My question is connected to rather unclear point of error correlation that many scholars encounter while conducting their SEM (structural equation modeling) analysis. It is a pretty often when scholars report procedures of correlating the error terms to enhance the overall goodness of fit for their models. Hermida (2015), for instance, provided an in-depth analysis for such issue and pointed out that there are many cases within social sciences studies when researchers do not provide appropriate justification for the error correlation. I have read in Harrington (2008) that the measurement errors can be the result of similar meaning or close to the meanings of words and phrases in the statements that participants are asked to assess. Another option to justify such correlation was connected to longitudinal studies and a priori justification for the error terms which might be based on the nature of study variables.
In my personal case, I have two items with Modification indices above 20.
lhs op rhs mi epc sepc.lv sepc.all sepc.nox
12 item1 ~~ item2 25.788 0.471 0.471 0.476 0.476
After correlating the errors, the model fit appears just great (Model consists of 5 latent factors of the first order and 2 latent factors of the first order; n=168; number of items: around 23). However, I am concerned with how to justify the error terms correlations. In my case the wording of two items appear very similar: With other students in English language class I feel supported (item 1) and With other students in English language class I feel supported (item 2)(Likert scale from 1 to 7). According to Harrington (2008) it's enough to justify the correlation between errors.
However, I would appreciate any comments on whether justification of similar wording of questions seems enough for proving error correlations.
Any further real-life examples of wording the items/questions or articles on the same topic are also well-appreciated.
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.
Dear Professor John D Crawford , many thanks for your reply. To be honest, I haven't expected any responses since I published this question several months ago.
Indeed, in my case, I have the wording of two items which might appear similar due to the core of both statements. That was my main concern regarding whether this point might be considered as a sound justification for correlating the error terms.
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