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st: RE: Ordinal to interval assuming normality

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: Ordinal to interval assuming normality
Date   Thu, 16 Oct 2003 13:19:37 +0100

Michael Ingre
> 1) Is there any way to recode an ordinal variable to an 
> interval scale if
> you can assume that the latent variable that you are 
> measuring are normally
> distributed?
> My problem is that I have variables (for example the 
> occurrence of sleep
> problems in five categories 1-5) that are skewed or have 
> less than perfect
> kurtosis. However, because I can assume that the latent 
> variable is normally
> distributed in the measured population the violations 
> against normality in
> my data should be due to errors in my instrument. More 
> specifically, the
> categories are not equally spaced. It should be possible to 
> recode the value
> of my categories so that my data would fit the normal 
> distribution and as a
> consequence the categories should be equally spaced on an 
> interval scale.

I am not quite sure of what you want, but something like 

invnorm(<mean rank / sample size>) 

might be appropriate. (Is this not (related to) the 
rankit transformation of Fisher and Yates?) 

<mean rank / sample size> is computable by the -ridit()- 
-egen- function from -egenmore- on SSC. 

Thus for example 

. sysuse auto 
. ssc inst egenmore 
. egen ridit = ridit(rep78) 
. gen pseudogauss = invnorm(ridit) 
. tabdisp rep78, c(ridit pseudogauss) 

> 2) If this is possible, would you consider this approach to 
> be statistically
> valid when interpreting for example Pearson correlation 
> coefficients between
> two recoded variables?
This would seem to go in a circle with your prior assumption. To the 
extent that you are confident that the underlying variable really 
is Gaussian, then this would seem to be defensible. In practice, 
there is always some granularity in the results which you would 
need to consider. 

[email protected] 

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