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First, sorry, i wrongly put part of this thread by mistake in the SEM topic. I'll try again.. I was wondering what one should do when one or several estimates are significant with Delta parameterization but not significant with Theta parameterization? I run the same CFA in delta and theta parameterization. While the model fits are good, and the delta model provides significant estimates, the theta model does not. One of my outcome variable is very highly related to its common latent factor (corr = 0.994 in delta and 0.996 in theta!). I think it's probably where the problem comes from in theta. But why isn't it a problem in delta modelisation? Any input would be greatly appreciated! Cheers, Do. 


The delta method is sometimes preferable to Theta  see Mplus Web Note #4 on our web site. 


Hello again, I was asking about this issue because ultimately I'd like to conduct measurement invariance bw 2 groups, and if possible, examining the residual variances (theta). I find quite worrying that the two parameterizations can lead me to two different conclusions. I have read the Mplus Web Note #4, but I have to admit why such a disparity could happen eludes me (statistics are not my strong point, i'm afraid!..). 


Typically, the two approaches do not give different significance results. But it is possible for this to happen in any given sample due to parameters following different sampling distributions in the two cases. It is also possible that you are not setting up the model in comparable ways in the two approaches  if you want that to be checked you can send your inputs and outputs for the two runs with data and your license number to support@statmodel.com. 


Hello Bengt, Would you mind elaborating a bit more on parameters following different sampling distribution? What could trigger this to happen? Regarding setting up the model in the two approaches, I thought that the only thing to change was adding in the 'Analysis', PARAMETERIZATION = THETA; Am i wrong? Thanks again for your explanations! 


Your first paragraph questions go back to general statistical inference. For instance, the sample mean and sample variance have different sampling distributions (normal and chisquare)  approaching significance happens at different sample sizes for those parameters. Regarding your second paragraph, the answer depends on the model; how you specify the residual variances versus the scale factors. We would have to see your run to say  so this is a support question. 

Eric Teman posted on Saturday, May 26, 2012  12:23 am



When WLSMV is used with theta parameterization for a threefactor CFA, for instance, it won't actually output residual variances, right? It isn't for me, anyway. 


You can estimate residual variances only in multiple group or multiple time points models not crosssectional models. 

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