Traditionally in linear regression your predictors must either be continuous or binary. Ordinal variables are often inserted using a dummy coding scheme. This is equivalent to conducting an ANOVA and the baseline ordinal level will be represented by the intercept.
However what if you want to plug further predictors into your model, some continuous and some also dummy coded ordinal? The rationale for the dummy coding does not make sense to me if there are other predictors also present. What does the baseline category represent in this scenario?
Furthermore, if you are constructing a minimal adequate model, you may end up in the situation where you are dropping some levels of your ordinal predictor but not others. This seems tantamount to saying that being labelled a "5" is informative but being labeled a "7" is not. Where you're only using the ordinal predictor I'd say this probably makes sense, but again when it is mixed in with many other predictors I'm uncertain of the rationale.
In cases where you have many levels to your ordinal predictor (in my case 18) some have advised me to treat it as "pseduo-continuous" which I'm wary of.
Can anyone offer me some better advice?
Generally people treat predictors in the models as continuous. Dummy coding isn't really appropriate though I think it can sometimes be interesting to use staircase coding (but it seems generally problematic with 18 categories). Generally it is considered more problematic to treat the outcome (Y) as continuous if it is ordinal than the predictors.
There are models that use ordinal predictors but they can be hard to interpret.
You seem to have two issues: interpreting intercepts and dealing with ordinal predictors.
first, how is the intercept interpreted with mixed categorial and metric predictors? That is, indeed, a mind-boggling issue. Most modern implementations of regression have the so-called treatment coding (or contrasts) as default. For categorial predictors, one category is chosen as the reference group and its expected value becomes the intercept, and all other parameters express the difference to that reference group. For purely metric predictors, the intercept is what we all learned in high school: the value of y, where x = 0. In a mixed situation, both definitions are combined: the intercept is y|x = 0 in the reference group.
The issue of ordinal predictors is a measurement problem. The so-called invariate property of an ordinal measure is the order. Let's see it positive: you may do all transformations on the ordinal predictor that preserve order. Hence, you could recode your variable, such that there is a clean linear relationship with the outcome y, ... as long as the relationship is monotonously increasing (or decreasing). On the downside, you may not interpret the linear coefficient metrically. So, when you get something like:
predictor beta p
x1 .234 .04
you may _not_ say: "the outcome increases by .234 with every step of x1", but: "there is a monotonous increase of y by x1"
18 points on a scale is a lot and I have seen fewer differentials on a scale that is described as continuous! In practice I would probably treat as continuous and evaluate a polynomial function of the variable and do residual analysis to check the underlying linearity assumption. I typically centre continuous variables around a central value ( mean or median) to make for a more interpretable intercept
For fewer ordinal categories I usually use orthogonal polynomials.
http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
Thank you for all the responses. I will look at assessing the linearity of the ordinal predictor and if it is linear, I will try treating it as continuous. That way if it is gets dropped from the model, the whole scale will go which makes more sense to me.
The inner-outer rule is described in the link:
https://books.google.co.uk/books?id=y54QDUTmvDcC&printsec=frontcover&dq=pinheiro+bates&hl=en&ei=_ZqkTaaOKMeB0QGWhcnBBQ&sa=X&oi=book_result&ct=result#v=onepage&q=inner&f=false
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