There is a four category classification system for individuals with HIV, labeled Stages 1, 2, 3, and 4, with higher stages indicating more advanced disease. Cell count is a continuous variable, and you are interested in comparing mean cell count between those in different stages.
My question is how does the model change if I treat the stages as nominal or ordinal? I hope my representations below are correct. What test could I use to see if using an ordinal relationship is appropriate, or see if one model has a better fit? My first thought was to look at the $R^2$ value, but that seems too simple.
$E(Y)=b_0+b_1X_1+b_2X_2+b_3X_3$, with $X_1, X_2, X_3$ all being indicators for the different stages.
Stage 1 is the reference stage such that $E(Y)=b_0$ for stage 1, $E(Y)=b_0+b_1$ for stage 2, etc
Do I basically treat the stages as a continuous variable?
$E(Y)=b_0+b_1X_1$, where $X_1$ consists of the stages:
stage 1=1, stage 2=2, etc.