While it is possible to get parameter estimates corrected for measurement error using -sem- like:

Code:
use http://www.stata-press.com/data/r15/sem_rel.dta, clear
sem (y <- x1)
sem (x1 <- X)(y <- X), reliability(x1 0.5)
It isn't possible to use the reliability option with the -gsem- command. Additionally, the command -eivreg- is known to incorrectly estimate the standard errors for the parameter(s) of interest (see Lockwood, J. R., McCaffrey, D. F., & Savage, C. (2017). Errors-in-variables: Why Stata's -eivreg- is wrong and what to do instead. Presented at 2017 Society for Research on Effective Education Conference. Retrieved from: https://www.sree.org/conferences/201...pdf&item=slide):

Code:
eivreg y x1, r(x1 0.5)
Additionally, the reliability option generalizes to the multilevel context as long as the model specified uses an identity link and gaussian family:

Code:
g byte school = rbinomial(4, 0.5)
// This model will fail to converge nearly immediately, but at least illustrates that it is possible to deal with covariate measurement error in the context of mixed effects
gsem (x1 <- X)(y <- X RE[school]), reliability(x1 0.65) link(identity) family(gaussian) difficult
So, I am wondering if anyone is aware of any ways to deal with covariate measurement error when the outcome is binary and the model includes random intercepts and a random coefficient? If context helps, we are trying to estimate the probability of students being retained in grade conditional on test scores (which are measured with a non-trivial amount of error), demographics, school-level random intercepts, and prior schooling indicators (random coefficients). I imagine it might be possible to deal with this in a Bayesian framework (as well as being able to specify priors that could keep estimates away from the boundaries), but don't have much experience with Bayesian modeling.