Calcite | Level 5

## How do I solve Negative Binomial convergence problem?

I am trying to use a Negative Binomial regression model with link=log in SAS 9 for some count data in which the dependent count variable takes on the values that range between 4 and 300 depending on the experiment. I get the following warning in the Log:

"WARNING: The relative Hessian convergence criterion of ##### is greater than the limit of 0.0001. The convergence is questionable.
WARNING: The procedure is continuing but the validity of the model fit is questionable."

The model has two independent variables: DOSE and HIGH where HIGH is an idicator variable (0 or 1).

proc genmod data=test_data1 ;
ods output parameterestimates=params ModelANOVA=pvalues ;
model NCOUNT = DOSE1 HIGH / dist=negbin link=log type3 ;
by PRODUCT S9 STRAIN REP;
run ;

The estimate for dispersion parameter is always 0 or near 0. When the estimate is 0, its followed by a standard error and missing values for the 95% Wald CIs. The estimates and standard errors for the independent variables equal those when using a Poisson regression model rather than a negative binomial regression  model.

Is there a solution for the convergence issue?

6 REPLIES 6
Super User

## Re: How do I solve Negative Binomial convergence problem?

```Make the number of iteration bigger ?

proc genmod data=sashelp.class;
model age=weight height/maxiter=200 dist=negbin link=log type3 ;
run;

```
Calcite | Level 5

## Re: How do I solve Negative Binomial convergence problem?

Thank you. I tried the suggestion but I still get the warnings.
SAS Super FREQ

## Re: How do I solve Negative Binomial convergence problem?

Lack of convergence often indicates that a model does not fit the data. In your case, you are fitting this model for each distinct combination of PRODUCT S9 STRAIN REP.   Did you get an additional NOTE in the log that says something like "The proceeding WARNING was for the following BY group: PRODUCT=1 S9=2 STRAIN=3 REP=4;"?  If so, it might be that there is one BY group that does not fit the model, perhaps because of missing values, small sample size, constant values, outliers, etc.  If the number of BY groups that do not converge is small, you might choose to handle those groups separately or exclude them from this analysis. If the WARNING is printed for most/all BY groups, you should rethink your model.

Fluorite | Level 6

## Re: How do I solve Negative Binomial convergence problem?

What is the best way to identify which distribution or link to use or are there rule of thumbs in place to make help make these choices.

SAS Super FREQ

## Re: How do I solve Negative Binomial convergence problem?

Hello,

A bit the same message here as the one @Rick_SAS has already put forward.

You are NOT making one (1!) model. You are fitting as many models as there are unique (distinct) combinations of  "PRODUCT S9 STRAIN REP" - levels.
The models all have the same "model form", but it's not one (overall) model.
Are you aware of that?

Submit the below and I suspect it may become clear why some of your models have convergence problems.

``````proc freq data=test_data1 ;
tables PRODUCT * S9 * STRAIN * REP / list ;
run ;

proc means data=test_data1 ;
class PRODUCT S9 STRAIN REP ;
var   NCOUNT DOSE1 HIGH ;
run ;``````

BR, Koen

SAS Super FREQ

## Re: How do I solve Negative Binomial convergence problem?

If you want to initiate a new discussion, you should create a new thread.

The quick answer is that it depends on the response data (Y) that you are trying to model. I assume you know about normal and lognormal links. If you are modeling count data, then Poisson and Negative Binomial are appropriate. The gamma distribution is used to model positive continuous data. The Tweedie distribution is used in the insurance industry to model data (like insurance payouts) that are positive but have a point-mass density at 0.

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