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Probit Regression | Mplus Annotated Output

This page shows an example of probit regression with footnotes explaining the output. 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.

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
  1. These are the percent of cases with 0 and 1 on the variable u1. Note that Mplus labels the values of a two-category variable “Category 1” and “Category 2” regardless of what the underlying values are in the data.
  2. These are the probit coefficients expressing the relationship between x1 x3 and u1 on the probit scale. Increases in both x1 and x3 are associated with increases in the probability that u1=1. The change in probability due to one-unit change in x1 is dependent on the value of x3 (and vice versa) because the probit link function is non-linear, so cannot be expressed as a single number. 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.