Multigroup SEM in lavaan: no variance in covariate in one group, how to proceed?

Question

I try to fit a multigroup SEM in lavaan.

In one of my groups all values for a specific covariate are the same (i.e., the people in group 2 all have the same age), in my group 1 however this covariate (age) varies between individuals. I want to compare coefficients between groups, while controling for age in group 1. (I scale the age in group one as a deviation from the age in group 2).

This seems to not be easily possible, lavaan gives the following error message: "lavaan ERROR: some variables have no variance in group 2: c".

Can someone give me advice on how to implement my intended analysis?

Here is a reproducible example:

library(lavaan)

N<-1000
a<-rnorm(N,0,1)
b<-a*0.5+rnorm(N,0,0.2)
c<-c(rnorm((N/2),0,0.2),rep(0,times=(N/2))) # covariate c has the same value for every case in group 2
group<-rep(c("1","2"),each=(N/2))
dtest<-cbind.data.frame(a,b,c,group)

m<-'a~b+c'
fit<-sem(model=m,data=dtest,group="group")

Answer 1

In lavaan, you can define different model per group, to exclude the constant from Group 2's model. The reprex is a little odd in that you simulate b as a function of a, but then regress a on b. But following from that example:

mod <- ' group: 1
  a ~ b + c
group: 2
  a ~ b
'
fit <- sem(mod, data = dtest, group = "group")

The interpretation of other slopes is still the same (i.e., "For a given age/c, a 1-unit increase in b is associated with a slope-unit increase in a"). It just so happens that in one group, everyone in fact has the same given age, so there is no age-related variance to partial out from a and b.

But in case you use c as a moderator in one group, then you should in fact center age in Group 1 at whatever value everyone's age is in Group 2, so that the estimated simple effect of b is the same across groups. From your description:

I scale the age in group one as a deviation from the age in group 2

it sounds like you already do this.

If you want to test whether the effect of your focal predictor (b) is the same across groups, just use labels to make the slopes equal (not moderated by group) and compare models.

mod0 <- ' group: 1
  a ~ slope*b + c
group: 2
  a ~ slope*b
'
fit0 <- sem(mod0, data = dtest, group = "group")
lavTestLRT(fit, fit0)