What examples of theoretical justifications do error correlations might imply on in SEM?
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Answer:
As a general principal, I think that allowing errors to be correlated can be justified if, at face value, that can be seen as taking care of method variance. That could occur if two or more items have response options that are the same or very similar, but different to other variables defining the same latent variable. That would include situations where the same Likert scales are used, but some items are positively worded, and others are negatively worded. Reverse coding the negatively worded items does not removed the tendency for the group of positively worded items, and the group of negatively worded ones, to be more highly inter-correlated. Also, if groups of items are administered at different occasions, those administered at the same occasion would tend to be more highly inter-correlated. Allowing residuals to be correlated is one way that such spurious effects can handled.
As a general principal, I think that allowing errors to be correlated can be justified if, at face value, that can be seen as taking care of method variance. That could occur if two or more items have response options that are the same or very similar, but different to other variables defining the same latent variable. That would include situations where the same Likert scales are used, but some items are positively worded, and others are negatively worded. Reverse coding the negatively worded items does not removed the tendency for the group of positively worded items, and the group of negatively worded ones, to be more highly inter-correlated. Also, if groups of items are administered at different occasions, those administered at the same occasion would tend to be more highly inter-correlated. Allowing residuals to be correlated is one way that such spurious effects can handled.