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I need to examine the relationship between an outcome variable (continuous) and a number of predictors. Since my data is non-normally distributed (i.e. the residuals from the multiple linear regression are not) I decided to use a rank-based regression using the Rfit function from the npsm package for R (Kloke and McKean https://cran.r-project.org/web/packages/npsm/npsm.pdf).

I can run the analysis with no problems, but I am struggling with the concept of rank-based correlation coefficients and how you can interpret them. I have read a few scientific articles which use Rfit (e.g. https://doi.org/10.1007/s10286-012-0158-6) and the original paper by Kloke and McKean (https://journal.r-project.org/archive/2012-2/RJournal_2012-2_Kloke+McKean.pdf) but I am still not clear on some issues.

I understand that it is safe to say that a significant negative (or positive) regression coefficient indicates a negative (or positive) association between the predictor and the outcome. But how can I obtain some information on the magnitude of the effect?

I am familiar with the use of unstandardized and standardized beta coefficients in multiple linear regression and with the fact that standardized coefficients are generally considered more appropriate to compare the different effects of the different predictors on the outcome

Would it be stupid to say that the rank-based regression coefficient is the amount of change in the outcome due to a change in one rank of the predictor ? And would this allow me to directly compare different predictors: i.e. would a larger coefficient mean a larger effect?

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  • $\begingroup$ i face the same problem like you but my data is categorical i wonder if it works $\endgroup$
    – Ammar Meza
    Commented Nov 27, 2021 at 13:22

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According to the authors of the Rfit package (John D. Kloke and Joseph W. McKean), the rank-based regression estimation is robust and analogous to the standard OLS regression. In addition, the interpretations of the beta coefficients are similar in both methods; it's only the method of estimating the betas that varies. More details can be found in their attached paper:

https://journal.r-project.org/archive/2012/RJ-2012-014/RJ-2012-014.pdf

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