When doing linear regression, in order to ensure the robustness of the model, I first included only key variables, but at this time some key variables did not pass the significance test. And when I put the control variables (personal characteristics) into the model, the key variables that did not pass the significance test before passed the significance test.
I know this is due to the interaction of some variables. The question is, can these first insignificant and then significant variables be used as conclusions?
The usual situation is that it is significant first and then not significant, which is generally considered not to be used as a conclusion, but this situation is the opposite, so I am confused.
For example, if the independent variable is the living environment and the dependent variable is depression, can it be concluded that the living environment has an effect on depression?
Often, this effect is due to suppression caused by high correlations between independent variables. If you google "suppressor effects in regression," you should be able to find more information.
In a robustness test, when a variable that was initially insignificant becomes significant after adding control variables, it can indeed influence the interpretation and conclusion of the analysis. This finding suggests that the control variable(s) may have a confounding effect on the relationship between the initially insignificant variable and the dependent variable.
Here are a few key points to consider in interpreting the results of such a robustness test:
In summary, when a variable that was initially insignificant becomes significant after adding control variables in a robustness test, it indicates the importance of considering confounding effects and strengthens the interpretation of the relationship. However, it is essential to interpret the findings cautiously and consider other factors, such as the context of the analysis and potential limitations of the data and methodology.
Christian Geiser is likely spot on, although "real" instances of suppressor effects are not uncommon as well. I would consider running lots of bootstrap replications, and analyzing the distribution of the effect coefficients across the multiple models.
But I would bet on seeing a correlation matrix that has clusters of some very high (~ 0.6+) correlations among the independent variables. If the high correlations are exclusively among the control variables, then a solution (dropping some of the control variables, or creating an index score) is also readily available.
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