Why does the variable become insignificant after adding mediators?

Question

I study an impact of long working hours on health. I run ordered logit on women subsample and the dummy variable responsible for working more than 40 hours becomes insignificant after adding mediators: smoking, alcohol, obesity and absence of physical activity. Basically it means that this mediators represent the mechanism of the influence. But is there another possible explanation? Or how can I check this?

Answer 1

Yes there is another possible explanation. It is possible that there is multicollinearity between the variables.

Multicollinearity occurs when two independent variables are highly correlated with each other. This is because the t-statistics of beta coefficient, which determines the significance, is given by:

$$t = \frac{\beta}{\frac{s}{\sqrt{n}}}$$

where $t$ is the test statistics, $\beta$ the coefficient, $s$ standard deviation and $n$ number of observations. The standard deviation in turn depends on the correlation between the independent regressors (i.e. independent variables) that you include in your regression.

In order to see if there is multicollinearity you can calculate variance inflation factor (VIF). VIF of above 10 (some sources say 5) would be considered an evidence for multicollinearity being sufficiently high that it affects $s$ in a non-trivial way, and that could be an explanation for why the coefficient becomes insignificant after adding more variables.