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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!

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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.

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