Separate standard errors from sam() for parameters constrained equal across groups

[marklhc]

From https://groups.google.com/g/lavaan/c/SvgKCKqiOoY. It seems that the equality constraint is currently not taking into accounting when computing the standard errors in multiple-group sam().

library(lavaan)
#> This is lavaan 0.6-9
#> lavaan is FREE software! Please report any bugs.

HS.model <- " visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9
              visual ~~ c(cov_v, cov_v) * visual "

# SEM
sem_fit <- cfa(HS.model,
    data = HolzingerSwineford1939,
    group = "school",
    group.equal = c("loadings")
)

subset(parameterEstimates(sem_fit), label == "cov_v")
#>       lhs op    rhs block group label   est    se     z pvalue ci.lower
#> 10 visual ~~ visual     1     1 cov_v 0.759 0.135 5.621      0    0.494
#> 46 visual ~~ visual     2     2 cov_v 0.759 0.135 5.621      0    0.494
#>    ci.upper
#> 10    1.023
#> 46    1.023

# SAM (Global)

samg_fit <- sam(HS.model, cmd = "cfa",
    data = HolzingerSwineford1939,
    sam.method = "global",
    group = "school",
    group.equal = c("loadings")
)

subset(parameterEstimates(samg_fit), label == "cov_v")
#>       lhs op    rhs block group label   est    se     z pvalue ci.lower
#> 10 visual ~~ visual     1     1 cov_v 0.647 0.151 4.295      0    0.352
#> 46 visual ~~ visual     2     2 cov_v 0.647 0.148 4.375      0    0.357
#>    ci.upper
#> 10    0.942
#> 46    0.937

^{Created on 2021-08-23 by the reprex package (v2.0.1)}

[yrosseel]

Just a sign of life. This turns out to be much more difficult to fix than expected. It may be that, due to the twostep nature of computing the standard errors, this will never work. At least not with the current approach. I will keep this issue open, as this is simply unresolved.