Preacher et al. (2008): Latent Growth Curve Modeling in Stata

The website accompanying Preacher et al.'s (2008) book on latent growth curve modeling provide syntax files for Lisrel, Mplus, and Mx, but not for Stata. These are the Stata commands for replicating the first four models presented in the book.

version 13

// Chapter 2

clear
// Read in data from clsn_cov.dat
ssd init clsn1 clsn3 clsn4 clsn5 clsn6 sex
ssd set observations 851
ssd set means 37.9542 37.2785 37.0463 36.5696 36.1363 0.49
#delimit ;
ssd set cov 
 6.3944 \
 3.2716 7.5282 \
 4.1435 6.0804 10.7290 \
 3.7058 5.1597 6.5672 10.2920 \
 4.1286 5.7608 7.2365 7.6463 12.9085 \
-0.0940 -0.0390 -0.1521 -0.1104 -0.1469 0.2502
;
#delimit cr

// Table 2.2
ssd list

// Model 0: The null model
// Only mean intercept and residual variance are estimated

sem (Intercept@1 -> clsn1, ) ///  // Set loadings to 1 
    (Intercept@1 -> clsn3, ) ///  // for estimating constant
    (Intercept@1 -> clsn4, ) ///
    (Intercept@1 -> clsn5, ) ///
    (Intercept@1 -> clsn6, ) ///
    (clsn1 <- _cons@a, ) ///      // Constrain means to be
    (clsn3 <- _cons@a, ) ///      // the same
    (clsn4 <- _cons@a, ) ///
    (clsn5 <- _cons@a, ) ///
    (clsn6 <- _cons@a, ) ///
  , latent(Intercept ) ///
    cov(Intercept@0 ///  Constrain intercept variance to 0
        e.clsn1@b e.clsn3@b ///  // Constrain residual variances
        e.clsn4@b e.clsn5@b ///  // to be the same
        e.clsn6@b) ///
    nocapslatent
estimates store m0
estat gof, stats(chi2 rmsea indices residuals)
// Non-normed fit index (NNFI) is called 
// Tucker-Lewis index (TLI) in Stata


// Model 1: Random intercept model (Table 2.3)
// Only mean intercept, intercept variance, and residual variance are 
// estimated



sem (Intercept@1 -> clsn1, ) ///  // Set loadings to 1 
    (Intercept@1 -> clsn3, ) ///  // for estimating constant
 (Intercept@1 -> clsn4, ) ///
 (Intercept@1 -> clsn5, ) ///
 (Intercept@1 -> clsn6, ) ///
 (clsn1 <- _cons@a, ) ///      // Constrain means to be
 (clsn3 <- _cons@a, ) ///      // the same
 (clsn4 <- _cons@a, ) ///
 (clsn5 <- _cons@a, ) ///
 (clsn6 <- _cons@a, ) ///
  , latent(Intercept ) ///
    cov(e.clsn1@b e.clsn3@b ///  // Constrain residual variances
        e.clsn4@b e.clsn5@b ///  // to be the same
        e.clsn6@b) ///
    nocapslatent
estimates store m1
di 5.27 / (5.27 + 4.68) // Random intercept model allows calculating an ICC
estat gof, stats(chi2 rmsea indices residuals)
                        // Poor model fit according to all tests
  // Likelihood ratio test:
lrtest m1 m0 // Massive improvement in fit for Model 1, though

// Model 2: Fixed intercept, fixed slope model (Table 2.4)
// Only mean intercept, intercept variance, and residual variance are 
// estimated



sem (Intercept@1 -> clsn1, ) ///  // Constrain paths to be 1
    (Intercept@1 -> clsn3, ) ///
    (Intercept@1 -> clsn4, ) ///
    (Intercept@1 -> clsn5, ) ///
    (Intercept@1 -> clsn6, ) ///
    (clsn1 <- _cons@a, ) ///     // Constrain intercepts to be the same
    (clsn3 <- _cons@a, ) ///
    (clsn4 <- _cons@a, ) ///
    (clsn5 <- _cons@a, ) ///
    (clsn6 <- _cons@a, ) ///
    (Slope@0 -> clsn1, ) ///     // Determine temporal structure
    (Slope@2 -> clsn3, ) ///
    (Slope@3 -> clsn4, ) ///
    (Slope@4 -> clsn5, ) ///
    (Slope@5 -> clsn6, ) ///
  , covstruct(_lexogenous, diagonal) ///
    latent(Intercept Slope ) ///
    cov(Intercept@0 ///        // Set intercept variance to 0
        Slope@0 ///            // Set slope variance to 0
 e.clsn1@b ///
        e.clsn3@b ///
        e.clsn4@b ///
        e.clsn5@b ///
        e.clsn6@b) ///
 means(Slope) ///           // Estimate slope
 nocapslatent
estimates store m2
estat gof, stats(chi2 rmsea indices residuals)
                     // Poor fit, even worse than Model 1

// Model 3: Random intercept, fixed slope (Table 2.5)



sem (Intercept@1 -> clsn1, ) ///  // Constrain paths to be 1
    (Intercept@1 -> clsn3, ) ///
    (Intercept@1 -> clsn4, ) ///
    (Intercept@1 -> clsn5, ) ///
    (Intercept@1 -> clsn6, ) ///
    (clsn1 <- _cons@a, ) ///     // Constrain intercepts to be the same
    (clsn3 <- _cons@a, ) ///
    (clsn4 <- _cons@a, ) ///
    (clsn5 <- _cons@a, ) ///
    (clsn6 <- _cons@a, ) ///
    (Slope@0 -> clsn1, ) ///     // Determine temporal structure
    (Slope@2 -> clsn3, ) ///
    (Slope@3 -> clsn4, ) ///
    (Slope@4 -> clsn5, ) ///
    (Slope@5 -> clsn6, ) ///
    , covstruct(_lexogenous, diagonal) ///
 latent(Intercept Slope ) ///
    cov(Slope@0 ///            // Set slope variance to 0
 e.clsn1@b ///
        e.clsn3@b ///
        e.clsn4@b ///
        e.clsn5@b ///
        e.clsn6@b) ///
 means(Slope) ///           // Estimate slope
 nocapslatent
estimates store m3
estat gof, stats(chi2 rmsea indices residuals)

  // Likelihood ratio test:
lrtest m3 m2 // Improvement in fit for Model 3

// Model 4: Random intercept, random slope (Table 2.6)


sem (Intercept@1 -> clsn1, ) ///  // Constrain paths to be 1
    (Intercept@1 -> clsn3, ) ///
    (Intercept@1 -> clsn4, ) ///
    (Intercept@1 -> clsn5, ) ///
    (Intercept@1 -> clsn6, ) ///
    (clsn1 <- _cons@a, ) ///     // Constrain intercepts to be the same
    (clsn3 <- _cons@a, ) ///
    (clsn4 <- _cons@a, ) ///
    (clsn5 <- _cons@a, ) ///
    (clsn6 <- _cons@a, ) ///
    (Slope@0 -> clsn1, ) ///     // Determine temporal structure
    (Slope@2 -> clsn3, ) ///
    (Slope@3 -> clsn4, ) ///
    (Slope@4 -> clsn5, ) ///
    (Slope@5 -> clsn6, ) ///
  , covstruct(_lexogenous, diagonal) ///
    latent(Intercept Slope ) ///
    cov(Intercept*Slope ///            // Include intercept-slope covariance
        e.clsn1@b ///
        e.clsn3@b ///
        e.clsn4@b ///
        e.clsn5@b ///
        e.clsn6@b) ///
 means(Slope) ///           // Estimate slope
 nocapslatent
estimates store m4
estat gof, stats(chi2 rmsea indices residuals)

  // Likelihood ratio test:
lrtest m4 m3 // Improvement in fit for Model 4

// Model 4 estimated as a multilevel model (Table 4.1):

// Read in data from clsn_cov.dat, this time using -corr2data-
#delimit ;
matrix input C = (
 6.3944,
 3.2716,  7.5282,
 4.1435,  6.0804, 10.7290,
 3.7058,  5.1597,  6.5672, 10.2920,
 4.1286,  5.7608,  7.2365,  7.6463, 12.9085,
-0.0940, -0.0390, -0.1521, -0.1104, -0.1469, 0.2502
 )
;
#delimit cr

corr2data clsn1 clsn3 clsn4 clsn5 clsn6 sex, n(851) ///
          means(37.9542 37.2785 37.0463 36.5696 36.1363 0.49) ///
    cov(C) cstorage(lower) clear
    
correlate, cov // Seems to work

gen id = _n // Create individual identifier

reshape long clsn, i(id) j(grade) // Convert to long format

mixed clsn grade || id: grade, var cov(uns)

Reference

Preacher, Kristopher J., Aaron L. Wichman, Robert C. MacCallum, and Nancy E. Briggs. 2008. Latent Growth Curve Modeling. Sage. doi: 10.4135/9781412984737