Are these latent variables too highly correlated in this Structural Equation Model?

Question

this is my first SEM I've done so I'm still getting my head around many of the concepts.

So I think I've created a hierarchical model of IQ (generaliq), with the latent variables: verbal_letter, matrix and rotate. verbal_letter was two latent vars lumped together due to a correlation >1 error. It's done using a rather odd data-set (not usual IQ measures, rather questions that are meant to link to underlying concepts, taken from a SAPA questionnaire) but anyhow it appears to be working.

dataset info here: http://vincentarelbundock.github.io/Rdatasets/doc/psych/iqitems.html

My relevant code is:

library(lavaan)
library(semPlot)

iqitems <- read_csv('http://vincentarelbundock.github.io/Rdatasets/csv/psych/iqitems.csv')

iq.model6 <- 'verbal_letters =~ reason.4 + reason.16 + reason.17 + reason.19 + letter.7 + letter.33 + letter.34 + letter.58
matrix =~ matrix.45 + matrix.55
rotate =~ rotate.3 + rotate.4 + rotate.6 + rotate.8
rotate.3 ~~ rotate.4 
generaliq =~ verbal_letters + matrix + rotate'

iq.fit6 <- cfa(model = iq.model6, data = iqitems)

summary(iq.fit6, standardized = TRUE, fit.measures = TRUE)

When I summarise my model, all seems fine in a model fit sense CFI and TLI >0.9, RMSEA and SRMR >0.05, I have enough DF for identification.

It's this part of the summary I'm concerned about:

Latent Variables:

  generaliq =~                                                           
    verbal_letters     1.000                               0.930    0.930
    matrix             1.344    0.132   10.164    0.000    0.959    0.959
    rotate             0.620    0.082    7.575    0.000    0.484    0.484

Are the 0.930 and 0.959 problematic? If so why and what can I do?

Otherwise if there are any other big problems I'd appreciate being made aware. For context, I'm doing this for a stats module in undergraduate psychology so the standard is not really high. I basically need to (amongst many other things) run an analysis of my own choice and report on it with a theoretical question, technical details and graphical analysis.

I've done the following diagram

semPaths(object = iq.fit6,
         whatLabels = "std",
         edge.label.cex = 1,
         layout = "tree",
         rotation = 2,
         what = "std",
         edge.color = "navy")

If anyone has any feedback on it, or advice on how to generally report a SEM, I would really appreciate that too. Previously I've been doing regressions like LMER and GLM so this is rather different.

Thanks a lot!

Answer 1

These high correlations mean that you have highly reliable measures. In particular, verbal_letters and matrix are highly correlated, and measure the same construct.

The only reason to be concerned about this is that your measure of generaliq has a lot to do with verbal_letters and matrix, and less to do with rotate.