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## 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   * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
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## 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 effect 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   * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/* *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/
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## st: AW: RE: Interpretation of Log Transformed Independent Variables in Ordered Logit

 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   * *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/* *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/* *   For searches and help try: *   http://www.stata.com/help.cgi?search*   http://www.stata.com/support/statalist/faq*   http://www.ats.ucla.edu/stat/stata/