Why are you asking about categorical explanatory variables specifically? Could it be that you are thinking about the k-1 indicator variables for a categorical variable with k categories?

In any case, take a look at this section of Frank Harrell's Author Checklist:

• https://discourse.datamethods.org/t/author-checklist/3407#multivariable-modeling-problems-21

Notice especially the comments under "Lack of insignificant variables in the final model".

Well, keeping the significance cut-off at p 0.05 is usually too stringent a criteria so what we usually do is to keep the sig. at .25 for allowing entry into MLR. Moreover, biological plausiblity is another criteria which overrides even the first one. It usually applies to categorical variables in epidemiological analyses.

In the end what experience has taught me is that the thinking and approach of the researcher is the most valuable asset that guide him/her in understanding the data set.

Current debate and experience shows is best using 0.25 cut off to include possible non-significant variables in your multivariate logistics regression prediction model instead of the usual cut off of 0.05.

Shukur Ali

Best answer? it depends.

If you used your univariate analysis as a goodness-of-fit test for the multivariate model, then i would suggest variables that were highly insignificant in the univariate analysis to be excluded, unless there is a very strong scientific or epidemiological backing for the reason of their inclusion. For example, if age groups or gender appear insignificant in the univariate model, they can still be included in the multivariate model because they are usually a confounder in whatever relationship you are analyzing.

So with sufficient scientific basis, you can include certain insignificant variables in your multivariate model, but they should have the backing of the scientific literature.

Also, there are other ways to exclude variables from the multivariate model such as stepwise regression and lasso/ridge regression. I suggest you read a bit about these models.

Hope my answer was of help.