SLSQP Confidence Intervals?

I'm sorry you're experiencing some trouble here. One of the things the OpenMx development team has been finding is that a feeling of certainty about ones results is often a consequence of limited options. That is, if you only have one optimizer then you think your optimizer works fine. Once you have options, idiosyncrasies can show.

One thing worth mentioning about the lavaan results is their confidence intervals are based purely on the standard errors. Many SEM programs do this. OpenMx does not. The confidence intervals provided by OpenMx are profile likelihood confidence intervals. They are not necessarily symmetric, and I believe they require less stringent assumptions than SE-based intervals. In theory they should be close to SE-based confidence intervals, but only when all the assumptions are met.

You can get SE-based confidence intervals for OpenMx models with something like


require(OpenMx)
data(demoOneFactor)
manifests <- names(demoOneFactor)
latents <- c("G")
factorModel <- mxModel("One Factor",
type="RAM",
manifestVars=manifests,
latentVars=latents,
mxPath(from=latents, to=manifests),
mxPath(from=manifests, arrows=2),
mxPath(from=latents, arrows=2, free=FALSE, values=1.0),
mxData(observed=cov(demoOneFactor), type="cov", numObs=500))
factorRun <- mxRun(factorModel)

sum.param <- summary(factorRun)$parameters
param <- sum.param[,5]
SE <- sum.param[,6]
res.ci <- param + t(outer(c(-1, 0, 1), qnorm(.975)*SE))
rownames(res.ci) <- sum.param[,1]
colnames(res.ci) <- c('lower', 'estimate', 'upper')
res.ci
# lower estimate upper
#One Factor.A[1,6] 0.36667556 0.39715240 0.42762924
#One Factor.A[2,6] 0.46792656 0.50366144 0.53939631
#One Factor.A[3,6] 0.53716407 0.57724201 0.61731995
#One Factor.A[4,6] 0.65571296 0.70277421 0.74983547
#One Factor.A[5,6] 0.74397964 0.79625052 0.84852139
#One Factor.S[1,1] 0.03530140 0.04081423 0.04632707
#One Factor.S[2,2] 0.03252078 0.03802004 0.04351931
#One Factor.S[3,3] 0.03464878 0.04082720 0.04700562
#One Factor.S[4,4] 0.03270578 0.03938705 0.04606833
#One Factor.S[5,5] 0.02907724 0.03628709 0.04349694


This could be put into a function.


confidenceIntervals <- function(model){
sum.param <- summary(model)$parameters
param <- sum.param[,5]
SE <- sum.param[,6]
res.ci <- param + t(outer(c(-1, 0, 1), qnorm(.975)*SE))
rownames(res.ci) <- sum.param[,1]
colnames(res.ci) <- c('lower', 'estimate', 'upper')
res.ci
}