MLR test statistic

[Mark Seeto]

Dear lavaan group,

The help page for the sem function says that '"MLR" will compute a test statistic which is asymptotically equivalent to the Yuan-Bentler T2-star test statistic', from which I infer that the MLR test statistic is not the same as the Yuan-Bentler T2-star test statistic. My question then is what is the MLR test statistic? Is the equation written down in an article somewhere?

I looked at the code for the testStatisticYuanBentler function in 08lavaantest.R, but I couldn't see the correspondence between that code and the Yuan & Bentler (2000) article.

Thanks,

Mark

[yrosseel]

On 11/28/2013 03:38 AM, Mark Seeto wrote:
> Dear lavaan group,
>
> The help page for the sem function says that '|"MLR"| will compute a
> test statistic which is asymptotically equivalent to the Yuan-Bentler
> T2-star test statistic', from which I infer that the MLR test statistic
> is not the same as the Yuan-Bentler T2-star test statistic. My question
> then is what is the MLR test statistic? Is the equation written down in
> an article somewhere?

Not in an article (that I know about). But I once gave a presentation
explaining the difference:

http://users.ugent.be/~yrosseel/lavaan/utrecht2010.pdf

(see slide 22).

Now, lavaan currently uses the 'Mplus' approach by default. The reason
is that I know how to handle 'fixed exogenous covariates' in this
setting, but I have not figured out how to do this for the original
Yuan-Bentler formulas (they assumed fixed.x=FALSE).

To get the original Yuan-Bentler formula, use mimic="EQS" (which will
imply fixed.x=FALSE)

In the source code (see file 08lavaanTest.R), we have two functions:

testStatisticYuanBentler
testStatisticYuanBentler.Mplus

implementing the 'two' versions.

Yves.

[Mark Seeto]

Thanks for your reply, Yves. It looks difficult to understand, but I'll give it a try.

Mark