Question about standardized loadings and ordinal items

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Kevin Reuning

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Nov 9, 2019, 2:59:56 PM11/9/19
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Hello, 

I am trying to make sure that I am not missing something obvious. In a project I am working on I am testing a measurement model using lavaan's cfa()
function. I have three latent variables, each with 4 unique indicators that are measured using a 4 point Likert scale. In estimating the model I set std.lv=T, to standardize the estimates. 

I report the estimated loadings and, although they are not the most important part of the paper, discuss how they vary. A reviewer is concerned that these estimates are not easily interpretable given that I am have ordered indicators. They ask that I report the variance explained instead. I am happy to do this, but from what I can gather the variance explained is just the square root of the standardized loadings and so would not really lead to much of a difference in interpretation from what I am already reporting. I also realize that I was not as explicit in explaining that the estimates were standardized by setting the latent variance to 1, so that might be part of the confusion. 

I am generally self-taught here, having read through Brown's CFA book, and I was hoping that someone could point me in the right direction if I am missing something. 

Thank you for any help, 

Kevin 

Terrence Jorgensen

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Nov 13, 2019, 9:41:26 AM11/13/19
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You are right.  In fact, if you used the default parameterization="delta", then the estimated loadings are already fully standardized, identical to the Std.all column.  But that means R-squared should be the square (not root) of the loadings, because standardized simple regression slopes are correlation coefficients.

All you can do is explain that fact politely in your response, and there's nothing wrong with adding a couple sentences to your Results telling readers how they can interpret your loadings this way.

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

Kevin Reuning

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Nov 13, 2019, 1:24:35 PM11/13/19
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Thank you very much for the help!. 
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