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I'm running a CFA in lavaan, and I understand that as a general rule of thumb, each item should have a standardized loading on the factor of <|0.3|. I've been making the mistake of reviewing the Estimate on the summary output to assess the loading, and I realize now this is not standardized since the value can exceed 1. To make a proper loading assessment, I have added standardized = TRUE to the summary output, and now see two additional columns: Std.Lv and Std.all.

So, my question is, which column should I reference to assess a good factor loading? Should I consider where just the latent variables are standardized, or where all are standardized, or both? Guidance on this would be helpful.

As a reference point, here's the summary output for the first factor in my CFA. Based on Std.all, all items would be a good enough fit. Based on Std.lv, V2.A.2.c would not work.

                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  analysis =~                                                           
    logic             1.000                               0.969    0.969
    quant             0.621    0.017   35.988    0.000    0.874    0.874
    V2.B.4.g          1.249    0.028   44.502    0.000    0.510    0.894
    V2.B.4.h          1.234    0.027   45.063    0.000    0.504    0.900
    V2.A.2.c          0.427    0.035   12.095    0.000    0.175    0.314
    V2.B.2.i          1.105    0.021   53.131    0.000    0.451    0.933
    V2.B.4.e          0.977    0.020   49.474    0.000    0.399    0.918
    wcom              1.187    0.026   45.063    0.000    0.886    0.886
    vcom              0.414    0.026   15.910    0.000    0.450    0.450
    V2.A.2.b          1.129    0.023   48.068    0.000    0.461    0.904
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Yes, @Zack, you are correct in applying the rule of thumb (i.e., retaining only items with loadings greater than 0.3) to the standardized loadings.

However, I feel obligated to push back a little regarding the appropriateness of that rule of thumb. More important than the magnitude of the loading itself are its standard error and the extent to which you believe the small loading reflects the item not being an appropriate measure for the construct of interest.

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  • $\begingroup$ Thanks for your additional commentary. I was taking the theoretical component as a given. When looking at standardized loading, do you consider Std.all? Regarding standard error, what's the rule of thumb there? $\endgroup$
    – Zack
    Sep 22, 2021 at 21:48

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