estitmator= MLMV vs MLMVS

[Njål Foldnes]

The mean and variance adjusted chi-square as proposed by Satorra and Bentler is now available as MLMVS, if I understand this correctly?

What is the difference between MLMV and MLMVS? The MLMV does not seem to adjust the df. 

Could anyone give a reference to where I can find the definition of MLMV fit statistic?

BTW: ULS offers the MV option, but not the MVS option, is there some particular reason for that?

[yrosseel]

On 02/28/2013 02:46 PM, Nj�l Foldnes wrote:
> The mean and variance adjusted chi-square as proposed by Satorra and
> Bentler is now available as MLMVS, if I understand this correctly?

Yes.

> What is the difference between MLMV and MLMVS? The MLMV does not seem to
> adjust the df.

Good question. MLMV and MLMVS are two different approaches to 'adjust'
the chi-square test statistic (and/or its degrees to freedom), to better
approximate the chi-square distribution.

Estimator="MLMV" and estimator="MLMVS" is short for

- estimator="ML"
- se="robust"
- test="mean.var.adjusted" (MLMVS, with S for Satterthwaite)
or
- test="scaled.shifted" (MLMV)

test="mean.var.adjusted" is the familiar 'Satterthwaite' approach
(adjusting both the mean and the variance), and is well documented in
the literature. One reference is:

Satorra, A., & Bentler, EM. (1994). Corrections to test statistics and
standard enors in covariance structure analysis. In A. von Eye & C.C.
Clogg (Eds.), Latent variables analysis: Applications for developmental
research (pp. 399-419). Thousand Oaks, CA: Sage.

available here:
http://www.econ.upf.edu/~satorra/CourseSEMVienna2010/SatorraBentler1994.pdf
(see eqs 16.23 and 16.24)


Now, for many years, estimator MLMV in Mplus referred to this
Satterthwaite correction. With the 'MV' standing for 'mean' and
'variance' adjusted. But from Mplus 6 onwards, they changed this, and
the *MV extension (in MLMV, ULSMV, WLSMV) is now by default referring to
a 'scaled-shifted' correction, documented here:

https://www.statmodel.com/download/WLSMV_new_chi21.pdf

Very, very few users noticed this. And the *MV extension is not helping
(it should be MLSS, for scale+shift). Note that apart of this web note,
there is no published paper about this (AFAIK).

In Mplus 6 and higher, it is still possible to request the Satterthwaite
version, but then you need to add an option 'Satterthwaite=on' somewhere.

In lavaan, the *MV extension refers to the scaled-shifted correction (as
in Mplus 6 and higher). The *MVS extension refers to the Satterthwaite
correction.

These estimator types are for Mplus users, and they should result in
identical results. Non-Mplus users are perhaps better off using the
'test' argument directly.

> BTW: ULS offers the MV option, but not the MVS option, is there some
> particular reason for that?

That is an oversight on my part. Both ULMVS and WLSMVS are now added to
the dev version (0.5-12).

Yves.

[Njål Foldnes]

Ok. I understand. 

So instead of asking for estimator MLMVS, it is better to write test="Satterthwaite", to obtain the same result. 

This will give the same statistic that is now c_4 in LISREL 9

Thanks!

kl. 11:29:08 UTC+1 mandag 4. mars 2013 skrev Yves Rosseel følgende:

[yrosseel]

On 03/04/2013 12:37 PM, Nj�l Foldnes wrote:
> Ok. I understand.
> So instead of asking for estimator MLMVS, it is better to write
> test="Satterthwaite", to obtain the same result.

and also se="robust"

Yves.