Consider this seemingly unrelated regression using Stata.
use https://stats.idre.ucla.edu/stat/stata/notes/hsb2 sureg (read write math science) (socst write math science)
Seemingly unrelated regression
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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 | .2376706 .0689943 3.44 0.001 .1024443 .3728968
math | .3784015 .0738838 5.12 0.000 .2335919 .5232111
science | .2969347 .0669546 4.43 0.000 .1657061 .4281633
_cons | 4.369926 3.176527 1.38 0.169 -1.855954 10.59581
-------------+----------------------------------------------------------------
socst |
write | .4656741 .0814405 5.72 0.000 .3060536 .6252946
math | .2763008 .0872121 3.17 0.002 .1053682 .4472334
science | .0851168 .0790329 1.08 0.281 -.0697848 .2400185
_cons | 8.869885 3.749558 2.37 0.018 1.520886 16.21888
------------------------------------------------------------------------------
You could preface the command with the bootstrap prefix, as illustrated below, to obtain bias corrected bootstrap standard errors based on 20,000 replications.
bootstrap, reps(20000) bca: sureg (read write math science) (socst write math science)
Seemingly unrelated regression
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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
----------------------------------------------------------------------
------------------------------------------------------------------------------
| Bootstrap
| Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
read |
write | .2376706 .0689077 3.45 0.001 .1026139 .3727272
math | .3784015 .072022 5.25 0.000 .2372409 .5195621
science | .2969347 .0732453 4.05 0.000 .1533766 .4404928
_cons | 4.369926 2.958737 1.48 0.140 -1.429093 10.16894
-------------+----------------------------------------------------------------
socst |
write | .4656741 .0915943 5.08 0.000 .2861525 .6451957
math | .2763008 .0941304 2.94 0.003 .0918087 .4607929
science | .0851168 .0842935 1.01 0.313 -.0800954 .250329
_cons | 8.869885 3.412316 2.60 0.009 2.181869 15.5579
------------------------------------------------------------------------------
The same analysis can be run in Mplus and obtaining bias corrected standard errors. Here we run this based on the https://stats.idre.ucla.edu/wp-content/uploads/2016/02/hsb2.dat data file. Note that in the analysis section we use the bootstrap = 20000; command to request 20,000 bootstrap iterations, and then in the output section we use cinterval (bcbootstrap); to request confidence intervals using bias corrected bootstrap standard errors (by using bootstrap in place of bcbootstap we would get bootstrap standard errors that were not bias corrected).
As you compare the first analysis (with standard confidence intervals) with the second analysis (with bootstrap confidence intervals), note the slight discrepancies in the confidence intervals for _cons for the two equations.
Title: Bootstrap standard errors. Data: File = https://stats.idre.ucla.edu/wp-content/uploads/2016/02/hsb2.dat ; Variable: Names = id female race ses schtyp prog read write math science socst; usevar = read socst write math science; Analysis: Type = meanstructure ; bootstrap = 20000; model: read on write math science ; socst on write math science; output: cinterval (bcbootstrap);
And here is the output.
MODEL RESULTS
Estimates S.E. Est./S.E.
READ ON
WRITE 0.238 0.070 3.410
MATH 0.378 0.072 5.271
SCIENCE 0.297 0.073 4.052
SOCST ON
WRITE 0.466 0.091 5.122
MATH 0.276 0.094 2.931
SCIENCE 0.085 0.085 1.004
SOCST WITH
READ 18.286 4.168 4.387
Intercepts
READ 4.370 2.947 1.483
SOCST 8.870 3.420 2.594
Residual Variances
READ 48.030 4.419 10.869
SOCST 66.922 6.326 10.579
CONFIDENCE INTERVALS OF MODEL RESULTS
Lower .5% Lower 2.5% Estimates Upper 2.5% Upper .5%
READ ON
WRITE 0.055 0.101 0.238 0.374 0.414
MATH 0.200 0.240 0.378 0.521 0.566
SCIENCE 0.101 0.148 0.297 0.434 0.478
SOCST ON
WRITE 0.226 0.284 0.466 0.640 0.694
MATH 0.036 0.093 0.276 0.461 0.523
SCIENCE -0.135 -0.083 0.085 0.249 0.303
SOCST WITH
READ 8.219 10.776 18.286 27.222 30.064
Intercepts
READ -3.200 -1.351 4.370 10.152 12.136
SOCST 0.140 2.260 8.870 15.653 18.054
Residual Variances
READ 38.242 40.671 48.030 58.322 61.399
SOCST 52.587 56.277 66.922 81.379 85.557
The first and last column represent the LCL and UCL for a 99% confidence interval, and the second and fourth columns represent the LCL and UCL for a 95% confidence interval. The middle (third) column contains the point estimate for each of the parameters.
Note how the Mplus confidence intervalue for the Intercepts change in a similar way to the Stata values for _cons when using the bootstrap confidence intervals.