Probit Regression

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 http://www.ats.ucla.edu/stat/mplus/output/ex3.4.dat, clear

tabulate u1u1 | Freq. Percent Cum. ------------+----------------------------------- 0 | 321 64.2064.20 1 | 179 35.80^{A}100.00 ------------+----------------------------------- Total | 500 100.00^{A}probit u1 x1 x3Iteration 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 | 1.022478.1262691 8.10 0.000 .7749951 1.269961 x3 | 2.474276^{B}.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.^{B}

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
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 0.642Category 2 0.358^{A}THE MODEL ESTIMATION TERMINATED NORMALLY <some output omitted to save space> MODEL RESULTS Estimates S.E. Est./S.E. U1 ON X1 1.022^{A}0.121 8.457 X3 2.474^{B}0.224 11.028^{B}

- 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.