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Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

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Regular Contributor
Posts: 204

Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

Dear Sir or Madam,

 

How are you?

 

I am writing to ask your advice on the adequacy between 2 Gamma models on log link from proc genmod. Is B better? Do I also have to look at the diagnostic plots? Thank you very much.

 

(1) One 5-level covariate(x)

             Criteria For Assessing Goodness Of Fit

 

Criterion                     DF           Value        Value/DF

 

Deviance                    9147       8893.7611          0.9723

Scaled Deviance             9147      10383.5112          1.1352

Pearson Chi-Square          9147      25589.8917          2.7976

Scaled Pearson X2           9147      29876.3286          3.2662

Log Likelihood                       -48608.2903

Full Log Likelihood                  -48608.2903

AIC (smaller is better)               97228.5806

AICC (smaller is better)              97228.5898

BIC (smaller is better)               97271.3110

 

 

(2) Two 5-level covariates(x and y) and their interaction term

             Criteria For Assessing Goodness Of Fit

 

Criterion                     DF           Value        Value/DF

 

Deviance                    9037       8296.5195          0.9181

Scaled Deviance             9037      10223.2934          1.1313

Pearson Chi-Square          9037      24705.1601          2.7338

Scaled Pearson X2           9037      30442.6575          3.3687

Log Likelihood                       -47833.7561

Full Log Likelihood                  -47833.7561

AIC (smaller is better)               95719.5123

AICC (smaller is better)              95719.6677

BIC (smaller is better)               95904.4202

Respected Advisor
Posts: 2,655

Re: Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

The IC criteria all point to the second model (B) as being superior, while none of the other GoF parameters really point to any difference between the two.  However, I would still examine the observed vs. predicted plot to check for any systematic bias.

 

Steve Denham

Regular Contributor
Posts: 204

Re: Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

[ Edited ]

Hi @SteveDenham.

 

Thank you for your insight.

 

Can I please ask you why is the p-value from the second model (2) so different between the Deviance and the Scaled Deviance?

As far as I have understand, the p-value from the deviance(p=0.999999992) says the model fits the data reasonably well. But why is it 0 from the Scaled deviance. I don't understand.

 

I plotted the histogram of deviance residual, standardized deviance residual and  likelihood residual from the model to check for normality and they do not indicate any departure from normality.

 

I further checked the actual value against the predicted value and it is hardly a straight line.

 

Any insight will be greatly appreciated.

 

 

4996  data _null_; p=1-probchi(8296.5195,9037); put p=; run;

p=0.9999999925
NOTE: DATA statement used (Total process time):
      real time           0.00 seconds
      cpu time            0.00 seconds


4997  data _null_; p=1-probchi(10223.2934,9037); put p=; run;

p=0

 

SAS Super FREQ
Posts: 3,319

Re: Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

You can read about estimates of scale in the GENMOD documentation.  You didn't show your code, so we don't know how the scale was estiamted, but with df=9037, there is bound to be a sizeable difference between the scaled and unscaled deviance.

 

The p-values are the probability of observing a random observation from the chisq(df=9037) distribution that is at least as great as 8297 (for the deviance) or 10223 (for the scaled deviance).  You can look at the reference lines in the following plot to confirm that the computations are correct.

 

%let df = 9037;
data PDF;
do x = 8000 to 10300 by 20;
   chi2 = pdf("chisquare", x, &df);
   output;
end;
run;

proc sgplot data=pdf;
series x=x y=chi2;
refline 10223 8297 / axis=x;
run;
Regular Contributor
Posts: 204

Re: Assessing Goodness Of Fit of Gamma on log link models from Proc Genmod

[ Edited ]

Hi @Rick_SASThank you for your reply.

I have read but sadly I still don't understand.

Please find my code below if that would be helpful.

Thank you very much.

ods graphics on;
proc genmod data=temp plots=all;
	class country raps;
	model occamt=country raps country*raps / dist=gamma link=log type3;
	lsmeans raps country country*raps / pdiff ilink adj=tukey;
	contrast 'linear' raps -2 -1  0  1  2;
	contrast 'quadratic' raps 2 -1 -2 -1  2 ;
	contrast 'cubic' raps -1  2  0 -2  1;
	output out=Residuals
		pred=Pred resraw=Resraw	reschi=Reschi resdev=Resdev
		stdreschi=Stdreschi stdresdev=Stdresdev	reslik=Reslik;
run;
proc univariate data=Residuals normal; 
	var Resraw Reschi Stdreschi Resdev Stdresdev Reslik;
	histogram/ normal;
run;
proc gplot data=residuals; plot Resdev*Pred; run; quit;
proc gplot data=residuals; plot Stdresdev*Pred; run; quit;
proc gplot data=residuals; plot Reslik*Pred; run; quit;
proc gplot data=residuals; plot occamt*Pred; run; quit;

 

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