Creating a Factor to describe residual variance

[Anthony Angueira]

Hello,

We have created a common factor model with 4 factors explaining various phenotypes. One of the phenotypes (Phen4) is explained by two of the factors and we are interested in what the nature of the residual variance is.

However, when I try to generate a model that creates a factor to explain that residual variance, it does not converge. Is there any way to identify a factor we can do GWAS on to understand the residual variance not explained by two factors?

Old Model
'F1 =~ Phen1+Phen2+Phen3+Phen4
F2=~NA*Phen6+Phen5+Phen4
F3=~Phen7+Phen8+Phen9+Phen10+Phen11
F4=~Phen12+NA*Phen13
F1 ~~ F2
F1 ~~ F3
F1 ~~ F4
F2 ~~ F3
F2 ~~ F4
F3 ~~ F4
Phen6~~b*Phen6
b>.001
Phen13~~a*Phen13
a>.001'

New Model with Phen4 Residual Factor- does not converge
'F1 =~ Phen1+Phen2+Phen3+Phen4
F2=~NA*Phen6+Phen5+Phen4
F3=~Phen7+Phen8+Phen9+Phen10+Phen11
F4=~Phen12+NA*Phen13
F5=~ Phen4
F1 ~~ F2
F1 ~~ F3
F1 ~~ F4
F2 ~~ F3
F2 ~~ F4
F3 ~~ F4
F1 ~~ F5
F2 ~~ F5
F3 ~~ F5
F4 ~~ F5
Phen6~~b*Phen6
b>.001
Phen13~~a*Phen13
a>.001'

Thanks,

Anthony

[agro...@gmail.com]

Hi Anthony, 

I would suggest adding a couple things to help make the model more interpretable and more likely to converge. The first is setting the residual of Phen4 to 0, so that the residual of Phen4 entirely feeds into the F5 variable and reflects what you want it to. This is also done so that part of the model is identified, since for a single item latent you only have the degree of freedom of the genetic variance of that variable and if you don't fix the residual of Phen4 to 0 then you are estimating two parameters: the variance in Phen4 and factor loading (or factor variance). 

The second is that you correlate the residual Phen4 factor (F5) with all factors, including the factors that Phen4 loads on, which I would consider uninterpretable and likely another source of model convergence issues. So I would fix the factor correlations between F5 and both F1 and F2 to 0 for this reason. The final thing I'll say is that you'll want to be careful to interpret those F5 correlations in light of how much genetic variance in Phen4 is actually left-over. That's to say, you already have Phen4 loading on the first two factors, and if we between the two of them Phen4 does not have a significant or sizeable residual then it may not being saying much to say what little is left-over in Phen4 is associated with the remaining factors (this may not be the case at all but wanted to flag this as something to consider since it is loading on two factors). 

Model I would suggest: 

'F1 =~ Phen1+Phen2+Phen3+Phen4
F2=~NA*Phen6+Phen5+Phen4
F3=~Phen7+Phen8+Phen9+Phen10+Phen11
F4=~Phen12+NA*Phen13
F5=~ Phen4

Phen4~~0*Phen4

F1 ~~ F2
F1 ~~ F3
F1 ~~ F4
F2 ~~ F3
F2 ~~ F4
F3 ~~ F4

F1 ~~ 0*F5
F2 ~~ 0*F5

F3 ~~ F5
F4 ~~ F5
Phen6~~b*Phen6
b>.001
Phen13~~a*Phen13
a>.001'

-Andrew

[Anthony Angueira]

Thank you very much, this is extremely helpful. I really appreciate it.

Best,

Anthony