Multiple-group latent change score model

[Patrick Forscher]

I'm trying to fit a multiple-group Latent Change Score Model (see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4259494/).  I have successfully fit a Latent Change Score Model and double-checked my results against this app (https://ajtorgesen.shinyapps.io/LGMComp/), so I'm fairly sure my basic syntax is correct.

However, when I try to fit a multiple-group version of the Latent Change Score Model, it appears that the equality constraints required to fit the model are only applied to one group and not the other -- i.e., in the model, below, the labels "Ve" and "Beta" are implemented for only one group, but not the other. See below.

Anyone know what's going on?  Is this a known issue when using the "group" argument in lavaan?

BEGIN CODE SNIPPET

m <- '

lv1 =~ 1*muslim_1

lv2 =~ 1*muslim_2

lv3 =~ 1*muslim_3

lv4 =~ 1*muslim_4

lv5 =~ 1*muslim_5

lv6 =~ 1*muslim_6

lv7 =~ 1*muslim_7

lv2 ~ 1*lv1

lv3 ~ 1*lv2

lv4 ~ 1*lv3

lv5 ~ 1*lv4

lv6 ~ 1*lv5

lv7 ~ 1*lv6

ld2 =~ 1*lv2

ld3 =~ 1*lv3

ld4 =~ 1*lv4

ld5 =~ 1*lv5

ld6 =~ 1*lv6

ld7 =~ 1*lv7

ld2 ~ Beta*lv2

ld3 ~ Beta*lv3

ld4 ~ Beta*lv4

ld5 ~ Beta*lv5

ld6 ~ Beta*lv6

ld7 ~ Beta*lv7

B1 =~ 1*ld2 + 1*ld3 + 1*ld4 + 1*ld5 + 1*ld6 + 1*ld7

B0 =~ 1*lv1

B0 ~~ B0

B1 ~~ B1

B0 ~~ B1

B0 ~ 1

B1 ~ 1

muslim_1 ~~ Ve*muslim_1

muslim_2 ~~ Ve*muslim_2

muslim_3 ~~ Ve*muslim_3

muslim_4 ~~ Ve*muslim_4

muslim_5 ~~ Ve*muslim_5

muslim_6 ~~ Ve*muslim_6

muslim_7 ~~ Ve*muslim_7'

fit <- lavaan(m, data=d, group="condition")

summary(fit)

Group 1 [ST]:

  ld2 ~                                               

    lv2     (Beta)   -0.986    0.194   -5.092    0.000

  ld3 ~                                               

    lv3     (Beta)   -0.986    0.194   -5.092    0.000

  ld4 ~                                               

    lv4     (Beta)   -0.986    0.194   -5.092    0.000

  ld5 ~                                               

    lv5     (Beta)   -0.986    0.194   -5.092    0.000

  ld6 ~                                               

    lv6     (Beta)   -0.986    0.194   -5.092    0.000

  ld7 ~                                               

    lv7     (Beta)   -0.986    0.194   -5.092    0.000

   .muslim_1  (Ve)   30.117    2.245   13.416    0.000

   .muslim_2  (Ve)   30.117    2.245   13.416    0.000

   .muslim_3  (Ve)   30.117    2.245   13.416    0.000

   .muslim_4  (Ve)   30.117    2.245   13.416    0.000

   .muslim_5  (Ve)   30.117    2.245   13.416    0.000

   .muslim_6  (Ve)   30.117    2.245   13.416    0.000

   .muslim_7  (Ve)   30.117    2.245   13.416    0.000

Group 2 [CST]:

  ld2 ~                                               

    lv2              -0.246    0.136   -1.804    0.071

  ld3 ~                                               

    lv3              -0.275    0.138   -1.994    0.046

  ld4 ~                                               

    lv4              -0.258    0.138   -1.872    0.061

  ld5 ~                                               

    lv5              -0.238    0.136   -1.751    0.080

  ld6 ~                                               

    lv6              -0.269    0.137   -1.964    0.049

  ld7 ~                                               

    lv7              -0.264    0.138   -1.919    0.055

   .muslim_1        140.628   33.796    4.161    0.000

   .muslim_2         33.625   10.114    3.325    0.001

   .muslim_3         18.438    5.191    3.552    0.000

   .muslim_4         20.105    4.696    4.281    0.000

   .muslim_5         32.292    7.024    4.597    0.000

   .muslim_6         13.042    3.851    3.386    0.001

   .muslim_7          7.834    4.134    1.895    0.058

[Ahabsfriend]

Hello, 

to fit a multi-group model, I would use the syntax. First, in doing so, you have the full control. My experience: It is also clearer for others to specify the syntax rather then using the function options.

In your case, you only have to change the syntax as follows to establish equality constraints for both groups.

...

ld2 ~ c(Beta,Beta)*lv2

...

muslim_1 ~~ c(Ve,Ve)*muslim_1

...

Best regards

[Patrick Forscher]

Thanks for your reply.  My problem is actually that, for group 1, the equality constraints across timepoints that I placed in my model declaration are respected, but they are not respected for group 2.  This is why I think there might be a subtle bug in how lavaan handles equality constraints within groups in multiple-group SEM.  See below.

Group 1

   .muslim_1  (Ve)   30.117    2.245   13.416    0.000

   .muslim_2  (Ve)   30.117    2.245   13.416    0.000

   .muslim_3  (Ve)   30.117    2.245   13.416    0.000

   .muslim_4  (Ve)   30.117    2.245   13.416    0.000

   .muslim_5  (Ve)   30.117    2.245   13.416    0.000

   .muslim_6  (Ve)   30.117    2.245   13.416    0.000

   .muslim_7  (Ve)   30.117    2.245   13.416    0.000

Group 2

[Manuel Torres Sahli]

Dear Patrick,

I think what AhabsFriend was pointing out is that labels are group-specific. So you need to specify one label per group:

m <- '

lv1 =~ 1*muslim_1

lv2 =~ 1*muslim_2

lv3 =~ 1*muslim_3

lv4 =~ 1*muslim_4

lv5 =~ 1*muslim_5

lv6 =~ 1*muslim_6

lv7 =~ 1*muslim_7

lv2 ~ 1*lv1

lv3 ~ 1*lv2

lv4 ~ 1*lv3

lv5 ~ 1*lv4

lv6 ~ 1*lv5

lv7 ~ 1*lv6

ld2 =~ 1*lv2

ld3 =~ 1*lv3

ld4 =~ 1*lv4

ld5 =~ 1*lv5

ld6 =~ 1*lv6

ld7 =~ 1*lv7

ld2 ~ c(Beta1, Beta2)*lv2

ld3 ~ c(Beta1, Beta2)*lv3

ld4 ~ c(Beta1, Beta2)*lv4

ld5 ~ c(Beta1, Beta2)*lv5

ld6 ~ c(Beta1, Beta2)*lv6

ld7 ~ c(Beta1, Beta2)*lv7

B1 =~ 1*ld2 + 1*ld3 + 1*ld4 + 1*ld5 + 1*ld6 + 1*ld7

B0 =~ 1*lv1

B0 ~~ B0

B1 ~~ B1

B0 ~~ B1

B0 ~ 1

B1 ~ 1

muslim_1 ~~ c(Ve1, Ve2)*muslim_1

muslim_2 ~~ c(Ve1, Ve2)*muslim_2

muslim_3 ~~ c(Ve1, Ve2)*muslim_3

muslim_4 ~~ c(Ve1, Ve2)*muslim_4

muslim_5 ~~ c(Ve1, Ve2)*muslim_5

muslim_6 ~~ c(Ve1, Ve2)*muslim_6

muslim_7 ~~ c(Ve1, Ve2)*muslim_7'

You may also use just the unnumbered original label for both groups to contrain equality if you need to. Or explicitly type:

Ve1 == Ve2

Beta1 == Beta2

Best,

Manuel