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.