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When we have nominal independent variables in Regression we model them by using binary dummies with levels equal to the levels of the nominal variable minus 1. I prefer the base to be zeros and not minus 1. How can I mathematically model an ordinal independent variable to maintain the order?

Thanks in advance,

Andreas

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The only approaches I've seen that respect the ordinal nature of such a predictor are

  • isotonic regression which forces the relationship between X and Y to be monotonic in X. I'm not clear if this works in the context of also adjusting for other variables.
  • Bayesian shrinkage priors where you model X as categorical with $k-1$ indicators for $k$ levels but connect the $k-1$ effects to shrink the differences between the parameter values. This is done automatically for ordinal predictors in the R brms package brm function.
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  • $\begingroup$ How do statistical software e. G. Sas do it? $\endgroup$ Commented May 27, 2021 at 14:16
  • $\begingroup$ R has these capabilities. I doubt SAS has very much. $\endgroup$ Commented May 27, 2021 at 18:05

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