Multigroup SEM constraining regression coefficients in lavaan

Question

I am trying to compare two groups of children and test whether executive function (EF) is a significant predictor of reasoning (CR) (and I also include other covariates) using SEM and the lavaan package in R.

1. Am I correctly doing that comparison with this code?
2. How do I interpret the lengthy output?
3. Is the only way to compare whether or not the regression coefficients are significantly different between groups is to compare two models with and without constraining the regressions to be equal?

Attempt 1:

mod1= ' 
CR =~ v1 +  v2
EF =~ ef1 + ef2 + ef3 + ef4 + ef5
CR ~  c(a1, a2)*v3 + c(b1,b2)*v4 + c(c1,c2)*v5 + c(d1, d2)*EF  
diff.a1a2 := a1 - a2 
diff.b1b2 := b1 - b2 
diff.c1c2 := c1 - c2 
diff.d1d2 := d1 - d2 '
fitnew<- sem(mod1, data=datamicescaled, 
             std.lv =T, group = "age.group",estimator = "MLR", missing = "fiml")
summary(fitnew, fit.measures=TRUE, standardized=TRUE)

Output 1:

Defined Parameters:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
    diff.a1a2        -0.049    0.509   -0.095    0.924   -0.063   -0.170
    diff.b1b2         0.948    4.497    0.211    0.833    0.020    0.026
    diff.c1c2         1.023    2.425    0.422    0.673    0.250    0.293
    diff.d1d2         0.945    4.823    0.196    0.845    0.070    0.070

Attempt 2:

mod2= ' 
CR =~ v1 +  v2 + v3
EF =~ ef1 + ef2 + ef3 + ef4 + ef5
CR ~  v4 + v5 + v6 + EF  '

fit2<- sem(mod2, data=datamicescaled, 
             std.lv =T, group = "age.group",estimator = "MLR", missing = "fiml", group.equal = c"regressions)
summary(fit2, fit.measures=TRUE, standardized=TRUE)

Thank you in advance for any help. I have been talking myself into circles all day, and I would really appreciate any input!

Answer 1

I am not sure if I completely understand your question. Nevertheless this my answer (hope it helps):

If you wan to compare groups you have to conduct an analysis of invariance where you restrict your model step by step, and only if you probe that the models gets worse when you constraint coefficients to be equal across group, then you can move to estimate coefficiente for every group.

This video is useful