I am running a model selection analysis with a continuous dependent variable and a variety of continuous and categorical explanatory variables. For two of my continuous explanatory variables I am fitting curvature terms as it looks like there is a quadratic relationship between them and the dependent variable.
When I run the model selection analysis using MuMIn in R, I get a variety of models out, some of which contain only the quadratic term, and not the lower order associated linear term, in them. In my head this seems mathematically incorrect - is the linear term not essential when fitting a higher order polynomial (unless that linear term = 0...)?
Is there anyway to get around this issue other than carrying out the model selection by hand (pretty impossible for me since I am trying to fit 24 parameters)? Can I tell R not to include any quadratic term in a model without its associated linear term?