Treating Categorical Data as nominal or ordinal?

Question

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.

Nominal Model:

$E(Y)=b_0+b_1X_1+b_2X_2+b_3X_3$, 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

Ordinal Model:

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.

"Cell count" alone may be obvious to some readers, but not to forum members in general. But you can apply what you call the "nominal model" to predictors thought of as ordinal. The key is that you expect a pattern to be shown by the coefficients, which should rise or fall in the same direction. What you call the "ordinal model" implies that stage has effects proportional to coding, which is occasionally plausible, but is usually dubious if not nonsensical. Either way the second model makes a much stronger and more specific assumption than is justified just by being ordinal. — Nick Cox, Sep 01 '14 at 14:55
On a different level, it is not clear how seriously to take linear models for cell counts. Even if counts (meaning concentrations???) may be approximately continuous in practice, they are necessarily non-negative and I would not expect linear models to be anything more than lousy first approximations; indeed they are wrong in principle as not forbidding negative responses. — Nick Cox, Sep 01 '14 at 14:59
Is this a homework or self-study question? Wording of first paragraph hints at such. If so, please flag as such and study our guidelines on self-study questions. — Nick Cox, Sep 01 '14 at 15:00
Thanks- I added the self-study tag. I am reviewing regression concepts that I seem to have missed in previous course. — user3731561, Sep 01 '14 at 15:08
possible duplicate of Continuous dependent variable with ordinal independent variable & Treating ordinal variables as continuous for regression problems — Scortchi - Reinstate Monica, Sep 02 '14 at 09:46
Also see Logistic regression and ordinal independent variables - orthogonal polynomials can be useful, in a sense interpolating between the nominal & continuous representations. — Scortchi - Reinstate Monica, Sep 02 '14 at 09:57

Treating Categorical Data as nominal or ordinal?

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