Categorical data goodness of fit question


I am trying to fit a log linear model with proc genmod and when i include all interactions (3 variables) i get the following:

Criterion DF Value Value/DF
Deviance 0 0.0000 .
Scaled Deviance 0 0.0000 .
Pearson Chi-Square . 0.0000 .
Scaled Pearson X2 . 0.0000 .
Log Likelihood 29180.8352
Full Log Likelihood -52.9296
AIC (smaller is better) 121.8593
AICC (smaller is better) .
BIC (smaller is better) 122.4948

The algorithm converged but i don't know how to interpret the above output.
Does the model fit the data good?
Any help please
Thank you


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It looks like you fit an overparameterized model (it seems like you have as many parameters as you do observations).
Dason thank you for your response.

I tried to fit a more simple model but it would not converge...
The only models that converge is the no interaction model and the saturated (3 variables all possible interactions).
For the no-interaction model, deviance and Pearson chi-sq have small P-value(<0.05) which means not good fit.
For the saturated model i get the above output...

Anyway i will try to figure this out.
Thank you for your help
I have 3 variables (yes or no response) and i want to see if there is any type of dependence. So i ran PROC FREQ to create the count variable. This was my response for the PROC GENMOD model count= var1 var2 var3 / DIST=POISSON link=log.
I started with the simple model but had poor fit. Then i tried all the 2-way interactions but i got the following warnings:

WARNING: The negative of the Hessian is not positive definite. The convergence is questionable.
WARNING: The procedure is continuing but the validity of the model fit is questionable.
WARNING: The specified model did not converge.
WARNING: Negative of Hessian not positive definite.

When i tried all the possible interactions i overparametrized the model...

Any idea for any alternatives?
Thank you!