# Coding for an ordered covariate

I am performing ordinal regression, I have 5 response categories and several predictors both continuous and categorical. I would like to add a predictor which is categorical but ordered (1, 2, 3, 4). I don't think it would be appropriate to apply the usual dummy coding for unordered categorical predictors, but when I searched for how to code this I did not find much information. In Steyerberg (2009) "linear coding" or "assuming linearity of the predictor effect" is mentioned, but without further details. Does it mean I just use my ordered values as they are, i.e. use them as a continuous variable?

• I think that is what is meant. I haven't seen a great solution to ordered categorical variables. It seems like it is either dummy coding, assume linearity, or use some overly complex non-linear function. – charles Nov 27 '13 at 3:14
• @Charles You could choose any simple nonlinear function you liked. You could also assign any numeric scores that make substantive sense, or use a variety of more systematic methods to assign scores based on the relative frequencies of the ordinal variable. – Nick Cox Nov 27 '13 at 10:40
• @NickCox Thank you. Great advice. Hopefully I'll remember next time I'm frustrated by an ordinal variable. – charles Nov 27 '13 at 15:36
• @Nick: What are those systematic methods? – Scortchi - Reinstate Monica Nov 27 '13 at 19:58
• Scores calculated from the data somehow, e.g. normal or logistic scores, scores from correspondence analysis. I mean any method not based on intuition, guesswork or convention. – Nick Cox Nov 27 '13 at 21:24

Rather than estimating the parameters by simple maximum likelihood methods we propose to penalize differences between coefficients of adjacent categories in the estimation procedure. The rationale behind is as follows: the response $y$ is assumed to change slowly between two adjacent categories of the independent variable. In other words, we try to avoid high jumps and prefer a smoother coefficient vector.