Options for dual domain latent growth curves (perhaps in lavaan?)

Question

I am trying to analyze three repeated measures of two outcome variables. It was recommended to use a latent growth curve model. I know in some software (SPSS) you can make growth curves with multiple measures, but it doesn't seem as straightforward in lavaan. Reading the lavaan tutorial it mentions multilevel SEM using sem() - is this appropriate for a repeated measures dataset? Or is there another package that allows multiple outcome growth curves in R?

Answer 1

To create a latent growth curve within lavaan is easy, see the example bellow (with 4 timepoints):

library(lavaan)
model <- ' i =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
           s =~ 0*t1 + 1*t2 + 2*t3 + 3*t4 '
fit <- growth(model, data=Demo.growth)
summary(fit)
#> lavaan 0.6-8 ended normally after 29 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                         9
#>                                                       
#>   Number of observations                           400
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                                 8.069
#>   Degrees of freedom                                 5
#>   P-value (Chi-square)                           0.152
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Expected
#>   Information saturated (h1) model          Structured
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   i =~                                                
#>     t1                1.000                           
#>     t2                1.000                           
#>     t3                1.000                           
#>     t4                1.000                           
#>   s =~                                                
#>     t1                0.000                           
#>     t2                1.000                           
#>     t3                2.000                           
#>     t4                3.000                           
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   i ~~                                                
#>     s                 0.618    0.071    8.686    0.000
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .t1                0.000                           
#>    .t2                0.000                           
#>    .t3                0.000                           
#>    .t4                0.000                           
#>     i                 0.615    0.077    8.007    0.000
#>     s                 1.006    0.042   24.076    0.000
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .t1                0.595    0.086    6.944    0.000
#>    .t2                0.676    0.061   11.061    0.000
#>    .t3                0.635    0.072    8.761    0.000
#>    .t4                0.508    0.124    4.090    0.000
#>     i                 1.932    0.173   11.194    0.000
#>     s                 0.587    0.052   11.336    0.000

However, if you want to model latent growth curve for 2 parallel processes (sleep and anxiety) you can use this approach:

library(lavaan)
#> This is lavaan 0.6-8
#> lavaan is FREE software! Please report any bugs.
model <- "
i1 =~ 1*t1 + 1*t2 + 1*t3 + 1*t4
s1 =~ 0*t1 + 1*t2 + 2*t3 + 3*t4


i2 =~ 1*c1 + 1*c2 + 1*c3 + 1*c4
s2 =~ 0*c1 + 1*c2 + 2*c3 + 3*c4

s1 ~ i2
s2 ~ i1
"
fit <- growth(model, data=Demo.growth)
#> Warning in lav_object_post_check(object): lavaan WARNING: covariance matrix of latent variables
#>                 is not positive definite;
#>                 use lavInspect(fit, "cov.lv") to investigate.
summary(fit)
#> lavaan 0.6-8 ended normally after 76 iterations
#> 
#>   Estimator                                         ML
#>   Optimization method                           NLMINB
#>   Number of model parameters                        20
#>                                                       
#>   Number of observations                           400
#>                                                       
#> Model Test User Model:
#>                                                       
#>   Test statistic                               156.195
#>   Degrees of freedom                                24
#>   P-value (Chi-square)                           0.000
#> 
#> Parameter Estimates:
#> 
#>   Standard errors                             Standard
#>   Information                                 Expected
#>   Information saturated (h1) model          Structured
#> 
#> Latent Variables:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   i1 =~                                               
#>     t1                1.000                           
#>     t2                1.000                           
#>     t3                1.000                           
#>     t4                1.000                           
#>   s1 =~                                               
#>     t1                0.000                           
#>     t2                1.000                           
#>     t3                2.000                           
#>     t4                3.000                           
#>   i2 =~                                               
#>     c1                1.000                           
#>     c2                1.000                           
#>     c3                1.000                           
#>     c4                1.000                           
#>   s2 =~                                               
#>     c1                0.000                           
#>     c2                1.000                           
#>     c3                2.000                           
#>     c4                3.000                           
#> 
#> Regressions:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   s1 ~                                                
#>     i2                6.115    3.785    1.615    0.106
#>   s2 ~                                                
#>     i1               -0.011    0.017   -0.644    0.519
#> 
#> Covariances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>   i1 ~~                                               
#>     i2                0.101    0.062    1.632    0.103
#>  .s1 ~~                                               
#>    .s2                0.021    0.017    1.205    0.228
#> 
#> Intercepts:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .t1                0.000                           
#>    .t2                0.000                           
#>    .t3                0.000                           
#>    .t4                0.000                           
#>    .c1                0.000                           
#>    .c2                0.000                           
#>    .c3                0.000                           
#>    .c4                0.000                           
#>     i1                0.615    0.077    8.009    0.000
#>    .s1                0.824    0.276    2.990    0.003
#>     i2                0.030    0.041    0.731    0.464
#>    .s2                0.002    0.024    0.063    0.950
#> 
#> Variances:
#>                    Estimate  Std.Err  z-value  P(>|z|)
#>    .t1                0.597    0.086    6.978    0.000
#>    .t2                0.673    0.061   11.056    0.000
#>    .t3                0.636    0.072    8.780    0.000
#>    .t4                0.507    0.124    4.095    0.000
#>    .c1                0.977    0.069   14.120    0.000
#>    .c2                0.892    0.064   14.016    0.000
#>    .c3                0.838    0.065   12.996    0.000
#>    .c4                0.803    0.080   10.010    0.000
#>     i1                1.931    0.173   11.193    0.000
#>    .s1                0.533    0.203    2.626    0.009
#>     i2                0.001    0.006    0.246    0.806
#>    .s2                0.007    0.006    1.033    0.302

^{Created on 2021-03-19 by the reprex package (v1.0.0)}