it's not clear which one). If SELF has an effect on RDM and is correlated with LEAD, then omitting SELF will result in a biased estimate for LEAD. If, however, SELF has no effect on RDM, it does not matter whether it is correlated or not with LEAD if you have missed another relevant variable that is correlated with both SELF and LEAD.
It can be happened due to the multicolinearity so, first you need to check the relationship between two independent variables. If they are related they can't give you the correct estimated parameters because the effect of one independent variable is already can be hidden by the other one. therefore, try to check correlation between them and try to detect it by using Principal component Analysis or Factor analysis.
If you add more independent variables the value of beta may increase or decrease. In fact the value of r square (coefficient of determination) can vary due to the combined effect of all variables. In you case I think it is happening due to multicolinearity.
This phenomena is known as suppression within the context of multiple regression. It can arise when predictors are correlated (multicollinearity) as noted.
Two things to consider:
i) if sample size is small or collinearity high (or both) then the suppression effect could easily just be produced by noise (because each predictor adds so little unique information). Look at diagnostics such as VIF or tolerance (1/VIF).
ii) if you have scales that are bounded then when leadership is high and self-efficacy high you might have ceiling effects and that might bias your estimates in these situations. It probably wouldn't cause a suppression effect but might make it worse.
Umar, if you have access to the book by Mosteller & Tukey (1977), take a look at Chapter 13 (Woes of Regression Coefficients). HTH.
https://www.pearsonhighered.com/program/Mosteller-Data-Analysis-and-Regression-A-Second-Course-in-Statistics/PGM154255.html
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