LAVAAN modification indices for constrained parameters I'm looking for a way to estimate the equivalent of modification indices for parameters that are not zero, but are constrained to be equal. See example below.
HS.model <- ' visual  =~ x1 + a*x2 + a*x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- lavaan(HS.model, data=HolzingerSwineford1939,
              auto.var=TRUE, auto.fix.first=TRUE,
              auto.cov.lv.x=TRUE)
modificationIndices(fit, sort = TRUE) %>% filter(rhs=="x2")

For example, parameters with a label of "a" in the above model are constrained to be equal. The modification indices output does not show what might happen were this constraint removed. I could, of course, run the model again without the constraint (i.e., remove the "a*") and this would provide what I want. The actual model I'm interested in, though, has a hundred or so constrained parameters (i.e., cross-level measurement invariance assumptions) and I would rather not program a loop to run the model a hundred times with each constraint removed. Is this possible? If so, how?


a way to estimate the equivalent of modification indices for parameters that are not zero

To be clear, these are not estimates of parameters.  They are (score) test statistics associated with freeing a fixed/constrained parameter.  They are asymptotically equivalent to Wald and likelihood-ratio test statistics:
https://doi.org/10.1080/00031305.1982.10482817
The modificationIndices() function only provides 1-df score tests for fixed parameters.  The more general lavTestScore() function can provide the same score tests (using the add= argument, to specify particular parameters you would be interested in freeing, rather than exploring all possible fixed parameters, a method which has been severely criticized).  But lavTestScore() can also return score tests for freeing equality constraints (using the release= argument), and can also provide score tests with multiple df (i.e., releasing multiple constraints simultaneously).
