Standardised vs Estimate

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Zach Howard

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Oct 15, 2018, 10:14:19 PM10/15/18
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Hi all,

Apologies if this has been answered before, I had a quick search and couldn't find anything definitive and am new to CFA and SEM in general.

I am trying to understand the difference between standardized (e.g. the output labelled std.all) and standardized ('Estimate') factor loadings. For instance, in the following output, the B and C variables have very low Estimates, but high 'standardized' coefficients. My understanding is that this is because those two variables are proportions (so range from 0-1 numerically) and the coefficient would refer to, say, a 1% increase, whereas most other variables are either binary (D-F) or ordered categorical (A) with a small number of categories. The standardized coefficients account for this and thus can be directly compared.

Is my understanding here correct? If so, when reporting should I report the standardized coefficients? This CFA will eventually be part of a larger SEM model so the reporting would predominantly be to highlight that the factors either (a) loaded well, or (b) were theoretically necessary.

Thanks in advance

Latent Variables:
                   Estimate  Std.Err  z-value  P(>|z|)   Std.lv  Std.all
  Unhealthiness =~                                                      
                A    0.959    0.013   72.235    0.000    0.959    0.959
                B    0.096    0.001   73.310    0.000    0.096    0.843
                C    0.082    0.001   71.026    0.000    0.082    0.503
                D    1.212    0.018   67.978    0.000    1.212    0.790
                E    0.833    0.013   66.599    0.000    0.833    0.833
                F    0.464    0.016   28.958    0.000    0.464    0.464

Terrence Jorgensen

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Oct 18, 2018, 7:23:55 AM10/18/18
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I am trying to understand the difference between standardized (e.g. the output labelled std.all) and standardized ('Estimate') factor loadings.

The "Estimate" column is the actual (unstandardized) estimate.  "std.lv" means that is what the estimate would have been if the latent variables had SDs==1, and "std.all" means that is what the estimate would have been if both the latent and observed variables had SDs==1.
 
when reporting should I report the standardized coefficients?

Report both.  You base inferences on the actual estimates, and use standardized coefficients as measures of effect size (like supplementing a t test with Cohen's d or a regression slope with a standardized slope).


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