Dispersion Parameter Estimate
Message/Author
 Rachel Roiland posted on Thursday, March 15, 2012 - 10:06 am
Hello Drs. Muthen,
I am trying to understand how one interprets the negative binomial dispersion parameter in my output. I just ran a very simple model (i.e., one count variable dependent variable regressed on to two continuous varibles) and received a dispersion parameter estimate of 0.114 and a two - tailed p-value of 0.461. I am familiar with the alpha dispersion estimate you receive from STAT and SAS and if the parameter isn't statistically significant, dispersion is not an issue and you can use a Poisson model. Can the parameter estimate provided in MPLUS output be interpreted in the same way?
Thank you!
 Bengt O. Muthen posted on Friday, March 16, 2012 - 8:40 am
Yes.
 Bengt O. Muthen posted on Friday, March 16, 2012 - 9:25 am
With the caveat of the problem of testing a parameter at the border of its admissible space (zero). I use BIC instead to choose between the various count models. See the Marital Affairs example on slides 39-41 in our Topic 5 handout on the website, showing the many variations on the count modeling theme available in Mplus.
 Rachel Roiland posted on Monday, March 26, 2012 - 6:55 am
Thanks so much!
 Lisa M. Yarnell posted on Tuesday, March 26, 2013 - 10:50 pm
Hi Bengt and Linda,

Is there a rule of thumb for how large the dispersion statistic should be in ZINB regression? Is it supposed to be close to 1.00 for the NB to be appropriate?

Or should I just be judging its significance, as stated above, as a reflection of whether NB is preferable over Poisson?

Tnanks.
 Linda K. Muthen posted on Wednesday, March 27, 2013 - 2:31 pm
It should be greater than zero. You can check the following reference for a maximum value:

Hilbe, J. M. (2007). Negative binomial regression. Cambridge,
UK: Cambridge University Press.

You can look at significance or you can compare the BIC's from the models with and without dispersion.
 Jen posted on Wednesday, July 30, 2014 - 9:53 am
Hello,

I had another question re: the dispersion parameter estimates. When negative binomial items serve as indicators of a latent factor, is the dispersion parameter estimate still relevant? For several of my indicators, the p-value is close to 1 for items that have significant dispersion when included as manifest variables in the model. Does this just mean that the 'residual' dispersion after modeling the latent factor is non-significant?

Thanks!
 Bengt O. Muthen posted on Wednesday, July 30, 2014 - 4:14 pm
The dispersion parameters are relevant also for indicators of factors. Perhaps you are right that the factor absorbs some of the unobserved heterogeneity that the dispersion parameters try to capture and therefore make them go insignificant when used as factor indicators.
 Brooke Magnus posted on Friday, August 04, 2017 - 9:48 am
Hello --

I am running a series of CFAs that include negative binomial indicators. Is there a way to constrain the dispersion parameter to a particular value (i.e., an estimate from a previous calibration)? After searching through the documentation, I cannot seem to find a way to reference the dispersion parameter in the code.

Thank you!
 Bengt O. Muthen posted on Friday, August 04, 2017 - 2:27 pm
Try referring to it like you would a variance.