Stat Computing > Mplus > Output

Annotated Mplus Output
Seemingly Unrelated Regression

This page shows an example of a seemingly unrelated 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. 

Example Using Stata

Here is an example of a seemingly unrelated regression using Stata. This model predicts read from write math science and also predicts socst from write math science. These two equations are estimated jointly.

use http://www.ats.ucla.edu/stat/stata/notes/hsb2
sureg (read write math science) (socst write math science)

Seemingly unrelated regression
----------------------------------------------------------------------
Equation          Obs  Parms        RMSE    "R-sq"       chi2        P
----------------------------------------------------------------------
read              200      3    6.930412    0.5408     235.54   0.0000
socst             200      3    8.180626    0.4164     142.73   0.0000
----------------------------------------------------------------------

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
read         |
       write |   .2376706A   .0689943     3.44   0.001     .1024443    .3728968
        math |   .3784015A   .0738838     5.12   0.000     .2335919    .5232111
     science |   .2969347A   .0669546     4.43   0.000     .1657061    .4281633
       _cons |   4.369926B   3.176527     1.38   0.169    -1.855954    10.59581
-------------+----------------------------------------------------------------
socst        |
       write |   .4656741A   .0814405     5.72   0.000     .3060536    .6252946
        math |   .2763008A   .0872121     3.17   0.002     .1053682    .4472334
     science |   .0851168A   .0790329     1.08   0.281    -.0697848    .2400185
       _cons |   8.869885B   3.749558     2.37   0.018     1.520886    16.21888
------------------------------------------------------------------------------

Below we obtain the residuals for read and for socst, and then obtain the variance of each of these residuals, as well as their covariance.

predict eread, residual equation(read)
predict esocst, residual equation(socst)
corr eread esocst, cov

             |    eread   esocst
-------------+------------------
       eread |   48.272C
      esocst |  18.3796D  67.2589C

The output is labeled with superscripts to help you relate the later Mplus output to this Stata output. To summarize the output, all three predictors are significantly related to read, while two of the three predictors (except science) are significantly related to socst. 

Mplus Example #1

Here is the same example illustrated in Mplus based on the hsb2.dat data file. 

Title:
  Seemingly unrelated regression;
Data:
  File = hsb2.dat ;
Variable:
  Names = id female race ses schtyp prog read write math science socst;
  usevar = read socst write math science;
Analysis:
  Type = meanstructure ;
model:
  read on write math science;
  socst on write math science;

THE MODEL ESTIMATION TERMINATED NORMALLY

MODEL RESULTS

                   Estimates     S.E.  Est./S.E.
 READ     ON
    WRITE              0.238A    0.069      3.445
    MATH               0.378A    0.074      5.122
    SCIENCE            0.297A    0.067      4.435

 SOCST    ON
    WRITE              0.466A    0.081      5.718
    MATH               0.276A    0.087      3.168
    SCIENCE            0.085A    0.079      1.077

 SOCST    WITH
    READ              18.286D    4.212      4.341

 Intercepts
    READ               4.370B    3.177      1.376
    SOCST              8.870B    3.750      2.366

 Residual Variances
    READ              48.030C    4.803     10.000
    SOCST             66.922C    6.692     10.000

1. These are the regression coefficients predicting the outcome variable from each predictor. These are interpreted as any standard OLS regression coefficient. For example, for a one unit increase in write we would predict a .466 unit increase in socst. These results are analogous to those produced by the sureg command from Stata.
2. These are the intercepts for each equation, and correspond to the values of _cons from the Stata output.
3. These are the variances of the residuals from each equation. In the Stata example, we generated these residuals and then displayed the covariance of them, with the variances appearing on the diagonal.
4. This is the covariance of the residuals, corresponding to the off diagonal value from the Stata covariance matrix of the residuals.

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