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Interpretation on Parameter Estimates from Gamma log link

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Regular Contributor
Posts: 226

Interpretation on Parameter Estimates from Gamma log link

Dear Sir or Madam,

 

Can I please ask your help on how to interpret the parameter estimates from Gamma log link? 

If a unit increase in x will increase y by Beta(x)? 

 

Thank you very much.

proc genmod data=temp plots=all;
	class raps(ref="0") help(ref="No") inv(ref="Zero") ob(ref="Zero") / param=ref;
	model occ=raps help inv ob / dist=gamma link=log type3;
	contrast 'linear' raps -2 -1  0  1  2;
	contrast 'quadratic' raps 2 -1 -2 -1  2 ;
	contrast 'cubic' raps -1  2  0 -2  1;
run;

 

Analysis Of Maximum Likelihood Parameter Estimates
Parameter DFEstimateStandard ErrorWald 95% Confidence LimitsWald Chi-SquarePr > ChiSq
Intercept 13.76670.02043.72663.806833928.8<.0001
raps110.54650.04260.4630.63164.73<.0001
raps210.65080.06180.52980.7718111.06<.0001
raps310.97990.10.78391.175896.07<.0001
raps410.84170.20550.43911.244416.79<.0001
helpYes10.38290.13030.12750.63838.640.0033
INVAt least once10.31160.08230.15030.472814.340.0002
OBAt least once10.15210.03180.08980.214422.88<.0001
Scale 12.23280.06632.10662.3666  
Super User
Posts: 9,782

Re: Interpretation on Parameter Estimates from Gamma log link

Sorry. I am not expert about it .Maybe some expert like @Steve @lvm should gave you right answer.

My opinion is.

Since all your independent variables are CLASS variables. Therefore the following could not be right .

"If a unit increase in x will increase y by Beta(x)"

maybe should say when the level change from the compared level(last level) into the current level , Beta(x) or Y will change 0.3116 .

 

the estimate coefficient of  CLASS variables represent the association between the current level of CLASS variable and the expect value of dependent variable E(Y) .

 

And since all the coefficient of  CLASS variables are constraint to 1 ,then you could know the last level's  estimate coefficient:

E.X.

INV At least once   0.3116

That means the another level of INV should have -0.3116 ,although it does not printed out.

So INV(At least once) have the positive correlation with E(log(occ)) and

     INV(another level) have the negative correlation with E(log(occ)) .

SAS Super FREQ
Posts: 3,556

Re: Interpretation on Parameter Estimates from Gamma log link

1. When you use reference parameterization, parameter estimates of CLASS main effects estimate the difference in the effect of each nonreference level compared to the effect of the reference level.

2. Since you do not have any continuous variables, your question is not exactly correct. You can ask "as a class variable changes from the reference value to a different value, how does the predicted value change?"  

 

The answer can be derived from the predicted model, which you were shown how to get in your last post:  To find the difference from the reference level, plug in the level of x and get the predicted value. Notice that because you are using a log link you also need to exponentiate: exp(beta*x).  You can compare this value to the predicted value when ALL parameters are at their reference level: exp(beta*x_ref).

 

 

 

 

Regular Contributor
Posts: 226

Re: Interpretation on Parameter Estimates from Gamma log link

Hi @Rick_SAS and @Ksharp.

 

Thank you for your explanation.

Can I please ask to check with you whether I have indeed understood?

Thank you very much.

 

y_pred=exp(3.7266+(raps=1)0.5465+(raps=2)0.6508+(raps=3)0.9799+(raps=4)0.8417+(help=Yes)0.3829+(INV=At least once)0.3116+(OB=At least once)0.1521)

 

If raps=1 vs raps=o,
exp(3.7266+0.5465)/exp(3.7266)=1.729(3d.p.), occ will increase by 1.729 when raps changes from 0 to 1 while holding other variables constant.

Super User
Posts: 9,782

Re: Interpretation on Parameter Estimates from Gamma log link

[ Edited ]

y_pred is depended on Design Matrix , you missed the reference level of CLASS variable.

 

If I was right:

Log(occ1)(When raps=1) = ...  0.5465*(raps=1).....

 

 Log(occ0)(When raps=0 -- average effect of the four levels of raps )  = ...  0.5465*(raps=0).....

 

==>

 

 

Log(occ-1/occ-0)= 0.5465

 

Which means E(log(occ)) will increase 0.5465

when raps turn from 0(average effect of the four levels of raps )  into 1(current level) .

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