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If we want to use categorical variables in regression context, we are allowed to use dummy codings such as these schemes.

Is this also required in a Bayesian (MCMC) context, such as with WinBUGS/OpenBUGS, that we have to model k factors with k-1 dummy variables – or are we allowed to use k dummy variables and linear dependency of the variables is not an issue?

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    $\begingroup$ Bayesian or non-bayesian is not an issue here. If you fit your regression using maximum likelihood or Bayesian estimation wouldn't affect how you code the dummy variables... $\endgroup$ Commented Jun 8, 2014 at 19:32
  • $\begingroup$ Bayesian regression with Normal priors on the regression coefficients corresponds to Ridge regression, which adds a penalty to the original regression objective. For penalized regression, there are strong arguments to use k not k-1 dummy variables, here and here $\endgroup$
    – Johannes
    Commented May 27, 2020 at 13:10

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