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:

[hidden email]
[mailto:

[hidden email]] Im Auftrag von Newson, Roger B

Gesendet: Dienstag, 2. Dezember 2008 19:44

An:

[hidden email]
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:

[hidden email]
Web page:

http://www.imperial.ac.uk/nhli/r.newson/Departmental Web page:

http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

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

-----Original Message-----

From:

[hidden email]
[mailto:

[hidden email]] On Behalf Of Florian Köhler

Sent: 02 December 2008 17:29

To:

[hidden email]
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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