Computing factor scores (with standard errors) for a follow-up Bayesian analysis

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Scott Claessens

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Aug 16, 2019, 12:59:48 AM8/16/19
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In lavaan, we can fit a confirmatory factor analysis model and compute predicted factor scores with standard errors.

HS.model <- ' visual  =~ x1 + x2 + x3 
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data = HolzingerSwineford1939)

pred <- lavPredict(fit, se = "standard") 

However, I was under the impression that this approach would give me a different standard error for every individual predicted factor score. Instead, we only get three standard errors, one for each latent variable.

attr(pred, "se")[[1]]

visual          textual         speed
0.4747366  0.3316382   0.3276657

I am employing this approach because I am using the predicted factor scores in a second Bayesian phylogenetic analysis using the brms package, and I would like to propagate their uncertainty forward (unfortunately, brms does not yet support latent variable estimation). For this method, I would need a separate standard error associated with every individual predicted factor score.

Is it okay to give every predicted score for the "visual" factor a standard error of 0.4747366, for example? Is that what this lavaan output is telling me? Or have I misunderstood what the se = "standard" argument within predict() actually does?

Many thanks in advance, lavaan is awesome!

Terrence Jorgensen

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Aug 17, 2019, 9:42:40 AM8/17/19
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However, I was under the impression that this approach would give me a different standard error for every individual predicted factor score.

Nope, that only happens if you use Bayes:

 
Instead, we only get three standard errors, one for each latent variable.
...
Is it okay to give every predicted score for the "visual" factor a standard error of 0.4747366, for example? 

Yes.

Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam

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