Factor score determinacy question

[Dave]

Hi,

I'm reading about factor score (in)determinacy in Rodriguez, Reise & Haviland (2016) and Beauducel (2011) and if I understand things correctly it is possible to estimate the degree to which factor scores are (in)determinate.

Beauducel, A. (2011). Indeterminacy of factor score estimates in slightly misspecified confirmatory factor models. Journal of Modern Applied Statistical Methods, 10(2), 16.

Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016). Evaluating bifactor models: calculating and interpreting statistical indices. Psychological methods, 21(2), 137.

So,

Phi = factor correlations

lambda = standardized factor loadings

Sigma is where I get a bit confused. Is sigma the same as in lavInspect(fit, what="cor.lv")? If so, is the code below correct I wonder? Feel free to modify in any way.

library("lavaan")
HolzingerSwineford1939

HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '
fit <- cfa(HS.model, data = HolzingerSwineford1939)

phi <- lavInspect(fit, what="cov.lv")
lambda <- lavInspect(fit, what="std")$lambda
sigma <- lavInspect(fit, what="cor.lv")
FD <- diag(phi %*% t(lambda) %*% solve(sigma) %*% lambda %*% phi)^0.5

[Mauricio Garnier-Villarreal]

Dave

I havent heard of this evaluation of the degree of indeterminancy

But I can answer the question for sigma. Sigma is the model implied correlation matrix, this is the "predicted" correlations between all the items. From lavaan you can extract the model implied covariance matrix and transfrom it into correlation

sigma <- cov2cor(lavInspect(fit, what="implied")$cov)

[Dave]

Excellent, thanks much for the response! If you're interested, much more information is available in Beauducel (2011): https://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1333&context=jmasm