Poisson Regression

This document 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).

1.0 Example using Stata

Here is a poisson regression example using Stata with two continuous predictors x1 and x2 used to predict a binary outcome variable, u1.

infile u1 x1 x3 using 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 

Poissonregression               Number of obs =500

                                            LR chi2(2)= 631.98

                                            Prob > chi2 =0.000

Log likelihood =-966.883    Pseudo R2  = 0.246 

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

u1 |       Coef.    S.E.       z       P>|z|       [95% CI]

-------------+-------------------------------------

x1 |       .533^C    .023   22.41   0.000   .486      .579

x3 |       .249^C    .024   10.03   0.000   .200      .298

_cons |1.025^D     .028   36.14   0.000   .970     1.081

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

 estat ic 

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

Model | Obs  ll(null)  ll(model)^A  df    AIC^B      BIC^B

-------------+-------------------------------------

.   |     500      -1282     -966      3    1939      1952

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

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 estatic command produces fit indices for the model including the loglikelihood for the empty (null) model, the log likelihood for the model, as well as the AIC and BIC fit indices.

2.0 Example using Mplus

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                        -966.884^A

Information Criteria

          Number of Free Parameters              3

          Akaike (AIC)                    1939.768^B

          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^C    0.027    19.808

    X3                 0.249^C    0.025     9.788

 Intercepts

B. These are the AIC and BIC values, see the AIC and BIC values from the estat ic command in Stata.

C. These are the coefficients for the poisson model expressing the relationship between x1x3 and u1, the same as those from the Stata poisson command.

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