[R] normalised/transformed regressions

Greg Snow Greg.Snow at imail.org
Tue Jul 22 17:42:56 CEST 2008

It is possible to write a function to do what you describe, but the real question is why would you want to do that?

It looks like you are trying to force your data to fit a set of assumptions that are not needed.  The normality assumption in regression models is that the residuals are normal, or that the y variable is conditionally normal given the x-values.  There is no requirement that the raw y-values come from a normal distribution.  And even then the normality assumption only applies to specific tests and is not needed just to fit the model and the central limit theorem applies to those tests, so they are still close approximations even when the residuals are not normal.

There is a derivation of the regression equations that assumes that the y variable and all the x's are from a multivariate normal distribution, but tranforming all the variables to have marginal normal distributions does not guarentee that they will be multivariate normal.  And if you are using the fixed x formulation (both lead to the same set of equations), then there are no assumptions/requirements about the distribution of the x's (other than being non-unique).

If you tell us what you are trying to accomplish, we may be able to give better advice than to show you down the potentially wrong path.

Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
(801) 408-8111

> -----Original Message-----
> From: r-help-bounces at r-project.org
> [mailto:r-help-bounces at r-project.org] On Behalf Of
> tolga.i.uzuner at jpmorgan.com
> Sent: Tuesday, July 22, 2008 7:50 AM
> To: r-help at r-project.org
> Subject: [R] normalised/transformed regressions
> Dear R Users,
> Are there any packages in R which carries out a normalisation
> to variables as follows:
> - find the empirical distribution function, using perhaps ecdf
> - use the empirical distribution function to transform the
> variables into a series between 0 and 1
> - use this series to map the variables into the normal
> distribution function, using qnorm
> - perform a regression on the transformed variables, which by
> construction will all be normally distributed
> - return some meaningful statistical test results and even
> better, a function which, given the independent variables,
> returns the dependent variable after inverting back through
> the transformed coefficients back into the original space
> Thanks in advance,
> Tolga
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