[Limdep Nlogit List] Deviance for unconditional fixed effects negative binomial regression model

rjcal at u.washington.edu rjcal at u.washington.edu
Wed Aug 12 00:23:38 EST 2009


Dear LIMDEP users:

Hi, I'm a fairly new LIMDEP user. So here's my question: I'm estimating an
unconditional negative binomial fixed effects regression model, and would like
to know the deviance. I'd like to know how to do one of three things:

1. Get LIMDEP to display the point estimates for the fixed effects, in order to 
calculate deviance manually using the LIMDEP output. 
2. Use the point estimates from the LIMDEP output as starting values for SAS, 
in order to get the SAS model to converge and get the deviance values that way. 
3. Add "deviance;" or something else equally simple to the LIMDEP syntax...(Dr. 
Greene, if that functionality doesn't exist yet, could you please consider 
writing it for the next LIMDEP release?)

Details follow. Thanks!

Richard


My reason for doing this is that Allison and Waterman ("Negative Binomial 
Regression Models," Sociological Methodology 32:247-265, 2003) argue that the 
unconditional model is more like a true fixed effects model than the 
conditional version, but the standard errors of estimated parameters are biased 
downwards for their simulated data. They recommend adjusting the 
standard errors for the unconditional model estimates upwards by dividing by 
the square root of the ratio of the deviance to the degrees of freedom for the 
model.

The benefit of running this model in LIMDEP (as opposed to manually adding the 
fixed effects to a regular negative binomial regression model in another 
package) is that Dr. Greene has done some wizardry to get these models to 
converge (although it's still unstable and I've had to deal with outliers ahead 
of time to avoid crashing LIMDEP). PROC GENMOD in SAS gives you the deviance,  
SAS is failing to converge.

Here's some standard code for the model so we're all on the same page:
SKIP
NEGBIN; Lhs = Y1
 	; Rhs = one, age, age2, X1
 	; Pds = grpsize
 	; Fem
 	$
NOSKIP

So I think it's possible to calculate the deviance manually by first getting 
the predicted values:
SKIP
NEGBIN; Lhs = RDLSM
 	; Rhs = one, age, age2, jbprsc
 	; Pds = grpsize
 	; fill; list
 	$
NOSKIP

That gives me a table with the following:
"Observation   Observed Y   Predicted Y   Residual  x(i)b Pr[Y*=y]"

So to get the deviance, I just need to know the overdispersion parameter 
lambda, the observed Y values, and values for the parameter mu_it, such that 
ln(mu_it) = delta_i + beta*X_it), where X is the vector of exogeneous variables 
used in the model and delta is the estimated fixed effect. (Just to confirm: 
it's correct to use the formula for mu from the Poisson distribution for the 
Negative Binomial, right? The only difference should be the overdispersion 
parameter...)

So I can see three options for getting the deviance:
1. Calculate it manually based on the output, but how do you get LIMDEP to 
display the point estimates for the fixed effects?
2. Use the point estimates from the LIMDEP output as starting values for SAS, 
in order to get the SAS model to converge and get the deviance values that way. 
If anyone knows how to do this, I'd love to know!
3. Add "deviance;" or something else equally simple to the LIMDEP syntax...(Dr. 
Greene, if that functionality doesn't exist yet, could you please consider 
writing it for the next LIMDEP release?)

Finally I'm noticing that I can get the models in LIMDEP to converge in two 
ways. My dependent variable is a scale, and I've gotten the model to converge 
by using a dependent variable constructed based on censoring the individual 
components of the scale and then adding them. I've just considered using a 
"regular" unconditional negative binomial fixed effects model on the outcome, 
but technically shouldn't I then be using a model for censored data?

Thanks everyone for your feedback!

Sincerely,

Richard Callahan

---
Richard Callahan
Graduate Student, Department of Sociology
University of Washington
(206) 769-9812
rjcal at u.washington.edu
http://students.washington.edu/rjcal/





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