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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?

Scortchi - Reinstate Monica
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Neodyme
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    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 03:14
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    @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
  • @Nick: What are those systematic methods? – Scortchi - Reinstate Monica Nov 27 '13 at 19:58
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    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

1 Answers1

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You could check out Gertheiss & Tutz, Penalized Regression with Ordinal Predictors, & their R package ordPens. They say:–

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.

Scortchi - Reinstate Monica
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    More active discussion is [here](http://stats.stackexchange.com/questions/33413/continuous-dependent-variable-with-ordinal-independent-variable). – Ilya V. Schurov Jan 14 '16 at 10:54