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Goodness of fit statistics in the Poisson model
Posted: Fri Jan 02, 2009 7:18 pm
by kamkitang
Dear moderator
Could you please tell me how R-squared and adjusted R-squared for the Poisson model are estimated in EViews? I notice that the Poisson model does not produced R-squared and adjusted R-squared statistics in the same way as in a linear regression model.
Thanks
KK
Re: Goodness of fit statistics in the Poisson model
Posted: Mon Jan 05, 2009 10:01 am
by EViews Gareth
The R-squared (and adjusted R2) are calculated in exactly the same way as for a linear regression model. I've written the following program to prove this:
Code: Select all
create u 100
rndseed 1
'first create the poisson/count model r2
series y1=nrnd>0
series x1 = nrnd
series ydiff1 = y1-@mean(y1)
scalar ydiffsumsq1 = @sumsq(ydiff1)
equation e1.count y1 c x1
scalar residsumsq1 = e1.@ssr
scalar r2_1 = 1- residsumsq1/ydiffsumsq1
'check r2 matches the reported r2:
scalar poisdiff = r2_1 - e1.@r2
'now do a standard ls model:
series y2=nrnd
series x2=nrnd
series ydiff2 = y2-@mean(y2)
scalar ydiffsumsq2 = @sumsq(ydiff2)
equation e2.ls y2 c x2
scalar residsumsq2=e2.@ssr
scalar r2_2 = 1-residsumsq2/ydiffsumsq2
'check r2 matches the reported r2:
scalar lsdiff = r2_2 - e2.@r2
Re: Goodness of fit statistics in the Poisson model
Posted: Mon Jan 05, 2009 2:58 pm
by kamkitang
Dear Gareth
Thanks for the clarification. I raised the original question after reading section 25.2.1 of Greene's "Econometric Analysis" 6th ed, which suggests a few different ways of computing R-squared for the Poisson model.
Thanks
KK
Re: Goodness of fit statistics in the Poisson model
Posted: Tue Jan 06, 2009 12:42 pm
by EViews Glenn
There are a number of goodness-of-fit statistics for limited dependent variables models (of which Poisson ML is one) that are on our list of things to look at...Suggestions regarding which ones people would like to see are always welcome.
Re: Goodness of fit statistics in the Poisson model
Posted: Tue Jan 06, 2009 6:50 pm
by kamkitang
Wooldridge (Introductory Econometrics: A Modern Approach, 1st ed, p.551) suggests to estimate R-squared as the square of the correlation between the actual and predicted value, since it is definitely non-negative and always being between 0 and 1, even though the estimates are not chosen to maximize such an R-squared. It is also useful when people want to compare the goodness-of-fit between Poisson and Tobit models.