This page shows an example of multinomial logit 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 3.6) 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.

Stata Example

Here is a multinomial 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/ex3.6.dat, clear

mlogit u1 x1 x3

Iteration 0:   log likelihood =  -539.2303
Iteration 1:   log likelihood = -446.49742
Iteration 2:   log likelihood = -434.20483
Iteration 3:   log likelihood =  -433.4331
Iteration 4:   log likelihood = -433.42628
Iteration 5:   log likelihood = -433.42628

Multinomial logistic regression                   Number of obs   =        500
                                                  LR chi2(4)      =     211.61
                                                  Prob > chi2     =     0.0000
Log likelihood = -433.42628                       Pseudo R2       =     0.1962

------------------------------------------------------------------------------
          u1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
0            |
          x1 |   .7686261C   .1567749     4.90   0.000      .461353    1.075899
          x3 |   2.259422C   .2144306    10.54   0.000     1.839146    2.679699
       _cons |  -.7488877E   .1702198    -4.40   0.000    -1.082512   -.4152631
-------------+----------------------------------------------------------------
1            |
          x1 |   .2798667D   .1131474     2.47   0.013     .0581018    .5016316
          x3 |    .885101D   .1402897     6.31   0.000     .6101382    1.160064
       _cons |   .2622508E   .1198104     2.19   0.029     .0274268    .4970748
------------------------------------------------------------------------------
(u1==2 is the base outcome)

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
           . |    500   -539.2303   -433.4263A      6     878.8526B    904.1402B
------------------------------------------------------------------------------

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 predicting the comparison of level 0 to level 2 of the
outcome variable, u1. Likewise, x1 and x3, are
significantly related to predicting the comparison of level 1 to level 2 of 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

Here is the same example illustrated in Mplus based on the ex3.6 data file.

TITLE:	
  this is an example of a multinomial
  logistic regression for an unordered
  categorical (nominal) dependent variable
  with two covariates
DATA:
  FILE IS https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.6.dat;
VARIABLE:
  NAMES ARE u1 x1 x3;
  NOMINAL IS u1;
MODEL:	
  u1#1 u1#2 ON x1 x3;

Number of observations                                         500
Estimator                                                      MLR

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Loglikelihood

          H0 Value                        -433.426A

Information Criteria

          Number of Free Parameters              6
          Akaike (AIC)                     878.853B
          Bayesian (BIC)                   904.140B
          Sample-Size Adjusted BIC         885.096
            (n* = (n + 2) / 24)

MODEL RESULTS
                   Estimates     S.E.  Est./S.E.

 U1#1       ON
    X1                 0.769C    0.165      4.670
    X3                 2.259C    0.203     11.148

 U1#2       ON
    X1                 0.280D    0.114      2.444
    X3                 0.885D    0.143      6.200

 Intercepts
    U1#1              -0.749E    0.158     -4.728
    U1#2               0.262E    0.120      2.192