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 Angel Arias posted on Tuesday, January 29, 2019 - 10:44 am
Asparouhov and Muthén (2018, p.3) stated that "to establish approximate fit [one] should include an inspection of the Mplus residual output to verify that the
residuals are many small values and there are no large residual values at all". My question is what can we consider a large residual value? Are there any guidelines for this? what do you recommend?

Thanks a lot!
 Tihomir Asparouhov posted on Tuesday, January 29, 2019 - 3:08 pm
Anything above 0.3 by absolute value on a correlation metric should be considered substantial/non - ignorable. Apart from that it is somewhat subjective but values below 0.1 are commonly accepted as ignorable. Values between 0.1 and 0.3 could be considered important if substantive meaning can be found. Alternatively, record all absolute value residuals and plot them. Values that look like outliers mean + 3*st dev (from the residual distribution) if above 0.2 should be considered important and possibly included in the model. Approximate fit is somewhat subjective - the above looks reasonable to me.
 Angel Arias posted on Tuesday, January 29, 2019 - 3:15 pm
Thanks for the prompt and detailed response, cheers!
 Franzi Kößler posted on Thursday, April 16, 2020 - 5:41 am
That cut-off is already very helpful. I assume that I have to look at the section "Residuals for Correlations" in the Residual output, right?

The other thing I was wondering about: How do I get rid of these large ones? My initial thought was allowing the correlations but then I end up with a lot of non-sense... So I was wondering whether there is another way around.

Thank you in advance!
 Tihomir Asparouhov posted on Thursday, April 16, 2020 - 4:34 pm
Yes - Residuals for Correlations if the correct section.

I would recommend looking at

output:mod;

This section can give you ideas of various parameters that could be included in a structural model to resolve misfit.
 Franzi Kößler posted on Thursday, April 16, 2020 - 11:50 pm
Thank you!
I did that but the confusing thing was that it recommended specifying correlations (WITH) between latent factors that are already regressed on each other (ON) - what does that mean? And why is it possible? In my understanding there is no big difference between ON and WITH, right?
 Bengt O. Muthen posted on Friday, April 17, 2020 - 6:12 am
Those modindices should be ignored.
 Franzi Kößler posted on Friday, April 17, 2020 - 7:36 am
Thank you! From a theoretical point I agree :-)
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