4
$\begingroup$

I’m running a linear regression where my response variable is mean satisfaction score of GP practices, while one of the predictor variables is funding received. I used a cube root transformation for this predictor but now I’m a bit lost as to the interpretation (a one unit change in funding is associated with ??? change in satisfaction).

I trawled through the site, and I can see the question has been asked before, but I haven’t been able to find a direct answer.

Improve this question
$\endgroup$
3
  • $\begingroup$ what was your reason for using a cube root transformation for the predictor? Was a log transformation (which has a more straightforward interpretation) not a good fit in your model? $\endgroup$
    – Marquis de Carabas
    Aug 15, 2015 at 19:46
  • 1
    $\begingroup$ Transformations are like drugs .. some are good for you and some are not ....See when and why stats.stackexchange.com/questions/18844/… $\endgroup$
    – IrishStat
    Aug 15, 2015 at 21:13
  • $\begingroup$ @marquisdecarabas - the predictor has negative and zero values so I cannot use a log transformation as I understand. I also understand that quadric will treat negative and positive values alike, and cubic ill make skewness much worse $\endgroup$
    – Luka Crnjakovic
    Aug 16, 2015 at 8:54

1 Answer 1

Reset to default
2
$\begingroup$

Since you took a cube root transformation of funding you now have to say that a one unit increase in the cube root of funding is related to the dependent variable. The effect of a one unit increase in the original variable on satisfaction will be different at different levels of funding.

An increase in funding from 2 to 8 would be associated with the same change in satisfaction as an increase from 8 to 27 or 27 to 64.

Transformations such as this are often unnecessary now that there are statistical methods that allow for non-normal residuals (e.g. robust regression, quantile regression, spline fits) one of those may work better for you.

Improve this answer
$\endgroup$
3
  • 3
    $\begingroup$ You might be thinking of transforming the response variable, which is the usual application of a cube root. However, the OP states that the predictor variable was transformed. That will only indirectly affect the residuals; it is done to achieve a linear relationship, not to stabilize or symmetrize residuals. $\endgroup$
    – whuber ♦
    Aug 15, 2015 at 23:12
  • 1
    $\begingroup$ Thank you Peter for that very helpful description. I'm more worried about non-linearity than residuals. I ran a test for normality of residuals and it seems fine. When it comes to other transformations, as the funding variable has zero and negative values I understand I cannot use log, quadric or cubic transformations. $\endgroup$
    – Luka Crnjakovic
    Aug 16, 2015 at 9:08
  • $\begingroup$ There are other possibilities, like spline regression, but they will have the same issue that a one unit change in the IV does not have the same meaning at different levels of the IV. That's more or less what non-linearity means. $\endgroup$
    – Peter Flom
    Aug 16, 2015 at 12:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.