This page shows an example of probit 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 drawn from the Mplus User’s Guide (example 3.4) 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 probit regression example using Stata with two continuous predictors
x1 and x2 used to predict a binary outcome variable, u1.

infile u1 x1 x3 using ex3.4.dat, clear

tabulate u1

         u1 |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        321       64.20A       64.20
          1 |        179       35.80A      100.00
------------+-----------------------------------
      Total |        500      100.00

probit u1 x1 x3

Iteration 0:   log likelihood = -326.12939
Iteration 1:   log likelihood = -161.14424
Iteration 2:   log likelihood = -122.87381
Iteration 3:   log likelihood = -111.40561
Iteration 4:   log likelihood = -109.52052
Iteration 5:   log likelihood = -109.45715
Iteration 6:   log likelihood = -109.45707

Probit regression                                 Number of obs   =        500
                                                  LR chi2(2)      =     433.34
                                                  Prob > chi2     =     0.0000
Log likelihood = -109.45707                       Pseudo R2       =     0.6644

------------------------------------------------------------------------------
          u1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   1.022478B  .1262691     8.10   0.000     .7749951    1.269961
          x3 |   2.474276B  .2276468    10.87   0.000     2.028096    2.920455
       _cons |  -.9838567   .1250848    -7.87   0.000    -1.229018    -.738695
------------------------------------------------------------------------------

note: 15 failures and 1 success completely determined.

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.

Mplus Example

Here is the same example illustrated in Mplus based on the
https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.4.dat data file. Note that by using
estimator=wls; (weighted least squares) the results are shown in a probit metric.
Had we specified something like estimator=ml; (maximum likelihood)
then the results would be shown in a logit scale.

TITLE:
  this is an example of a probit regression
  for a binary or categorical observed
  dependent variable with two covariates
DATA:
  FILE IS ex3.4.dat;
analysis:
  estimator=wls;
VARIABLE:
  NAMES ARE u1 x1 x3;
  CATEGORICAL = u1;
MODEL:	
  u1 ON x1 x3;

SUMMARY OF ANALYSIS

Number of observations                                         500
Estimator                                                      WLS
<some output was omitted to save space>

SUMMARY OF CATEGORICAL DATA PROPORTIONS

    U1
      Category 1    0.642A
      Category 2    0.358A

THE MODEL ESTIMATION TERMINATED NORMALLY
<some output omitted to save space>

MODEL RESULTS

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

 U1       ON
    X1                 1.022B    0.121      8.457
    X3                 2.474B    0.224     11.028