Programming the statistical procedures from SAS

Equation from Gamma on log link

Reply
Regular Contributor
Posts: 204

Equation from Gamma on log link

[ Edited ]

Dear Sir or Madam,

How are you?

Can I please ask your help on how can I write the equation out from the model below and how the Least Squares Means are calculated given the ML Parameter Estimates?

Your help is greatly appreciated.

 

 

proc genmod data=temp plots=all;
class raps help inv ob;
model occ=raps help inv ob / dist=gamma link=log type3;
contrast 'linear' raps -2 -1 0 1 2;
lsmeans raps help inv ob / pdiff ilink;
run;

Analysis Of Maximum Likelihood Parameter Estimates Standard Wald 95% Wald Parameter DF Estimate Error Confidence Limits Chi-Square Pr > ChiSq Intercept 1 4.9922 0.2273 4.5466 5.4377 482.19 <.0001 raps 0 1 -0.8423 0.2053 -1.2447 -0.4399 16.83 <.0001 raps 1 1 -0.2972 0.2080 -0.7049 0.1104 2.04 0.1529 raps 2 1 -0.1911 0.2112 -0.6050 0.2229 0.82 0.3657 raps 3 1 0.1381 0.2247 -0.3023 0.5786 0.38 0.5388 raps 4 0 0.0000 0.0000 0.0000 0.0000 . . Help No 1 -0.3832 0.1302 -0.6384 -0.1280 8.66 0.0032 Help yes 0 0.0000 0.0000 0.0000 0.0000 . . INV At least once 1 0.3124 0.0822 0.1513 0.4735 14.44 0.0001 INV Zero 0 0.0000 0.0000 0.0000 0.0000 . . OB At least once 1 0.1512 0.0316 0.0892 0.2132 22.85 <.0001 OB Zero 0 0.0000 0.0000 0.0000 0.0000 . . Scale 1 2.2357 0.0661 2.1099 2.3690 raps Least Squares Means Standard Standard Error of raps Estimate Error z Value Pr > |z| Mean Mean 0 4.1900 0.07543 55.55 <.0001 66.0259 4.9803 1 4.7351 0.08240 57.46 <.0001 113.87 9.3837 2 4.8413 0.08641 56.02 <.0001 126.63 10.9427 3 5.1704 0.1148 45.04 <.0001 175.99 20.2018 4 5.0323 0.2064 24.39 <.0001 153.29 31.6330 Differences of raps Least Squares Means Standard raps _raps Estimate Error z Value Pr > |z| 0 1 -0.5450 0.04245 -12.84 <.0001 0 2 -0.6512 0.06169 -10.56 <.0001 0 3 -0.9804 0.09989 -9.81 <.0001 0 4 -0.8423 0.2053 -4.10 <.0001
...

 

 

 

SAS Super FREQ
Posts: 3,317

Re: Equation from Gamma on log link

The easiest way to see the model is to use the CODE statement to create DATA step statements that evaluate (or "score") the model. Then look at the file that is created.

 

Based on your parameter estimates, the model will look something like this:


eta = 4.9922 +
(raps=0)*( -0.8423) +
(raps=1)*( -0.2972) +
(raps=2)*( -0.1911) +
(raps=3)*( 0.1381) +
(Help="No")*( -0.3832) +
(INV="At least once")*(0.3124) +
(OBS="At least once")*(0.1512);
Pred_occ = exp(eta);

 

If the Help and INV and OBS variables have formats on them, then use the unformatted (raw) values instead of the formatted values.

 

The LSMEANS are linear combinations of the parameter estimates. Because you used the ILINK option, those estimates are then transformed to the data scale. For details see  the GLM documentation.  You might also want to read "CONTRAST and ESTIMATE Statements Made Easy: The LSMESTIMATE Statement"

Regular Contributor
Posts: 204

Re: Equation from Gamma on log link

Hi @Rick_SAS

Thank you for your reply and all the links.

I'm still trying to understand them.

Ask a Question
Discussion stats
  • 2 replies
  • 175 views
  • 1 like
  • 2 in conversation