topic Backtransform link=logit in Statistical Procedures

Backtransform link=logit

mthorne — Tue, 24 Nov 2020 20:36:24 GMT

How would you back transform values that were a result of dist=beta link=logit?

ods graphics on;
proc glimmix data=nocheck method=laplace plots=studentpanel; by site;
  class site trt rep;
  model d3 = trt / dist=beta link=logit;
 random intercept / subject=rep;
 store equirate;
run;
ods graphics off;

Re: Backtransform link=logit

ballardw — Tue, 24 Nov 2020 22:36:13 GMT

You might specify which values.

Depending there are places where there are options like ILINK that computes items in terms of the data and not the link function.

Re: Backtransform link=logit

Rick_SAS — Wed, 25 Nov 2020 11:43:36 GMT

There are two scales for predictions in generalized linear models: the data scale and the linear scale. The ILINK function tells you how to transform betwen the scales.

If you use the LOGIT function for the link, then the inverse-link function is the LOGISTIC function. For details and further discussion, see "Predicted values in generalized linear models: The ILINK option in SAS."

Re: Backtransform link=logit

mthorne — Wed, 25 Nov 2020 17:15:04 GMT

Thanks for the link to the document on Ilink options!

So, according to the document, the inverse of the logit is described as follows:

The inverse of the logit function is called the logistic function:
g-1(η) = logistic(η) = 1 / (1 + exp(-η))

So, using this, to back transform the estimate in Excel, I would use the following equation?:

=1/((1+EXP(-estimate)))

This seems to make sense as the back transformed values are very similar to the raw means.