This page shows an example of zero inflated Poisson regression with footnotes explaining the output. First an example is shown using Stata, and then an example is shown using Mplus, to help you relate the output you are likely to be familiar with (Stata) to output that may be new to you (Mplus). We suggest that you view this page using two web browsers so you can show the page side by side showing the Stata output in one browser and the corresponding Mplus output in the other browser.

This example is from the Mplus User’s Guide (example 3.8) and we suggest that you see the Mplus User’s Guide for more details about this example. We thank the kind people at Muthén & Muthén for permission to use examples from their manual.

**Example Using Stata**

Here is a logit regression example using Stata with two continuous predictors
**x1** and **x3** used to predict a binary outcome variable, **u1**.
These same predictors are used to predict the zero inflation in **u1** as
well.

infile u1 x1 x3 using https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.8.dat, clear

zip u1 x1 x3, inflate(x1 x3)<some output omitted> Zero-inflated Poisson regression Number of obs = 500 Nonzero obs = 282 Zero obs = 218 Inflation model = logit LR chi2(2) = 209.64 Log likelihood = -758.855 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- u1 | x1 | .5478153.0398304 13.75 0.000 .4697492 .6258814 x3 | .3087748^{C}.0416855 7.41 0.000 .2270728 .3904768 _cons | 1.06087^{C}^{D}.0380128 27.91 0.000 .9863659 1.135373 -------------+---------------------------------------------------------------- inflate | x1 | 1.629311^{E}.2163157 7.53 0.000 1.20534 2.053282 x3 | 1.054722^{E}.1717856 6.14 0.000 .718028 1.391415 _cons | -.9500156^{F}.1674828 -5.67 0.000 -1.278276 -.6217554 ------------------------------------------------------------------------------estat ic------------------------------------------------------------------------------ Model | Obs ll(null) ll(model) df AIC BIC -------------+---------------------------------------------------------------- . | 500 -863.6735 -758.855^{A}6 1529.71^{B}1554.998^{B}------------------------------------------------------------------------------

The output is labeled with superscripts to help you relate the later Mplus
output to this Stata output. To summarize the output, both predictors in this model, **x1 **and** x3, **are
significantly related to the outcome variable, **u1**, and both predictors
are related to the zero inflation in **u1**. The **estat ic** command produces fit indices for the
model including the log likelihood for the empty (null) model, the log
likelihood for the model, as well as the AIC and BIC fit indices.

**Mplus Example #1**

Here is the same example illustrated in Mplus based on the https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.8.dat data file. The output has been edited and condensed to save space.

TITLE: this is an example of a zero-inflated Poisson regression for a count dependent variable with two covariates DATA: FILE IS https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.8.dat; VARIABLE: NAMES ARE u1 x1 x3; COUNT IS u1 (i); MODEL: u1 ON x1 x3; u1#1 ON x1 x3;SUMMARY OF ANALYSIS Number of observations 500 TESTS OF MODEL FIT Loglikelihood H0 Value -758.855^{1}Information Criteria Number of Free Parameters 6 Akaike (AIC) 1529.710^{2}Bayesian (BIC) 1554.998^{2}Sample-Size Adjusted BIC 1535.953 (n* = (n + 2) / 24) MODEL RESULTS Estimates S.E. Est./S.E. U1 ON X1 0.5480.041 13.308 X3 0.309^{3}0.041 7.619 U1#1 ON X1 1.629^{3}^{5}0.237 6.871 X3 1.055^{5}0.181 5.827 Intercepts U1#1 -0.950^{6}0.170 -5.596 U1 1.061^{4}0.041 26.115

1. This is the log likelihood value associated with the model (see the ll(model) )
from the **estat ic** command in Stata.

2. These are the AIC and BIC values, see the AIC and BIC values from the
**estat ic** command in Stata.

3. These are the coefficients for the Poisson model expressing the relationship between
**x1 x3** and **u1**, the same as those from the Stata **zip** command.

4. This is the intercept for the Poisson model, the same as that
from the Stata **poisson** command.

5. These are the coefficients for the zero inflation part of the
model model expressing the relationship between **x1 x3**
and the zero inflation in **u1**, the same as those from the **inflate**
part of the model from the Stata **zip** command.

6. This is the intercept for the zero inflation part of the model, the same as
the intercept from the **inflate** part of the model from the Stata **
zip** command.