Annotated Mplus Output
Poisson Regression

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 http://www.ats.ucla.edu/stat/mplus/output/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

------------------------------------------------------------------------------
          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
------------------------------------------------------------------------------

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)A     df          AICB         BICB
-------------+----------------------------------------------------------------
           . |    500   -1282.874    -966.884      3     1939.768    1952.412
------------------------------------------------------------------------------

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 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 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

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