Can someone explain the fit indices here?

[Christopher Desjardins]

I am trying to understand what's going on with the fit indices with this categorical CFA and where the information for the variances is coming from.  Here is my example.

data(LSAT, package = "ltm")

LSAT.ord <- as.data.frame(LSAT)

LSAT.ord[,1:5] <- lapply(LSAT.ord[,1:5], ordered)

names(LSAT.ord) <- paste0("item", 1:5)

cat.mod <- '

  lawsch =~ item1 + item2 + item3 + item4 + item5

'

fit <- cfa(cat.mod, data = LSAT.ord, ordered=c("item1","item2","item3","item4", "item5")) 

summary(fit, standardized = T, fit.measures = T)

If you inspect the fit, you see it's estimating 4 loadings, 5 threshold, and the variance of the factor. I should have 5 df, which the summary output states that I do. Here are my two questions:

1. Why is my RMSEA 0 and my TLI, CFI 1 or >1?  

2. If the specify variables for my manifest variables isn't be estimated, how is this calculated?

Thanks,

Chris

[Terrence Jorgensen]

1. Why is my RMSEA 0 and my TLI, CFI 1 or >1?  

If you look at the formulas, you may notice that this will happen whenever the chi-squared is less than its expected value (the df).

2. If the specify variables for my manifest variables isn't be estimated, how is this calculated?

On the assumption that there is a latent normal variable underlying each observed ordered variable:

http://www.statmodel.com/download/webnotes/CatMGLong.pdf

http://psycnet.apa.org/journals/met/9/3/301/

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Christopher Desjardins]

Thanks, Terrence. That first reference is especially helpful and that makes sense about the fit indices.