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!
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.
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?
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.