GLM Categorical IV Predictor vs Group by Analysis I am modeling a continuous dependent variable with a couple of covariates (known a priori) and a variable of interest. 
I ran into an issue of interpretation which I'd like to clear up. When I include a categorical predictor (Sex) my variable of interest is no longer significant. However, when I run two separate models (one for males, one for females) the variable of interest is only significant in females. 
In the full model (with sex as an IV) the interaction between variable of interest * sex is non-significant. 
How do I proceed? How do I know for sure I have justification to run two separate GLMs based on sex? I tried plotting the the variable of interest by sex  vs. my dependent variable and observed no significant difference in the slopes (although visually these were strikingly different and the lines intersected)  and significant difference in intercept.
 A: Model selection based on $p$-values will bias the coefficients of the final model towards significance. This is a form of stepwise regression and should be avoided if the goal is confirmation through $p$-values. The actual chance of a false positive will be much higher than the chosen level of significance. This has been discussed in several places on CV, most notably here. 
You should therefore go with the model you originally intended to use for inference, which I'm assuming is the full model with interaction. 
Even (or especially) if you have expert knowledge suggesting that gender affects the variable of interest, a single model using an interaction with gender is preferred. The interaction allows you to model gender-specific effects while having a single model has multiple advantages (most importantly: more observations). 
Note that just because the effect isn't significant doesn't mean it isn't there. You just couldn't demonstrate it. This might be because (1) your sample size is limited compared to the number of parameters, (2) the effect size is small, (3) the variance of the effect is large, or a combination of these reasons. For this reason, model selection based on $p$-values usually isn't very helpful. 
