Goodness of fit statistics in the Poisson model

[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

[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


[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

[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.

[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.