Fit Statistics from FMM & Genmod

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Fit Statistics from FMM & Genmod

[ Edited ]

How are you?

This post is related to the other here that Generalized Poisson distribution is better than Negative Binomial with scale=Pearson due to lower Log likelihood, AIC, AICC and BIC.

I further fitted other models i.e. the Zero-inflated Poisson/Negative Binomial and Poisson hurdle and the Fit Statistics shows ZINB and Generalised Poisson are similar in magnitude.

Can I please ask why are the Fit Statistics are not identical for ZINB from proc fmm and genmod for Zero-Inflated Negative Binomial? Did I have the code wrong?

Secondly, is ZINB the best due to lower Fit Statistics? But if so, overdispersion still presents.. Why is that? Could it be that there is no other (important) explanatory variables?

 PROC FMM PROC GENMOD Poisson Poisson hurdle ZIP ZINB Generalized Poisson ZINB Poisson Fit Statistics -2 Log Likelihood 889.8 735.6 735.6 714.1 709.9 AIC (smaller is better) 899.8 755.6 755.6 736.1 721.9 719.5241 899.7862 AICC (smaller is better) 899.8 755.7 755.7 736.3 721.9 719.658 899.8166 BIC (smaller is better) 927.7 811.5 811.5 797.6 755.4 781.0401 927.748 Pearson Statistic 4544.5 2444 2444 2568.4 2280.3 Effective Parameters 10 10 11 Effective Components 2 2 1 Deviance 697.5241 727.6564 Scaled Deviance 697.5241 727.6564 Pearson Chi-Square 2156.2724 4544.5249 Scaled Pearson X2 2156.2724 4544.5249 Log Likelihood -348.762 -383.701 Full Log Likelihood -348.762 -444.8931
``` proc genmod data=tmp order=formatted;
title "Genmod: ZINB";
where occ>0; format raps raps.; class raps;
model inv=raps / dist=zinb maxit=1000;
zeromodel raps;
output out=zinb predicted=pred pzero=pzero;
ods output ParameterEstimates=zinbparms;
ods output modelfit=fit;
run;
data fit;
set fit(where=(criterion="Scaled Pearson X2"));
format pvalue pvalue6.4;
pvalue=1-probchi(value,df);
run;
proc print data=fit noobs; var criterion value df pvalue; run;
/*
Criterion               Value      DF    pvalue
Scaled Pearson X2       2156.2724    1973    0.0022
*p-value<0.05 indicating rejection of the null hypothesis of no overdispersion at 5% confidence levels;
*/

proc fmm data=tmp;
title "FMM: ZINB";
where occamt>0;	format raps raps.; class raps;
model Inv = raps / dist=negbin;
model Inv = / dist=constant;
probmodel raps;
run;```

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