I have several covariates in my calculation for a model, and not all of them are statistically significant. Should I remove those that are not?
This question discusses the phenomenon, but does not answer my question: How to interpret non-significant effect of a covariate in ANCOVA?
There is nothing in the answer to that question that suggests that non-significant covariates be taken out, though, so right now I am inclined to believe that they should stay in. Before even reading that answer, I was thinking the same since a covariate can still explain some of the variance (and thus help the model) without necessarily explaining an amount beyond some threshold (the significance threshold, which I see as not applicable to covariates).
There is another question somewhere on CV for which the answer seems to imply that covariates should be kept in regardless of significance, but it is not clear on that. (I want to link to that question, but I was not able to track it down again just now.)
So... Should covariates that do not show as statistically significant be kept in the calculation for the model? (I have edited this question to clarify that covariates are never in the model output by the calculation anyway.)
To add complication, what if the covariates are statistically significant for some subsets of the data (subsets which have to be processed separately). I would default to keeping such a covariate, otherwise either different models would have to be used or you would have a statistically significant covariate missing in one of the cases. If you also have an answer for this split case, though, please mention it.