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 |   .5478153C   .0398304    13.75   0.000     .4697492    .6258814
          x3 |   .3087748C   .0416855     7.41   0.000     .2270728    .3904768
       _cons |    1.06087D   .0380128    27.91   0.000     .9863659    1.135373
-------------+----------------------------------------------------------------
inflate      |
          x1 |   1.629311E   .2163157     7.53   0.000      1.20534    2.053282
          x3 |   1.054722E   .1717856     6.14   0.000      .718028    1.391415
       _cons |  -.9500156F   .1674828    -5.67   0.000    -1.278276   -.6217554
------------------------------------------------------------------------------

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
           . |    500   -863.6735    -758.855A      6      1529.71B    1554.998B
------------------------------------------------------------------------------

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                        -758.8551

Information Criteria

          Number of Free Parameters              6
          Akaike (AIC)                    1529.7102
          Bayesian (BIC)                  1554.9982
          Sample-Size Adjusted BIC        1535.953
            (n* = (n + 2) / 24)

MODEL RESULTS
                   Estimates     S.E.  Est./S.E.

 U1         ON
    X1                 0.5483    0.041     13.308
    X3                 0.3093    0.041      7.619

 U1#1       ON
    X1                 1.6295    0.237      6.871
    X3                 1.0555    0.181      5.827

 Intercepts
    U1#1              -0.9506    0.170     -5.596
    U1                 1.0614    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.