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This question I think was already asked here but I can't fully understand the answer.

I have a number of ordinal predictors that I'm transforming into dummy variables and I'm wondering whether the hierarchical multiple regression linear relationship assumption (linear relationship between each predictor and the outcome variable - also the composite and outcome) needs to be met for each dummy variable?

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  • $\begingroup$ How do you transform ordinal variables into dummies keeping the ordinal relationship? $\endgroup$ – Aksakal Jul 28 '16 at 11:28
  • $\begingroup$ @Aksakal - my plan wasn't to try to maintain the ordinal relationship as by dummy coding them they become either an instance or not (0 or 1). For example, I have one ordinal variable that has three 'groups' (low, med, high) so I create two dummy variables and keep one of the groups (for me it'll be the 'low' one) as the reference group which the other two groups get compared to in the analysis (at least that's my understanding). $\endgroup$ – SwingingStrawberry Jul 28 '16 at 12:49
  • $\begingroup$ This setup also inherently allows for the fourth state: med and high at the same time. $\endgroup$ – Aksakal Jul 28 '16 at 12:57
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There's nothing to check!

Linearity is automatically met for binary (/dummy) variables.

However you set them up, the IV (x) takes only two values (say 0 and 1 but it doesn't actually matter in any substantive way as long as they're any two distinct values). If the DV (y) has a different mean at those two values, the coefficient measures that difference, and that difference corresponds precisely to the term entering the model linearly -- the slope on a 0/1 variable is the mean difference.

If the values differ by something other than 1, then the slope will change but the resulting mean change will be the coefficient times the change in the dummy (that is, the linear model always picks up exactly the mean difference).

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  • $\begingroup$ He's talking about ordinal predictors which he transforms into dummies. For instance ordinal Mood variable with values Down, Neutral and High would become MoodDown and MoodNeutral dummies, but then the ordinal relationship is lost. So, it's not as simple as you seem to suggest $\endgroup$ – Aksakal Jul 28 '16 at 2:19
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    $\begingroup$ @aksakal I know he's talking about ordinal variables he converted to dummies but the question was specifically about linearity assumption for the dummy variables: "...needs to be met for each dummy variable". As the question currently stands I think it is really this simple. There's no assumption about linearity for the ordinal variable and (at least to my reading) the OP didn't ask about that. $\endgroup$ – Glen_b -Reinstate Monica Jul 28 '16 at 2:44
  • $\begingroup$ Thanks Glen_b that's saved me a lot of reading around trying to work out something that didn't need to be worked out. $\endgroup$ – SwingingStrawberry Jul 28 '16 at 12:45

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