Maximum likelihood objective function

[Mark Seeto]

Dear lavaan group,

At https://github.com/yrosseel/lavaan/blob/master/R/lav_objective.R the function estimator.ML contains the following code:

if(!meanstructure) {
  fx <- (Sigma.hat.log.det + sum(data.cov * Sigma.hat.inv) -
         data.cov.log.det - nvar)
}

In Bollen's book "Structural Equations With Latent Variables" (equation 8.29 on p. 334), he has the trace of (data.cov * Sigma.hat.inv) instead of the sum of all elements.

What's the reason for using sum(data.cov * Sigma.hat.inv) instead of sum(diag(data.cov * Sigma.hat.inv))?

Thanks,

Mark

[Mark Seeto]

Sorry, I just realised the answer to my question.

data.cov * Sigma.hat.inv is an elementwise product, not a matrix multiplication. Because these matrices are symmetric,

sum(data.cov * Sigma.hat.inv)

is the same as

sum(diag(data.cov %*% Sigma.hat.inv)).