R – Difference Between Bootstrapped Standard Error and Lavaan Default Output Standard Error

lavaanrstructural-equation-modeling

I am doing sem with lavaan in R, and I found that even I don't input the bootstrap parameters, the output of sem will give me the standard error by default.

I am wondering what is the difference between the default output standard error and the bootstrapped standard error?

Best Answer

It depends on the type of estimator. The default without ordered= outcomes is maximum likelihood, in which case the second derivative of the likelihood function (Hessian matrix) is used to obtain the SEs analytically. There are different flavors depending on (in)complete data, or robust corrections for nonnormality. This recent paper provides and nice overview of the options:

https://doi.org/10.1080/10705511.2021.1877548

A bootstrap SE is simply the SD of a statistic in the empirical bootstrap distribution.

Related Solutions

Solved – How to compute and interpret the mean of a latent variable in structural equation modeling using lavaan

Means and intercepts of latent variables are kind of weird.

It looks to me like you've constrained the means of the intercepts to zero. If you haven't, then model is not identified.
You estimate the intercepts freely with:
```
A1 ~ 1
```
I don't think you did that. (But post your output if you want me to be sure.)
Means (and intercepts) of latent variables are not directly interpretable, because they are arbitrary. You can set the mean to be any value you want it to be. You can interpret latent variable means relative to each other - e.g. you can constrain one latent mean to be equal to 0 and (as long as there are identifying constraints), a second mean might be 1 - you can then say that the second mean is one unit higher than the first. But you can also constrain the first mean to be 16.5, and then you'll discover that the second mean is 17.5, so it's one unit higher.

Solved – Why does the SEM (‘lavaan’) return covariance estimates for all pairwise variable combinations that were not specified in the model

Welcome Kirby!

lavaan usually defaults to estimating correlations between observed variables (and when you specify them--it doesn't appear you have--latent variables) unless you tell it to otherwise. lavaan provides a shorthand option for overriding this default when dealing with latent variables (using orthogonal = TRUE in cfa or sem), but this won't help you here because all of your correlations are among observed variables--you'll need to manually fix each of these to a value of zero (i.e., thereby indicating you are not interested in estimating them/are comfortable assuming they take on a value of 0).

The tutorial materials on the lavaan website give a good overview of how to fix parameters in this fashion, but as an example, fixing all the correlations to 0 involving the mgmt01 variable would look like this:

mgmt01 ~~ 0*avgprecip + 0*pctsavanna + 0*riverkm_perkm2 + 0*roadkm_perkm2 + 0*distboundarykm + 0*distedgekm + 0*avg_FRP

The tl;dr: here is that with lavaan, it's often valuable (though potentially annoying) to specify everything that you do/do not want estimated, in order to be sure you're getting exactly the model you want.

Regarding the warning messages you're getting, I find it's sometimes helpful to sketch out your path diagram to make sure identification isn't a problem and that you haven't coded a linear dependency somewhere--in this case, I share your intuition that identification isn't the problem. A more plausible candidate, in my opinion, is that you're asking for an awful lot of estimates/inferences from a relatively modest sample of data, and estimation errors under these kinds of conditions aren't uncommon. This might clear up after you constrain all those correlations you don't want to zero, but otherwise it might be a case where you need more data.

Best Answer

Related Solutions

Solved – How to compute and interpret the mean of a latent variable in structural equation modeling using lavaan

Solved – Why does the SEM (‘lavaan’) return covariance estimates for all pairwise variable combinations that were not specified in the model

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