How would I know whether to use Poisson or negative binomoial regression for a count variable? And if the variable is zero-inflated, which technique should I choose - zero-inflated Poisson or zero-inflated negative binomial? What effect does my choice have on the results of the analysis?
And what is the Mplus syntax for specifying a variable as negative binomial?
I am running a negative binomial regression with a continuous DV and a continuous IV. Is there a way to request that mplus provide me with the effect size for each IV? If that's not the case, is there a way that I can calculate the effect size from the mplus output?
It sounds like you are asking for standardized coefficients which are typically not used with count outcomes (although standardizing wrt covariates can be done in Mplus). One common metric to report coefficients in is using incidence rate ratios (Hilbe, p.109), that is, exp(b) where b is the regression slope for a covariate; this can be done in Model Constraint. Hilbe's book is referred to in the UG.
I am running a negative binomial regression and I have a question regarding the assumptions of using this approach. With linear regression, there are several assumptions (e.g., homoskedasticity, normality of the residuals). Do these assumptions also apply when considering a negative binomial regression?
Count models don't have residuals so those issues aren't relevant. You can compare the observed and estimated counts to see how good the model is (see Chapter 6 in our RMA book and also our Topic 11 video and handout).