Latent factor with 2 Indicators

[Liam Veltman]

Hello everyone,

I am currently having issues with parameter estimates for a latent factor with only 2 indicators and was wondering if any one has encountered a similar issue previously and knows of any potential solutions.

I am trying to test a 2 factor model of the big-5 personality traits that has been described previously in the psychological literature to see if the same model would apply to the genetic correlations between the traits. The problem is that one of these higher order factors are defined as the shared variance between openness and extraversion (only two indicators). The factor for the other 3 traits seems hold up well across all models I have tested below.

The genetic correlation matrix produced by LDSC regression suggests that this higher factor structure may also hold up genetically as well,  extraversion and openness are correlated at 0.38, the strongest correlation out of all the traits (matrix below).

         agree          consc                extra         invneuro       openn
[1,] 1.00000000  0.22913633 0.2218264 0.36282889  0.09954667
[2,] 0.22913633  1.00000000 0.1553970 0.11042669 -0.09678278
[3,] 0.22182644  0.15539701 1.0000000 0.20712439  0.38345179
[4,] 0.36282889  0.11042669 0.2071244 1.00000000  0.01510956
[5,] 0.09954667 -0.09678278 0.3834518 0.01510956  1.00000000


When I test the below model I get decent fit metrics, however the estimates for extraversion are highly out of bounds due to the latent factor only having 2 indicators (F2~extra = 1.9, extra~extra = -2.7).

F1=~NA*agree+invneuro+consc
F2=~NA*openn+extra
F1~~1*F1
F2~~1*F2

      chisq       df      p_chisq      AIC              CFI       SRMR
df 32.50444  4 1.508672e-06 54.50444 0.935647 0.03967861




I then tested a model constraining the extraversion residual to be within bounds which produced similar fit indices, however now the latent factor becomes almost identical to extraversion when standardised (F2~extra = 1.0, F2~open = 0.36; LDSC correlation between openness and extraversion is 0.38).

F1=~NA*agree+invneuro+consc
F2=~NA*extra+openn
F1~~1*F1
F2~~1*F2
extra~~a*extra
a > 0.001

      chisq       df      p_chisq      AIC              CFI           SRMR
df 39.08002  4 6.706292e-08 61.08002 0.9208017 0.04307385




Out of curiosity I then tested the same model however I input openness before extraversion which produces standardised estimates which look much more sensible (F2~extra = 0.38, F2~open = 0.36) with almost identical fit indices.
 
F1=~NA*agree+invneuro+consc
F2=~NA*openn+extra
F1~~1*F1
F2~~1*F2
extra~~a*extra
a > 0.001

      chisq      df      p_chisq      AIC                CFI          SRMR
df 39.07998  4 6.706409e-08 61.07998 0.9208018 0.04307385




Is there any other ways of improving the quality of estimates for the openness/extraversion factor or are my hands tied by the data I have available?

If there is no work around, could I continue forward with the model based on prior theory with the big caveat that the openness/extraversion factor is likely empirically under-identified or should I just dump the factor altogether?

Apologies for the long post, I just wanted to be thorough. I'm very new to genomic SEM and would very much appreciate any insight.

Thanks heaps!

Liam

[Michel Nivard]

Hi,

a latent variable based on 2 indicators isn't identified without further constraints. 2 traits means 2 variances and 1 covariance. Simplifying the problem (i.e. there are other concerns if the latent variable relates to other latent variables we won't get into now) you cannot use more than 3 parameters to describe that relationship as it consists of 3 pieces of information.

you have some options:

1. fix the latent variance to a constant, and set the loadings to be equal, and freely estimate the residual variances for the traits.

2. fix the lodigns to a constant (usually 1) and free the latent variance, free the residual variances.

3. a more esoteric thing where you constrain the residuals to be equal,  fix the factor variance and freely estimate the loadings.

All these should give you solutions that can be "translated" into each other, in other words their 3 parameterisation to describe the same thing. Which one you choose may depend on your needs in the rest of the model.

These limitations arise from SEM and are not specific to GenomicSEM.

Best,

Michel

[B]

Dear Michel and Liam,

Thank you for sharing information and posting on the forum regarding model with latent factor with two indicators.

I wanted to ask if the applying the constraints to a latent factor with two indicators in a two-factor model 

(example:  model_2factor <-"F1=~ NA *trait1 + trait2 +trait3 + trait4    

F2=~ NA *b * trait5 + b * trait6
F1~~F2
F1~~1*F1
F2~~1*F2" ) also requires to apply constraints, such as fix the latent variance to a constant and set the loadings to be equal. Or is this not applicable to a two factor model where only one latent factor has two indicators?

Thank you very much in advance for your time and insight!

Best regards,

Barbara Sakic

Op vrijdag 21 februari 2025 om 10:24:07 UTC+1 schreef m.g.n...@gmail.com:

[Elliot Tucker-Drob]

When fixing two loadings to be equal, you still need the usual constraint to identify the scale of the factor. You can either fix the variance of the factor to 1.0 or you can set a loading to 1.0. For the latter, fixing a loading to 1.0 and constraining both loadings to be equal means that you are fixing both loadings to 1.0.

Regardless of which of these choices you make, fixing two loadings to be equal makes an assumption that they are on the same scale and equally affected by the factor. This means, for example, if you go on to estimate SNP effects on the factor, the expectation is that the individual SNP effects on both phenotypes are equal.

--
You received this message because you are subscribed to the Google Groups "Genomic SEM Users" group.
To unsubscribe from this group and stop receiving emails from it, send an email to genomic-sem-us...@googlegroups.com.
To view this discussion visit https://groups.google.com/d/msgid/genomic-sem-users/e0549145-3535-4f3e-94a4-f411cfd49546n%40googlegroups.com.