This page shows an example of 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 3.7) 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 **x2** used to predict a binary outcome variable, **u1**.

infile u1 x1 x3 using https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.7.dat, clear

poisson u1 x1 x3Iteration 0: log likelihood = -966.8842 Iteration 1: log likelihood = -966.88398 Iteration 2: log likelihood = -966.88398 Poisson regression Number of obs = 500 LR chi2(2) = 631.98 Prob > chi2 = 0.0000 Log likelihood = -966.88398 Pseudo R2 = 0.2463 ------------------------------------------------------------------------------ u1 | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- x1 | .5330611.0237869 22.41 0.000 .4864395 .5796827 x3 | .2494125^{C}.0248628 10.03 0.000 .2006822 .2981427 _cons | 1.025773^{C}.0283819 36.14 0.000 .9701454 1.0814 ------------------------------------------------------------------------------^{D}estat ic------------------------------------------------------------------------------ Model | Obs ll(null) ll(model)df AIC^{A}BIC^{B}-------------+---------------------------------------------------------------- . | 500 -1282.874 -966.884 3 1939.768 1952.412 ------------------------------------------------------------------------------^{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**. 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/ex3.7.dat data file.

TITLE: this is an example of a Poisson regression for a count dependent variable with two covariates DATA: FILE IS https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.7.dat; VARIABLE: NAMES ARE u1 x1 x3; COUNT IS u1; MODEL: u1 ON x1 x3;

SUMMARY OF ANALYSIS Number of observations 500 THE MODEL ESTIMATION TERMINATED NORMALLY TESTS OF MODEL FIT Loglikelihood H0 Value -966.884Information Criteria Number of Free Parameters 3 Akaike (AIC) 1939.768^{A}Bayesian (BIC) 1952.412^{B}Sample-Size Adjusted BIC 1942.890 (n* = (n + 2) / 24) MODEL RESULTS Estimates S.E. Est./S.E. U1 ON X1 0.533^{B}0.027 19.808 X3 0.249^{C}0.025 9.788 Intercepts U1 1.026^{C}0.030 34.080^{D}

- This is the log likelihood value associated with the model (see the ll(model)
from the
**estat ic**command in Stata. - These are the AIC and BIC values, see the AIC and BIC values from the
**estat ic**command in Stata. - These are the coefficients for the poisson model expressing the relationship between
**x1 x3**and**u1**, the same as those from the Stata**poisson**command. - This is the intercept for the poisson model, the same as that
from the Stata
**poisson**command.