This page shows an example of 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 3.5) 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/ex3.5.dat, clear

tabulate u1

         u1 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        327       65.40A       65.40
          1 |        173       34.60A      100.00
------------+-----------------------------------
      Total |        500      100.00

A. These are the percent of cases with 0 and 1 on the variable u1

logit u1 x1 x3

Iteration 0:   log likelihood = -322.46763
Iteration 1:   log likelihood = -216.57883
Iteration 2:   log likelihood = -203.79479
Iteration 3:   log likelihood = -202.63515
Iteration 4:   log likelihood = -202.61995
Iteration 5:   log likelihood = -202.61995

Logistic regression                               Number of obs   =        500
                                                  LR chi2(2)      =     239.70
                                                  Prob > chi2     =     0.0000
Log likelihood = -202.61995                       Pseudo R2       =     0.3717

------------------------------------------------------------------------------
          u1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   1.071767E  .1428573     7.50   0.000      .791772    1.351762
          x3 |   1.838588E  .1794923    10.24   0.000     1.486789    2.190386
       _cons |  -1.025842D  .1369173    -7.49   0.000    -1.294195   -.7574886
------------------------------------------------------------------------------

logit , or

Logistic regression                               Number of obs   =        500
                                                  LR chi2(2)      =     239.70
                                                  Prob > chi2     =     0.0000
Log likelihood = -202.61995                       Pseudo R2       =     0.3717

------------------------------------------------------------------------------
          u1 | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   2.920536F   .4172198     7.50   0.000     2.207304    3.864229
          x3 |   6.287652F   1.128585    10.24   0.000     4.422872    8.938663
------------------------------------------------------------------------------

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)B    df         AICC        BICC
-------------+----------------------------------------------------------------
           . |    500   -322.4676   -202.6199      3     411.2399    423.8837
------------------------------------------------------------------------------

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 x2, are
significantly related to the outcome variable, u1. The coefficients from
the logit output can be exponentiated to obtain odds ratios, as shown in
the output from the logit, or command. For a one unit increase in x1,
the odds of u1 equaling 1 (as compared to u1 equaling 0) increases
by a factor of 2.92. 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/ex3.5.dat data file.

TITLE:	
  this is an example of a logistic
  regression for a categorical observed
  dependent variable with two covariates
DATA:
  FILE = https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.5.dat;
VARIABLE:
  NAMES = u1 x1 x3;
  CATEGORICAL = u1;
ANALYSIS:
  ESTIMATOR = ML;
  ! need to use estimator = ml to make this a logistic model;
MODEL:
  u1 ON x1 x3;

SUMMARY OF ANALYSIS
Number of observations                                         500
Estimator                                                      MLR

<some output was omitted to save space>

SUMMARY OF CATEGORICAL DATA PROPORTIONS

    U1
      Category 1    0.654A
      Category 2    0.346A

TESTS OF MODEL FIT

Loglikelihood

          H0 Value                        -202.620B

Information Criteria

          Number of Free Parameters              3
          Akaike (AIC)                     411.240C
          Bayesian (BIC)                   423.884C
          Sample-Size Adjusted BIC         414.362
            (n* = (n + 2) / 24)

MODEL RESULTS

                   Estimates     S.E.  Est./S.E.

 U1         ON
    X1                 1.072D    0.143      7.502
    X3                 1.839D    0.179     10.243

 Thresholds
    U1$1               1.026E    0.137      7.492

LOGISTIC REGRESSION ODDS RATIO RESULTS

 U1         ON
    X1                 2.921F
    X3                 6.288F

Mplus Example #2

Here is another version of this example in Mplus. Note that by using
estimator=ml; (maximum likelihood) the results are shown in a logit metric.
Had we specified something like estimator=wls; (weighted least squares)
then the results would be shown in a probit scale. Because this analysis does
not use the type=logistic option (unlike example #1), the format of the
output is somewhat different (notably omitting odds ratios from the output).

TITLE:
  this is an example of a logistic
  regression for a categorical observed
  dependent variable with two covariates.
DATA:
  FILE = https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.5.dat;
VARIABLE:
  NAMES = u1 x1 x3;
  CATEGORICAL = u1;
! note using Maximum Likelihood produces results in Logit scale
! using GLS produces results in Probit scale
analysis:
  estimator=ml;
MODEL:
  u1 ON x1 x3;

SUMMARY OF ANALYSIS
Number of observations                                         500
Estimator                                                       ML
<some output omitted to save space>

SUMMARY OF CATEGORICAL DATA PROPORTIONS

    U1
      Category 1    0.654A
      Category 2    0.346A

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Loglikelihood

          H0 Value                        -202.620B

Information Criteria

          Number of Free Parameters              3
          Akaike (AIC)                     411.240C
          Bayesian (BIC)                   423.884C
          Sample-Size Adjusted BIC         414.362
            (n* = (n + 2) / 24)

MODEL RESULTS

                   Estimates     S.E.  Est./S.E.
 U1         ON
    X1                 1.072E    0.143      7.503
    X3                 1.839E    0.179     10.245

 Thresholds
    U1$1               1.026D    0.137      7.493