## Interpretation on Parameter Estimates from Gamma log link

Regular Contributor
Posts: 234

# Interpretation on 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 DF Estimate Standard Error Wald 95% Confidence Limits Wald Chi-Square Pr > ChiSq Intercept 1 3.7667 0.0204 3.7266 3.8068 33928.8 <.0001 raps 1 1 0.5465 0.0426 0.463 0.63 164.73 <.0001 raps 2 1 0.6508 0.0618 0.5298 0.7718 111.06 <.0001 raps 3 1 0.9799 0.1 0.7839 1.1758 96.07 <.0001 raps 4 1 0.8417 0.2055 0.4391 1.2444 16.79 <.0001 help Yes 1 0.3829 0.1303 0.1275 0.6383 8.64 0.0033 INV At least once 1 0.3116 0.0823 0.1503 0.4728 14.34 0.0002 OB At least once 1 0.1521 0.0318 0.0898 0.2144 22.88 <.0001 Scale 1 2.2328 0.0663 2.1066 2.3666
Super User
Posts: 10,213

## 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: 3,839

## 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: 234

## Re: Interpretation on Parameter Estimates from Gamma log link

Hi @Rick_SAS and @Ksharp.

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: 10,213

## 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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