I'm working with a structural equation model to study influenza infection risk. As age is a known risk factor to explain infection, I therefore adjusted my infection outcome on the subjects age class. After regressing my outcome on several latent variables, the age class is not significant anymore. My question is : should a non-significant adjustment variable be kept in a (structural) regression model or removed ?
Beyond considering the SEM discussion in comment from @NickCox, I'd test different codings of your age variable before ruling out its inclusion. I'm assuming you've transformed to categorical since the age relationship will be non-linear (very young and old people are more likely to be infected, everyone in between less so). If you have enough data perhaps you could test as a continuous covariate with a quadratic age variable model; otherwise explore how you bin the ages into different sub groups to make sure that's not confounding the variable's influence.