The following example shows the output in Mplus, as well as how to reproduce
it using Stata. For this example we will use the same dataset we used for our
poisson
regression data analysis example. You can download the dataset for Mplus here: poissonreg.dat.
The model we specify for this example includes four variables, three predictors
and one outcome. We use student’s gender (male), the student’s score on a
standardized test in math (math), and the student’s score on a standardized
test in language arts (langarts) to predict the number of days a student was absent from
school during a single school year (daysabs). The Mplus input for this
model is:

    DATA:
      File is "D:datapoissonreg.dat" ;
    VARIABLE:
      Names are id school male math langarts daysatt daysabs;
      usevariables are langarts math daysabs male;
      count is daysabs;
    MODEL:
      daysabs on male math langarts;
    OUTPUT: stand

Below are the results from the model described above. Note that Mplus produces
two types of standardized coefficients “Std” which are in the fifth column of
the output shown below,
and “StdXY” which are in the sixth column. The Std column contains coefficients standardized using the variance of continuous latent variables.
Because all of the variables in this model are manifest (i.e. observed) the
coefficients in this column are identical to those in the column of regular
coefficients (i.e. the “Estimates” column). The StdXY column contains the
coefficients standardized using the variance of the background and/or outcome
variables, in addition to the variance of continuous latent variables.

MODEL RESULTS

                   Estimates     S.E.  Est./S.E.    Std     StdYX

 DAYSABS    ON
    MALE              -0.401    0.139     -2.877   -0.401   -0.652
    MATH              -0.004    0.008     -0.462   -0.004   -0.205
    LANGARTS          -0.012    0.005     -2.299   -0.012   -0.709

 Intercepts
    DAYSABS            2.688    0.218     12.340    2.688    8.750

Now, from the latent variable point of view, there is a latent variable
behind the observed count variable and this latent variable is the true
outcome variable. In other words, the poisson regression is simply modeling
the latent variable (y*) using the linear relationship:

y* = beta_0 + beta_1* male + beta_2*math + beta_3*langarts

Notice that there is no random residual term here. Therefore, the
variance of y* is the variance of the linear prediction. In other words, V(y*)
= V(xb). This is how Mplus calculates the variance of the “latent” outcome
variable.

Now, we will replicate these coefficients in Stata. The first bold line below opens
the dataset, and the second runs the Poisson regression model in Stata. Note
that the unstandardized coefficients from Stata and Mplus are within rounding
error of each other, this should be the case, since we are running the same
model.

use https://stats.idre.ucla.edu/stat/stata/dae/poissonreg, clear
poisson daysabs male math langarts

Iteration 0:   log likelihood = -1547.9709  
Iteration 1:   log likelihood = -1547.9709  

Poisson regression                                Number of obs   =        316
                                                  LR chi2(3)      =     175.27
                                                  Prob > chi2     =     0.0000
Log likelihood = -1547.9709                       Pseudo R2       =     0.0536

------------------------------------------------------------------------------
     daysabs |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        male |  -.4009209   .0484122    -8.28   0.000     -.495807   -.3060348
        math |  -.0035232   .0018213    -1.93   0.053     -.007093    .0000466
    langarts |  -.0121521   .0018348    -6.62   0.000    -.0157483   -.0085559
       _cons |   2.687666   .0726512    36.99   0.000     2.545272     2.83006
------------------------------------------------------------------------------

In order to calculate a standardized coefficient we will need three pieces of
information, the standard deviation of y* (the linear prediction), the standard
deviation of the predictor variable for which we want to create a standardized
coefficient, and the unstandardized coefficient for that predictor variable.

Let’s say that we need to calculate the standardized coefficient for
male. Here is what we need to do. First of all, calculate the standard
deviation of y*, which is the linear prediction. This is stored in a local
macro variable called “ystd”. Secondly, we need to
obtain the standard deviation for the linear predictor male. We
summarize the predictor variable,
in this case male, and use the results that Stata saves after a command is run to place
it’s standard deviation into a local macro called “xstd.” Since Stata
automatically stores the coefficients from the last regression we ran, we can
access the coefficient for male by typing _b[male]. Now we are
ready to actually calculate the standardized coefficients. The second to
last command below creates a new local macro called “male_std” and sets it equal
to the standardized coefficient for male (i.e. _b[male]*`xstd’/`ystd’).
The last command shown below tells Stata to display the contents of “male_std”
which is the standardized coefficient for the relationship between male
and log of the predicted count of daysabs. This value is approximately
-0.652, looking at the Mplus output above, we see that the standardized
coefficient (StdYX) for male is also estimated to be -0.652 by Mplus.

predict xb, xb
sum xb

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
          xb |       316    1.712138    .3076592   .8868849   2.671879

local ystd=r(sd)
sum male

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        male |       316    .4873418    .5006325          0          1

local xstd = r(sd)

local male_std = _b[male]*`xstd'/`ystd'
display "`male_std'"
-.6523909465586064

The commands and output below show the same process for the other two predictor variables
in the model.

sum math

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
        math |       316    48.75101    17.88076   1.007114   98.99289

local xstd = r(sd) 
local math_std = _b[math]*`xstd'/`ystd'
display "`math_std'"
-.2047650322590808

sum langarts

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
    langarts |       316    50.06379    17.93921   1.007114   98.99289

local xstd = r(sd)
local langarts_std = _b[langarts]*`xstd'/`ystd'
display "`langarts_std'"
-.7085747822838703

Cautions, Flies in the Ointment

See Also