Correlated residuals of manifest variables

Here is something modified from the Home page


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, values=.4),
mxPath(from=latents, arrows=2,
free=FALSE, values=1.0),
mxPath(from=manifests[1], to=manifests[2],
free=TRUE, arrows=2, values=.3), # Added covariance between manifests[1] and manifests[2]
mxData(cov(demoOneFactor), type="cov",
numObs=500))
summary(mxRun(factorModel))


This is easy in OpenMx: You just add paths between the variables you think have correlated residuals...
e.g., Here I add a correlation between x2 and x3 in the front-page example. it turns out to be a non-significant correlation:


require(OpenMx)
data(demoOneFactor)
manifests <- names(demoOneFactor)
latents <- c("G")
m1 <- mxModel("One Factor", type="RAM",
manifestVars = manifests,
latentVars = latents,
mxPath(from = latents, to = manifests),
mxPath(from = manifests, arrows = 2),
mxPath(from = latents, arrows = 2, values = 1),
mxData(cov(demoOneFactor), type = "cov", numObs = nrow(demoOneFactor))
)
m1 = mxRun(m1)
m2 = mxRun(mxModel(m1, mxPath("x2", "x3", arrows = 2, values=.01), name="correlated_X2_X3"))
mxCompare(m2, m1)

base comparison ep minus2LL df AIC diffLL diffdf p
1 correlated_X2_X3 12 -3649.803 3 -0.1389409 NA NA NA
2 correlated_X2_X3 One Factor 11 -3648.281 4 -0.6159977 1.522943 1 0.2171746