Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Home
- /
- Analytics
- /
- Stat Procs
- /
- Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

- RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Mute
- Printer Friendly Page

🔒 This topic is **solved** and **locked**.
Need further help from the community? Please
sign in and ask a **new** question.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Posted 07-05-2011 01:49 PM
(16795 views)

Hi,

I am fitting a GLM with gamma log link usng proc genmod log link. I have a difficult time of interpreting the coeffient of independent variables of this model.

For example, if I get a estimate coefficient of - 0.05 for the predictor X under gamma log link model, how can I interpret it as a relationship with the response variable?

Also, what are the criteria for assessing the goodness of fit for gamma log link model using Proc Genmod?

Thank you for your help!

1 ACCEPTED SOLUTION

Accepted Solutions

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

With a log link and a continuous predictor, you are fitting the model:

ln(mu) = beta0 + beta1*X,

where mu is the expected value. Then, e raised to the left and right sides gives:

mu = exp(beta0 + beta1*X) = exp(beta0)*exp(beta1*X)

In other words, you have a model for the mean as an exponential function of X. With a negative beta1, you have an exponential decay function.

Goodness of fit is not a trivial matter, and one could have a very long discussion on the subject. It usually best done in comparing competing models rather than in an absolute sense. To start with, look at the scaled deviance in the output. The smaller the better (in general), but the goal is not to get it down to 0. The scaled deviance divided by the df (displayed in the output) should be close to 1. There are good ODS GRAPHICS as well.

3 REPLIES 3

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

With a log link and a continuous predictor, you are fitting the model:

ln(mu) = beta0 + beta1*X,

where mu is the expected value. Then, e raised to the left and right sides gives:

mu = exp(beta0 + beta1*X) = exp(beta0)*exp(beta1*X)

In other words, you have a model for the mean as an exponential function of X. With a negative beta1, you have an exponential decay function.

Goodness of fit is not a trivial matter, and one could have a very long discussion on the subject. It usually best done in comparing competing models rather than in an absolute sense. To start with, look at the scaled deviance in the output. The smaller the better (in general), but the goal is not to get it down to 0. The scaled deviance divided by the df (displayed in the output) should be close to 1. There are good ODS GRAPHICS as well.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Hi lvm,

Thanks so much! Now I finally understand the basic components of writing a gamma log link model.

Is there any literature supporting the (scaled deviance)/df =1 as a good measure of goodness of fitness?

Thank you,

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

**Available on demand!**

Missed SAS Innovate Las Vegas? Watch all the action for free! View the keynotes, general sessions and 22 breakouts on demand.

What is ANOVA?

ANOVA, or Analysis Of Variance, is used to compare the averages or means of two or more populations to better understand how they differ. Watch this tutorial for more.

Find more tutorials on the SAS Users YouTube channel.