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?
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2$\begingroup$ 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. $\endgroup$– charlesNov 27, 2013 at 3:14
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2$\begingroup$ @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. $\endgroup$– Nick CoxNov 27, 2013 at 10:40
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$\begingroup$ @Nick: What are those systematic methods? $\endgroup$– Scortchi - Reinstate Monica ♦Nov 27, 2013 at 19:58
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3$\begingroup$ 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. $\endgroup$– Nick CoxNov 27, 2013 at 21:24
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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.
answered Nov 27, 2013 at 10:27
Scortchi - Reinstate Monica♦Scortchi - Reinstate Monica
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