Number of cases for WLSMV estimation PreviousNext
Mplus Discussion > Categorical Data Modeling >
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 Dieter Urban posted on Monday, November 22, 1999 - 9:11 pm
In a SEMNET discussion this year G. Gregorich stated ´It (the WLSMV estimator) appears to have good small sample performance for relatively small models, but I believe that it still requires N > p* (where p = the number of manifest variables and p* = p[p+1]/2). That is because a central matrix of order p* x p* needs to be inverted and thus must be positive-definite.´ Would the authors of Mplus support that fully?
 Bengt O. Muthen posted on Wednesday, November 24, 1999 - 11:07 pm
It is not the case that we must have n > p* for p*=p(p+1)/2 for WLSM or
WLSMV. Although the weight matrix has p* rows, this matrix need not be
inverted in WLSM or WLSMV, only in WLS. However, the quality of estimates
may not be good for n < p*. Simulation studies are needed.
 Anonymous posted on Saturday, August 16, 2003 - 3:00 pm
Why doesn't the weight matrix need inverted for WLSM and WLSMV?

Is WLSM equivalent to applying the Satorra-Bentler correction with the WLS estimator?

How is WLSMV different?
 Bengt O. Muthen posted on Saturday, August 16, 2003 - 10:43 pm
Weight matrices are inverted in the generalized least squares fitting function. WLSM and WLSMV however do not use GLS but a diagonal weight matrix. In the standard error and chi-square computation, the full weight matrix is involved but not inverted.

Yes, WLSM is analogous to the Satorra-Bentler correction to the WLS estimator with continuous outcomes.

WLSMV is different because it improves the chi-square approximation by not only adjusting the mean but also adjusting the variance.
 Valeriana posted on Monday, March 06, 2006 - 5:52 pm
ADF or WLS estimation requires very large samples.
WLSM / WLSMV / DWLS methods have the same characteristic of use only the diagonal of the weight matrix. So that, they are better for small samples.
I´d like to know how can I compute the sample size for these methods that uses only the diagonal of the matrix?
Do you have any reference?
 Linda K. Muthen posted on Monday, March 06, 2006 - 8:18 pm
Are you asking how many subjects you would need for WLSMV for example? Or are you asking for a study where the number of subjects needed has been studied?
 Valeriana posted on Monday, March 06, 2006 - 8:31 pm
I´d like to know how many subjects I need. Like we have the formula to compute the sample size for ADF estimation p+1/2p(p+1), don´t we have something similar for the methods which uses only the diagonal of the weight matrix?
 Linda K. Muthen posted on Monday, March 06, 2006 - 10:58 pm
I am not aware of such a formula. We recommend a simulation study to determine the number of subjects needed because the number of subjects needed depends on so many factors. See the following paper:

Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620.
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