How does Lavaan deal with standarize coefficients?

[lari...@gmail.com]

I just read Dr. Grace's article "Interpreting the results from multiple regression and structural equation models" published in 2005. He criticized the use of standarized deviations as coefficients when interpreting the results. Since I am entirely new to Lavaan, I am wonderting which kind of standerized coefficients that Lavaan reports,  standarized deviations or standarized by relative ranges. If the former is used, is there any particular reason to not incoporate Dr. Grace's modification in Lavaan? Thanks!

[Sunthud Pornprasertmanit]

They were all standardized by standard deviations. See p. 15 in this Mplus note:

https://www.statmodel.com/download/techappen.pdf

On Wed, Oct 29, 2014 at 11:09 AM, <lari...@gmail.com> wrote:

I just read Dr. Grace's article "Interpreting the results from multiple regression and structural equation models" published in 2005. He criticized the use of standarized deviations as coefficients when interpreting the results. Since I am entirely new to Lavaan, I am wonderting which kind of standerized coefficients that Lavaan reports,  standarized deviations or standarized by relative ranges. If the former is used, is there any particular reason to not incoporate Dr. Grace's modification in Lavaan? Thanks!

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[Terrence Jorgensen]

lavaan standardizes in the sense that the variances of observed and/or latent variables are rescaled to 1.  For anyone else interested in this topic, the article mentioned by the original poster can be downloaded here:

http://dx.doi.org/10.1890/0012-9623(2005)86[283:ITRFMR]2.0.CO;2

This article deals with path analysis only, not latent variable models.  Latent variables have arbitrary scales anyway, so interpreting standardized factor loadings is simply asking "how strongly correlated is this indicator with the construct it measures?", and even latent regression slopes are arbitrary because what is a 1-unit change in a variable without measurable units?  Standardized paths are just a way to ask how large the effect is, knowing it can't exceed +/- 1, although perhaps the arguments against interpreting "explained variance" in a latent variable might still apply if there is range-restriction in the indicators.

But in path analysis and multiple regression, I agree with Grace & Bollen (and several others in a long history of literature) about the limitations of interpreting "standardized" coefficients.  Although their particular suggestion is interesting (and can be calculated by a lavaan user from model results), it is by no means the only possible rescaling solution.  Andrew Gelman suggested dividing continuous predictors by 2 SDs instead of one because in most cases, that will give them roughly the same SD as binary indicators.

http://andrewgelman.com/2006/06/21/standardizing_r/

It's just another arbitrary rescaling to allow potentially less misguided comparison of different effects in the same model.  I'm not a fan of rescaling variables in any way that is not meaningful (i.e., I only want to ask how much Y changes as X changes by some amount), but when dealing with latent variables with arbitrarily set scales, I don't think we have that option.  Even using marker variables or effects-coding to identify a latent construct does not actually put the scale of a latent variable on the scale of the item (or average across items), but on the scale of the common variance in that item (e.g., see http://dx.doi.org/10.1037/1082-989X.7.2.210).

So long story short, although this is an important point to keep in mind when running path analyses in lavaan and interpreting coefficients, I don't see why Grace & Bollen's method in particular should be implemented as a preferred standardized solution in lavaan.  If syntax could be written general enough to apply to several examples, perhaps someone could make it an addition to the semTools package.

Terry

[lari...@gmail.com]

Terry, thanks a lot. Your answer is exactly what I need.

[lari...@gmail.com]

Dear Sunthud Pornprasertmanit,

    Thank you for the answer. Larix Yang