Why does the variable become insignificant after adding mediators?

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?

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.

• Have just checked this. All GVIFs are about 1. Probably there’s no multicollinearity. Is there anything else? Mar 28, 2022 at 6:58
• @Daria 1. Then it is either because conditional on other covariants it is actually not significant or because you have small sample so the tests lack precision that you would get in larger sample. 2. You already got a lot of answers on this site. If you get an answer that answers your question you should consider accepting it unless you think that the answer did not answered your question
– 1muflon1
Mar 28, 2022 at 10:44