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
- These are the percent of cases with 0 and 1 on the variable u1, see output of tabulate command from Stata
- These are the probit coefficients expressing the relationship between x1 x2 and u1 in the probit scale, corresponding to the results of the Stata probit command. This is followed by the S.E. column (standard error) and the estimate divided by the standard error (Est./S.E). This final column is used for assessing significance by treating this like a Z test.