Interpratation of zero-inflated models
Message/Author
 Matthew McBee posted on Friday, October 24, 2008 - 9:35 am
Can you clarify: when fitting a zero-inflated binomial or poisson model, how is the outcome coded for the categorical part of the model? Does a "1" indicate that the outcome is zero or non-zero? In other words, if the same covariate is included in both parts of the model and has the same direction of effect in both, is the coefficient in both parts of the model positive or is it negative in the categorical model?
 Matthew McBee posted on Friday, October 24, 2008 - 10:02 am
Sorry, by "categorical" I meant "binary" since both parts are categorical!
 Bengt O. Muthen posted on Friday, October 24, 2008 - 6:21 pm
In the binary part Mplus does logistic regression for Prob(u#=1), where u# is a binary latent inflation variable and u#=1 indicates that the individual is unable to assume any value except 0. This is called the zero class.

For the non-zero class, any count value can be assumed and is modeled via regular Poisson.

So I guess one can say that the direction is not the same in the two parts.
 Matthew McBee posted on Saturday, October 25, 2008 - 1:08 pm
Thank you for answering my question.

Why is the MLR estimator the default for these models? Is it common to get biased standard errors using the ML estimator?
 Bengt O. Muthen posted on Sunday, October 26, 2008 - 8:56 am
The idea is that MLR may be more robust to model misspecification. You can do simulations to see what seems best in your setting.
 Kevin M. King posted on Tuesday, June 09, 2009 - 3:58 pm
I have a question about interpreting coefficients from zero-inflated negative binomial models.

We are predicting count variables that fit a zero-inflated negative binomial distribution from latent growth factors (intercept and linear slope, whose indicators are continuous).

Specifically, how do we interpret the significance of an effect of a growth factor on either the binary portion or the count portion?

In several cases, the unstandardized effect will not be significant, but the standardized effect will be (or vice versa). Is there an explanation for this, and which is the more reliable estimate?
 Linda K. Muthen posted on Wednesday, June 10, 2009 - 7:59 am
Usually the two parts are not separately interpreted. See the following references for further information:

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

Agresti, A. (2002). Categorical data analysis. Second edition. New York: John
Wiley & Sons.

Agresti, A. (1996). An introduction to categorical data analysis. New York:
Wiley.

In ZIP regression, the unstandardized is most common. If the differences between raw and standardized are large, please send the output to support@statmodel.com.
 Arina Gertseva posted on Thursday, June 25, 2009 - 8:31 am
Dear Linda,
I am trying to run growth models for two parallel processes allowing each of the processes to have zero inflated distributions, probably negative binomial. Each process (offending and victimization) is measured annually during 5 years. Can Mplus do this type of analysis?
If yes, could you please direct me to where I can find examples of syntax, etc.
Thanks, Arina.
 Bengt O. Muthen posted on Thursday, June 25, 2009 - 9:38 am
Yes, Mplus can do this - combine UG ex6.7 and 6.13. Also, see (hear) the web talk on count regression modeling on our web site. And for count growth (mixture) modeling, look for instance at

Kreuter, F. & Muthen, B. (2008). Analyzing criminal trajectory profiles: Bridging multilevel and group-based approaches using growth mixture modeling. Journal of Quantitative Criminology, 24, 1-31.

which you find on our web site too.
 Dustin Pardini posted on Friday, May 06, 2011 - 12:41 pm
When running a negative binomial model with a single predictor I continually get a stdyx estimate of 1. In these models the p-value for the undstandardized coefficient is highly significant, while the standardize p is not. This problem does not seem to occur when multiple predictors are entered into the model. I am having a hard time understanding why this is occurring.
 Linda K. Muthen posted on Saturday, May 07, 2011 - 11:07 am
It probably does not make sense to use StdYX with a count outcome. I would use the raw coefficient or at most StdX which you would have to compute yourself.
 Daniel Lee posted on Thursday, March 26, 2020 - 9:13 am
Hi Dr. Muthen,

I am reading the Regression and Mediation Analysis Using Mplus, and I wonder if there is any way to get predicted counts for a zero-truncated negative binomial model. That is, if the mean of all covariates are set at their respective mean, a unit increase in X would predict Y expected counts.

I'm guessing that Model Constraint is involved. If so, can you point me to syntax or provide maybe a simple example (2 covariates) to get me started.

Thank you so much!
 Bengt O. Muthen posted on Thursday, March 26, 2020 - 11:30 am
Don't have the syntax but check the Hilbe and Long refs I give on page 262.