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Unbiased SRMR/CRMR estimators

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bwiernik's picture
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Joined: 01/30/2014 - 19:39
Unbiased SRMR/CRMR estimators

Maydeu-Olivares and colleagues have recently derived unbiased estimators and confidence intervals for the standardized root mean square residual and correlation root mean square residual (https://link.springer.com/article/10.1007%2Fs11336-016-9552-7), and these seem to perform quite well (https://www.tandfonline.com/doi/abs/10.1080/10705511.2017.1389611). In general, I find the residual-based fit statistics appealing for their interpretibility, particularly when combined with other fit indices that include parsimony penalty. I was wondering whether OpenMx might re-consider adding these unbiased estimators to summary.MxModel()?

mhunter's picture
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Joined: 07/31/2009 - 15:26
Considering

Given the articles you referenced, I think some re-consideration of SRMR (and perhaps CRMR) is merited. The first article at least addresses the issue of bias. The other two criticisms of these listed on the help page for summary.MxModel remain. First, these fit indices only apply to a relatively narrow set of models: covariance data, or raw data with completely ignorable missingness, no definition variables, no sample weights, no ordinal data, and so on. Second, there is no adjustment for model complexity: more complicated models will always fit better in terms of SRMR. This is not ideal.

Still for the cases in which SRMR is possible, the version proposed by Maydeu-Olivares has merit. I can read the papers more thoroughly over the coming weeks and see if implementation in OpenMx is a good idea.

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