Automatically computing residual variances for a specified RAM matrix

EDIT: Hmm, I don't think I answered your question, if you're curious about writing a function for general-purpose SEM (i.e., not necessarily using OpenMx), and inputting a matrix of RAM paths. The below might still be useful to you, though.

Are you running OpenMx version 1.3/1.4, or the beta of 2.0? If it's the latter, there is a built-in function, mxStandardizeRAMpaths(), that will give you the values of the path coefficients when all variables, both latent and observable, have total variance of 1.

If you want the A and S matrices containing the values reported by mxStandardizeRAMpaths(), then assuming you've already made your model as myModel and all of its two-headed paths have nonzero start values, you could do this:

myModelZ <- mxModel(model=myModel,
mxMatrix(type="Iden",nrow=nrow(myModel$A@values),name="I"),
mxAlgebra( vec2diag(diag2vec( solve(I-A)%*%S%*%t(solve(I-A)) )%^%-0.5) ,
name="InvSD"),
mxAlgebra( InvSD %*% A %*% solve(InvSD),
name="Az",dimnames=dimnames(myModel$A@values)),
mxAlgebra( InvSD %*% S %*% InvSD,
name="Sz",dimnames=dimnames(myModel$S@values))
)
myFitZ <- mxRun(myModelZ)

Then, Az and Sz would be algebras contained in myFitZ. This should work in 1.3/1.4 as well as 2.0 beta.

If what you're really after is a model-implied correlation matrix for the manifest variables, then in 1.3/1.4, you could do cov2cor(myModel@objective@info$expCov). In the 2.0 beta, the equivalent command would be cov2cor(myModel$fitfunction$info$expCov).

Does any of this help?

I've been thinking about the problem you've posed, and I'm a bit confused about what is assumed known versus what you want your function to find. It looks as though what is known is a matrix of RAM paths, and what you want the function to do is produce the model-expected correlation matrix. More specifically, what is known in from the matrix of RAM paths in the present case are the asymmetric paths (factor loadings) and a covariance between manifest variables 9 & 10. Is that right?

In any event, there are several parts of your syntax that don't do what I'm pretty sure you want it to. I've cleaned it up a little:

#### create a RAM model for testing
RAM = data.frame(matrix(c(
"F1", "A1", 1, .4,
"F1", "A2", 1, .4,
"F1", "A3", 1, .4,
"F2", "A4", 1, .4,
"F2", "A5", 1, .4,
"F2", "A6", 1, .4,
"F3", "A7", 1, .4,
"F3", "A8", 1, .4,
"F3", "A9", 1, .4,
"A10", "A9", 2, .5), ncol=4, byrow=T
),stringsAsFactors=F)
names(RAM) = c("From", "To", "Arrows", "Values")
RAM$Arrows <- as.integer(RAM$Arrows)
RAM$Values <- as.numeric(RAM$Values)

##### create symmetric matrix (temporarily fill in endogenous variances)
end = rownames(mA)[which(rowSums(mA)>0)]
mS <- diag(1,length(all.vars))
dimnames(mS) <- list(c(observed,unobserved),c(observed,unobserved))
for (i in 1:nrow(RAM)){
if (RAM$Arrows[i] == 2){
col = which(colnames(mS) == RAM$To[i])
row = which(rownames(mS) == RAM$From[i])
mS[col,row] = RAM$Values[i]
mS[row,col] = RAM$Values[i]
}
}
#### I'M STUCK!