Calcite | Level 5

## Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

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?

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Rhodochrosite | Level 12

## Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

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.

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Rhodochrosite | Level 12

## Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

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.

Calcite | Level 5

## Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

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,

Rhodochrosite | Level 12

## Interpretation of Coefficient and Goodness of Fit for Gamma Log Link

The User's Guide for GENMOD (you can get on-line) discusses goodness of fit measures for generalized linear models. Good luck.

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