Likelihood ratio test for exact poisson regression

[Mona Dave]

Good afternoon,

I am trying to assess model fit for multivariate regression analysis using the liklihood ratio test on exact poisson regression models (using exact poisson due to a small sample size).

See code below:
expoisson Outcome Exposure1 Expousre2 Exposure3 Exposure4, irr
est store m1
expoisson Outcome Exposure1 Expousre2 Exposure3 Exposure4 Exposure5 , irr
est store m2
lrtest m1 m2

I get the following error messages:
(m1 does not contain matrix e(V); rank = 0 assumed)
m1 does not contain scalar e(ll)

Is there an alternative method for exact models?

Many thanks

[Rich Goldstein]

exact models, as used here, are not maximum likelihood models and thus a likelihood ratio test is not possible

[Mona Dave]

Thanks Richard. So would I have to use another model or are there other tests for models such as these? I wondered if the AIC (estat ic) could be used here. Many thanks

[Rich Goldstein]

AIC, etc., are also based on likelihoods and thus us also not appropriate

the issue is in what sense do you mean "model fit"? i.e., what exactly are you worried about? remember that, in a sense, this is an exact estimator

[Maarten Buis]

The test you want to do is equivalent to the test that the coefficient of exposure 5 equals 0 in model 2.

[Mona Dave]

In reply to Richard, I'm trying to do forward stepwise regression. What I've been taught is to use a test based on liklihood to arrive at the final model in multivariate analysis. However, I've not used exact regression before which is where I've come a bit stuck with methodology. That's useful to know that the other tests based on liklihood won't work here.

[Rich Goldstein]

what is your N? you appear to have either 4 or 5 predictors/covariates (or whatever you want to call them) and my worry right now is that your N is too small for this many predictors

[Mona Dave]

N=23