Second order latent class factor and large factor loading

[Xavier Farre]

Hi everyone,

I am trying to run a second order latent class factor and I want to be sure I am doing this properly.

The model: 

model3CFA <- 'F1 =~ NA*AS + CO + T2
F2 =~ NA*IB + PS + MU
F3 =~ NA*T1 + LS + RH
L1 =~ F1 + F2 + F3
F1 ~~ a*F1
F2 ~~ b*F2
F3 ~~ c*F3
a > .001
b > .001
c > .001
L1~~1*L1'

chisq: 64.7013

df: 24 

p_chisq: 1.346291e-05

AIC: 106.7013

CFI: 0.951786

SRMR: 0.04704835

The factor loadings for F2 are way higher than 1, do I need to fix this? or can I run a GWAS on the L1 factor with this? 

I would appreciate your feedback on this

 

[Elliot Tucker-Drob]

To be clear this is not a latent class analysis. latent class analysis refers to finite mixture modelling. this is a latent factor analysis, i.e. a confirmatory factor analysis.

In the STDALL column, the factor loading for F2 on L1 is in bounds. you may have been looking at one of the other columns, which are not fully standardized and thus not theoretically bounded by -1,1. That said, the loading is not significant which is curious given its standardized value.

You are using unit variance identification which can cause problems in a hierarchical factor model in which the variances specified for the first order factors are actually residuals after taking into account the higher order factor. This can blow up estimates and lead to numerical instability when the proportion of residual variance is actually very low, as it appears to be here. I suggest using unit loading identification, at least for the first order factors. (We do also suggest unit loading ID when any factor is regressed on an external variable, such as a SNP).

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[Xavier Farre]

Thank you so much for your answer.

I hope I got it right.

So ideally the model for a GWAS on the higher order factor should look like this?

model3CFA <- 'F1 =~ AS + CO + T2
F2 =~ IB + PS + MU
F3 =~ T1 + LS + RH

L1 =~ F1 + F2 + F3
F1 ~~ a*F1
F2 ~~ b*F2
F3 ~~ c*F3
a > .001
b > .001
c > .001

L1~SNP'

thank you again for your help

[Elliot Tucker-Drob]

yea, that seems right, although i'd first run without a SNP to make sure you get sensible estimates, then run with just a small number of snps again to confirm everything looks right.

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