This page shows an example of censored 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 3.2) 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 https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.2.dat, clear

summarize u1

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
          u1 |      1000    .9240341    1.113079          0A   6.579389

tobit u1 x1 x3, ll(0)

Tobit regression                                  Number of obs   =       1000
                                                  LR chi2(2)      =     697.44
                                                  Prob > chi2     =     0.0000
Log likelihood = -1142.8851                       Pseudo R2       =     0.2338

------------------------------------------------------------------------------
          u1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
          x1 |   1.074801D   .0419657    25.61   0.000     .9924498    1.157152
          x3 |   .4947541D   .0378985    13.05   0.000     .4203842     .569124
       _cons |   .5154865E   .0405066    12.73   0.000     .4359986    .5949743
-------------+----------------------------------------------------------------
      /sigma |   1.071333F   .0316242                      1.009276    1.133391
------------------------------------------------------------------------------
  Obs. summary:        376  left-censored observations at u1<=0
                       624     uncensored observations
                         0 right-censored observations

estat ic

------------------------------------------------------------------------------
       Model |    Obs    ll(null)   ll(model)     df          AIC         BIC
-------------+----------------------------------------------------------------
           . |   1000   -1491.605   -1142.885B      4      2293.77C    2313.401C
------------------------------------------------------------------------------

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/ex3.2.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 censored 
  regression for a censored dependent
  variable with two covariates
DATA:
  FILE IS https://stats.idre.ucla.edu/wp-content/uploads/2016/02/ex3.2.dat;
VARIABLE:
  NAMES ARE y1 x1 x3;
  CENSORED ARE y1 (b);
ANALYSIS:	
  ESTIMATOR = MLR;
MODEL:	
  y1 ON x1 x3;

SUMMARY OF ANALYSIS

<some output omitted to save space>
Number of observations                                        1000

<some output omitted to save space>
SUMMARY OF CENSORED LIMITS
      Y1                 0.000A

THE MODEL ESTIMATION TERMINATED NORMALLY

TESTS OF MODEL FIT

Loglikelihood

          H0 Value                       -1142.885B

Information Criteria

          Number of Free Parameters              4
          Akaike (AIC)                    2293.770C
          Bayesian (BIC)                  2313.401C
          Sample-Size Adjusted BIC        2300.697
            (n* = (n + 2) / 24)

MODEL RESULTS
                   Estimates     S.E.  Est./S.E.
 Y1         ON
    X1                 1.075D    0.043     25.101
    X3                 0.495D    0.037     13.344

 Intercepts
    Y1                 0.515E    0.040     12.810

 Residual Variances
    Y1                 1.148F    0.067     17.235