In lavaan, we can fit a confirmatory factor analysis model and compute predicted factor scores with standard errors.
HS.model <- ' visual =~ x1 + x2 + x3
textual =~ x4 + x5 + x6
speed =~ x7 + x8 + x9 '
fit <- cfa(HS.model, data = HolzingerSwineford1939)
pred <- lavPredict(fit, se = "standard")
However, I was under the impression that this approach would give me a different standard error for every individual predicted factor score. Instead, we only get three standard errors, one for each latent variable.
visual textual speed
0.4747366 0.3316382 0.3276657
I am employing this approach because I am using the predicted factor scores in a second Bayesian phylogenetic analysis using the
brms package, and I would like to propagate their uncertainty forward (unfortunately, brms does not yet support latent variable estimation). For this method, I would need a separate standard error associated with every individual predicted factor score.
Is it okay to give every predicted score for the "visual" factor a standard error of 0.4747366, for example? Is that what this lavaan output is telling me? Or have I misunderstood what the se = "standard" argument within predict() actually does?
Many thanks in advance, lavaan is awesome!