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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 positivedefinite.´ Would the authors of Mplus support that fully? 


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  9:00 am



Why doesn't the weight matrix need inverted for WLSM and WLSMV? Is WLSM equivalent to applying the SatorraBentler correction with the WLS estimator? How is WLSMV different? 


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 chisquare computation, the full weight matrix is involved but not inverted. Yes, WLSM is analogous to the SatorraBentler correction to the WLS estimator with continuous outcomes. WLSMV is different because it improves the chisquare approximation by not only adjusting the mean but also adjusting the variance. 

Valeriana posted on Monday, March 06, 2006  11:52 am



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? 


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  2:31 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? 


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, 599620. 

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