22 Aug 2011
Stata 12's SEM option

Stata 12 can do structural equation modeling (SEM). One can reference factor loadings, means and intercepts, and residual variances and variances of both observed and latent variables. Parameters can be freed, constrained, etc. This report provides examples of a CFA, multitrait multimethod matrix, and a latent growth model. Example 1 illustrates some generic Stata SEM syntax useful to most projects. Results from Stata's SEM package are compared with those from MPLUS in Examples 2-3. The intent here is to explore the building blocks and not to put the building blocks together in unique combinations. That is left to the investigator.

Specific capabilities in Stata 12

--Constrain paths, coefficients.
--Get all the regular fit statistics.
--Request stdyx results.
--SEM works seamlessly with lincom, test, predict (to get factor scores), and other built-in Stata functions we know and love.
--Get modification indices (cutoff of your choosing, you can even select types of modification indices you wish to see)
--Request LISREL-style output with estat framework, which comes with friendlier return matrices but does not provide standard errors for those parameters. Example 3 uses this to pull values from matrices (Example 2 does it using normally returned matrices). A limitation is that standard errors of estimates are not returned with estat framework.
--Read data from a covariance/correlation matrix.
--Like its regression, Stata's default way of handling missing data in SEM is listwise complete deletion, but there is an extra option method(mlmv) that asks for MAR estimates.
--Estimate a latent growth model, multiple-group model, and other fancy things.
--Draw a diagram of your model, and even use the diagram to specify and run your model. Recall sweet memories of long nights with Amos.

Limitations in Stata 12 compared to MPLUS

--You can estimate a model by drawing a path diagram, and it'll put estimates on your picture for you. But I am not sure you can produce a path diagram using model syntax. That would be too fantastic.
--Stata drops any rows with missing data by default. They have options for assuming data are MAR, but it is different than MPLUS' MAR estimator and incompatible with certain other post-command options in Stata12.
--No mention of categorical dependent variables in the user's guide, or any mention of thresholds. If you live by categorical outcomes, stick to MPLUS.
--No mention of categorical latent variables.

In the following examples, I show syntax and emphasize comparisons of parameter estimates and standard errors between MPLUS and Stata12. Emphasis is not on substantive interpretation. MPLUS is run through Stata using Dr. Jones' RunMPLUS.ado, which is freely available with findit runmplus.

Example 1. CFA.

This example presents a single factor CFA. Here, we demonstrate some of the
cool features available in Stata 12 and benefits of the package being integrated with existing
features in Stata. We use baseline data from the ACTIVE study. Below is a basic diagram of the model:

If you ever want to see syntax for how to refer to a given parameter, like a covariance or error or path loading, add coeflegend to the SEM command after the comma.

If you want to estimate a model in a multiple groups framework, for example by sex or intervention group, add group(groupvarname)  to the SEM command after the comma.

Data. Three functional measures (IADL, ADL, IQCODE) were measured for each individual using both self and proxy reports. Reporting type are the methods factors; traits are handled with correlations because there are only 2 indicators for each trait.

use http://www.stata-press.com/data/r12/sem_lcm, clear
tex \newpage
tex {\bf Example 3. Growth model. }
tex
tex RunMPLUS Syntax (output omitted):
quietly {
   * MPLUS
   runmplus lncrime0 lncrime1 lncrime2 lncrime3, ///
      model(i s | lncrime0@0 lncrime1@1 lncrime2@2 lncrime3@3; ///
      lncrime0 - lncrime3 (a); ///
      ) output(!stdyx;)
   mat fooestmplus=r(estimate)
   mat foosemplus=r(se)
   mat list fooestmplus
   local test: rowfullnames fooestmplus
   display "`test'"
   capture mat drop semplus
   mat semplus  = J(26,1,.)
   forvalues i=1/26 {
      mat semplus[`i',1] = foosemplus[`i',1]
   }
   capture mat drop estmplus
   mat estmplus = J(26,1,.)
   forvalues i=1/21 {
      mat estmplus[`i',1] = fooestmplus[`i',1]
   }
   mat estmplus[22,1]=`r(CFI)'
   mat estmplus[23,1]=`r(RMSEA)'
   mat estmplus[24,1]=`r(chisquare)'
   mat estmplus[25,1]=`r(chisquare_df)'
   mat estmplus[26,1]=`r(chisquare_P)'
}

Rows are particular parameter estimates (which ones? please see earlier output). The last 5 rows show the CFI, RMSEA, chi2, chi2 df, and chi2 p-value, respectively.