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

 From "Newson, Roger B" To Subject st: RE: Interpretation of Log Transformed Independent Variables in Ordered Logit Date Tue, 2 Dec 2008 18:43:34 -0000

```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
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:

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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