Message/Author 

Kaja posted on Thursday, July 07, 2005  4:52 pm



Hi there, We are trying to interpret a situation in which we have huge modification indices for all of the WITH statements, even though we are accounting for what we think is the best factor structure for this data. This suggests to us that our model violates the assumption that the errors are uncorrelated. If we add the residual correlations to the model, the fit improves substantially. We are wondering how people usually interpret this kind of result given that we think we have found the best factor structure for the data. Thanks for your help, Kaja 


Residual covariances can sometimes capture minor factors or methods factors. I would suggest going back and starting with an EFA to see if perhaps some of your items are not behaving as expected. EFA is a good way to find problematic items, that is, items that may load on factors not intended. 

Liu Xiao posted on Wednesday, September 12, 2007  11:25 am



Hi, I read the Mplus user's guide, and I read that "residuals are not correlated as default" in Growth Modeling. How to free the residual correlations? In the following: i1 s1 y1@0 y2@1 y3@2 y4@3; i2 s2 x1@0 x2@1 x3@2 x4@3; y1 with y2; x1 with y1; Does "y1 with y2" define the residual correlation or just the correlation between two observation variables y1 and y2? Thanks in advance. 


y1 WITH y2 describes a covariance or a residual covariance depending on whether the variables are exogenous or endogenous variables in the model. In your situation, a residual covariance is specified. 

Ina Prokjev posted on Friday, November 08, 2013  8:02 am



Hi Linda, within a "combined" CFA model I want to correlate the residual variances of the latent first order factors of two second order models (both with a latent second order generalfactor at the apex and three latent content specific groupfactors on the firstorder level below g). (I´m interested in the interaction of the contentspecific firstorder factors across batteries) my question follows the post above. When I use the "with" statement for the correlation between the firstorder factors, can I be sure, that mplus uses the residual variances of the firstorder factors instead of factor variances? thanks for a clarifying answer... Ina 


Some but not all of the residual covariances among the firstorder factors can be identified. It is the residuals that are covaried. 

Ina Prokjev posted on Friday, November 08, 2013  5:37 pm



Thanks for your fast reply. But, one thing: what what do you mean by "Some but not all of the residual covariances among the firstorder factors can be identified."? Which of the residuals can not be identified? and why? Thanks again, Ina 


They cannot all be identified. A certain number can be not particular residual covariances. You would need to try adding them and see if they are identified. 

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