## Algebraic notation for variance in negative binomial model

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LiamMS90
Posts: 3
Joined: Sat Jul 28, 2018 1:56 pm

### Algebraic notation for variance in negative binomial model

Dear Colleagues,

I'm using version 3.02 to run a two level negative binomial model. There seems to be a difference between the algebraic notation for the level 1 variance displayed in the equations window and the notation in teaching materials referencing earlier versions of mlwin and more generally in the literature.

In 3.02 I see..... pi + pi^2*a

Elsewhere I see.... pi + pi^2/v

Is this a bug or is there another explanation?

Many thanks,

Liam

ChrisCharlton
Posts: 1182
Joined: Mon Oct 19, 2009 10:34 am

### Re: Algebraic notation for variance in negative binomial model

Hi Checked this with Professor Kelvyn Jones who initially requested the change in notation and he provided the following explanation:
The equation is now correct- there are two ways of doing this and we have always estimated it this way but the specification used to be incorrect

It is what Hilbe calls NB2

https://www.encyclopediaofmath.org/imag ... t_data.pdf

“This form of negative binomial has been termed NB2, due to the quadratic nature of its variance function “
image001.png (13.87 KiB) Viewed 2426 times
NBD2 has 2 parameters for the level-1 variance; that is quadratic level-1 variance,

α is the over-dispersion parameter; if α > 0 then NBD; if α=0, NBD reduces to Poisson;

in stored model results α estimate is associated with Bcons2.1 label

Lips data
image002.png (14.88 KiB) Viewed 2426 times
And results
image003.png (14.97 KiB) Viewed 2426 times