Standardized factor loading larger than 1

[Austin Park]

Hi all,

If I understood correctly, for the model under Heywood case, the standardized factor loading could be larger than 1 due to the presence of negative variance. And this could be resolved by constraining the variance to be > 0.001. I have tried this, but one variable loaded on a latent factor is still giving standardized factor loading larger than 1. I would like to ask your suggestion on this. What should I look into in order to fix this problem?

I really appreciate your help.

Best,

Austin

[Elliot Tucker-Drob]

Note that the STD_Genotype standardization is only with respect to the GWAS phenotypes. To standardize with respect to latent factors, you'd need to make sure that you use unit variance identification rather than unit loading identification. Or you can look at STD_All. The other possibility is that you have an indicator that loads highly on multiple factors (e.g. if you are allowing many cross loadings), which can sometimes produce standardized estimates>1. In circumstances in which the estimates are out-of-bounds, you should consider that your model is misspecified- i.e. that the model simply doesn't represent the data well, and whether alternatives are with considering. Generally speaking, if a standardized parameter is highly out of bounds (and not just a little over the line), I would strongly reconsider whether my model is appropriate unless the CI is huge.

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[Austin Park]

Hi,

Thanks for the response.

I have a few follow-up questions, and below is a brief explanation of my model.

The model has 4 endogenous latent variables, which are then loaded to a second-order latent factor. During model specification, I used unit variance identification so that when I read STD_ALL, the second-order latent factor has variance of 1.

If I understood correctly, I believe that I have to use STD_ALL values when there are endogenous latent variables. But STD_ALL has no SE values, so I’m not sure if CI can be calculated and make a decision on whether it is out of bounds. The value of factor loading itself that I’m getting is 1.057.

My question is that if the standardized factor loading is just a little over the line, can I use this model, or should I consider another model?

Thank you,

Austin

[B]

Dear all,

Thank you for posting this question and information. I wanted to follow-up on a similar situation:

I have the following 2-factor model:

-F1=~ NA *trait1 + trait2 +trait3 + trait4    

F2=~ NA * trait5 +  trait6  + trait7
F1~~F2

trait5 ~~ a*trait5
a > .001
F1~~1*F1
F2~~1*F2"

I used Heywood case constraint for trait 5, but after this I still observe standardized factor loading of 1.0079210. Moreover, I also tried to constraining the residuals to be greater than 0.0001 (so instead of 'a > .001' use 'a > .0001')

After CFA I get the following  model fit for the model (which I understood to be good/acceptable):

$modelfit
      chisq df      p_chisq      AIC       CFI       SRMR
df 216.1566 13 6.471231e-39 246.1566 0.9547636 0.09127556

Does this mean that my model is misspecified, and should not use the model or adjust?

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

Best regards,

Barbara

Op vrijdag 14 januari 2022 om 06:33:39 UTC+1 schreef Austin Park: