std.lv = TRUE does not produce equal factor loadings in estimate- and std.lv-columns

[Luisa Horsten]

Hi,

I'm again having trouble with standardized estimates. This one is really peculiar, though, as it only occurs for one specific latent factor.

My model looks like this:

model <- "
D =~ d1 + d2 + d3 + ... + d36
H =~ h1 + h2r + h3 + ... + h32

P =~ p1 + p2 + p3 + ... + p9
G =~ g1

P ~ D + H
G ~ D + H
D ~~ HH
"

I then estimate the model via

model.fit  <- cfa(model,
                  data = data.model,
                  missing = "fiml",
                  std.lv = TRUE)

summary(model.fit,
        fit.measures = TRUE,
        standardized = TRUE,
        rsquare = TRUE)

As should be, for each latent factor, the factor loadings in the estimate and std.lv columns are equal. Well, for each factor except P. Same goes for the regression coefficients: the estimated and std.lv regression coefficients of each predictor for G are equal, but not for P. Example below:

Latent Variables:
              Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
D =~                                                                  
    d1          0.333    0.071    4.670    0.000    0.333    0.411
H =~                                                                
    h1          0.235    0.078    2.997    0.003    0.235    0.270
P =~                                                              
    p1          0.169    0.061    2.779    0.005    0.440    0.395
G =~                                                                
    g1          2.172    0.136   15.916    0.000    2.185    1.000

Regressions:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  G ~                                                                  
    D                 0.013    0.149    0.090    0.928    0.013    0.013
    H                -0.120    0.150   -0.798    0.425   -0.119   -0.119
  P ~                                                                
    D                -1.252    0.489   -2.558    0.011   -0.482   -0.482
    H                 3.167    0.915    3.462    0.001    1.218    1.218

I can reproduce this behavior in another dataset, in which I have D, H, and P, too. All factors behave normally, except for P. Do you have any idea, what could be causing this? Is there anything wrong with my code? Should I check the data for peculiarities?

Thanks a lot in advance for any hint!

[jpma...@gmail.com]

Hi Luisa,

You have a strong multicollinearity problem with in the regression part of the model. Check also for extreme Sk and Ku of items in the measurement part of the model….

Best,

João Marôco

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[Luisa Horsten]

Hi João,

thanks for taking the time!

Yes, D and H are indeed very strongly correlated. But why would that only cause problems for the regression of P but not of G? And how does that explain the weird loadings on P itself?

Thanks again!
Best, Luisa

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[Edward Rigdon]

Is the HH in the last line of model syntax an error?

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[Luisa Horsten]

Ugh, yes, sorry about that! That is a typo indeed, should be D ~~ H instead.

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