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 x3
Iteration 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
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u1 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
x1 | .5330611C .0237869 22.41 0.000 .4864395 .5796827
x3 | .2494125C .0248628 10.03 0.000 .2006822 .2981427
_cons | 1.025773D .0283819 36.14 0.000 .9701454 1.0814
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estat ic
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Model | Obs ll(null) ll(model)A df AICB BICB
-------------+----------------------------------------------------------------
. | 500 -1282.874 -966.884 3 1939.768 1952.412
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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 -966.884A
Information Criteria
Number of Free Parameters 3
Akaike (AIC) 1939.768B
Bayesian (BIC) 1952.412B
Sample-Size Adjusted BIC 1942.890
(n* = (n + 2) / 24)
MODEL RESULTS
Estimates S.E. Est./S.E.
U1 ON
X1 0.533C 0.027 19.808
X3 0.249C 0.025 9.788
Intercepts
U1 1.026D 0.030 34.080
- 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.