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st: AW: RE: Interpretation of Log Transformed Independent Variables in Ordered Logit


From   Florian Köhler <florian.koehler@tu-berlin.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: AW: RE: Interpretation of Log Transformed Independent Variables in Ordered Logit
Date   Wed, 3 Dec 2008 11:14:04 +0100

Roger,

Thanks for your comments.

Maybe I did not make myself clear enough, but I was referring to marginal
changes in predicted outcome probabilities, in my case pr(outcome=3). The
STATA command after ologit would be mfx compute, predict(outcome(3)).

This means I (approximately) get the effect of a unit change in my x-variate
on Pr(outcome=3). If my variable was the "number of employees" everything is
clear, I get the effect of having one more employee on Pr(outcome=3). But
since my x-variate is "log(number of employees)" I was confused. If I
understand you right, I then get the effect of raising my original variable
(employees) by the factor e on Pr(outcome=3).  

In OLS, though,  the interpretation of coefficients of log-transformed
variables can be done in terms of percent change, right? (A one percent
increase in the independent variable raises/decreases the dependent variable
by (coefficient/100) units) 
That´s why I thought I could do an interpretation in my ologit example via
percent changes as well. 


Thanks a lot,

Florian


 


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Newson, Roger B
Gesendet: Dienstag, 2. Dezember 2008 19:44
An: statalist@hsphsun2.harvard.edu
Betreff: st: RE: Interpretation of Log Transformed Independent Variables in
Ordered Logit


Neither of these versions is exactly right. In the ordinal logistic model,
the linear predictor is not a probability, but a log odds ratio. And it is
not just a simple binary odds ratio, but an odds ratio for the event of the
discrete ordinal Y-variable being at or above a threshold value Y_0. And,
under the assumptions of the ordinal logistic model, this odds ratio is the
same for any threshold value Y_0 selected from the set of possible values of
Y (except for the lowest one). So the parameters of the ordinal logistic
regression model are not easy to explain to non-mathematicians, except if
these non-mathematicians already understand the concept of an odds ratio,
and understand it well.

If the X-variate is the log of an original variate (eg number of employees),
then its parameter is the log odds ratio associated with a unit increase in
the X-variate. If the X-variate is a natural logarithm, then its odds ratio
is the odds ratio associated with scaling up the original variable (eg
number of employees) by a foactor of e=exp(1), which is approximately
2.7182818. If the X-values are binary logs (derived by dividing the natural
logs by the natural log of 2), then its odds ratio is the odds ratio
associated with doubling the original variable (eg number of employees).
And, if the X-values are logs to the base 1.10 (derived by dividing the
natural logs by the natural log of 1.10), then the odds ratio associated
with scaling the original variable (eg number of employees) by a factor of
1.10, or, in other words, with increasing the original number of employees
by 10 percent. Remember that, if the model is an ordinal logistic
regression, then the odds ratio is an ef!  fect on the odds of a Y-value
being at OR ABOVE a threshold.

I hope this helps.

Best wishes

Roger


Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk 
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgene
tics/reph/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Florian Köhler
Sent: 02 December 2008 17:29
To: statalist@hsphsun2.harvard.edu
Subject: st: Interpretation of Log Transformed Independent Variables in
Ordered Logit

Hey Statalisters,

Using the command ologit I ran some Ordered Logit regressions with one of
the covariates (number of a firm´s employees) in a log transformed form
(since theory suggest a declining marginal effect)

My question concerns the interpretation of the marginal effects of the
log-transformed variable "number of employees" (mfx are computed with
respect to the outcome variable =3) .

I would think the following interpretation is right: 
	- A marginal increase in the log-transformed number of employees
changes the probability of my outcome variable being 3 		  by XXX
percentage points.

But: By log-transforming my continous variable "employees" I could (or have
to) interpret the changes in terms of percent changes, something like
	- A one percent increase in the number of employees (the actual
number, not the log-transformed)changes the probability 		of
my outcome variable being 3 by XXX percentage points.


Any hints on which version is right? Both, none?

Thanks

Florian

 


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