I'm making a scale adaptation. In the CFA there is a high correlation between error terms of 2 measured variables under the same latent variable. And I presume this is because this 2 item also explains another latent variable which isn't in the scope of scale or the research (based on the answers I get in the pilot study where I also asked participants what they understand from each item) And because I couldn't quite understand what creating covariances does beside raising model fit I can't decide whether I should eliminate the item with lower estimate or create covariances between two. (All of the items has higher std. estimates than 0.7 by the way)
I would be very happy if you guide me about this situation what would be better to do and why.
Thank you in advance
Elimination of one of the items may be a solution but you might also consider adding a residual method (or specific) factor for the two items in question that reflects what they have in common above and beyond the larger common factor. You would set both of the unstandardized loadings on the specific factor to 1 for identification and the covariance between the specific factor and the larger common factor to 0. That way, you can examine the proportion of variance in the items that is accounted for by each factor (common vs. specific vs. error).
Hi Christian Geiser
that is an intriguing approach. I dealt with possible "hidden" latent factors myself as indicated by correlated error variances. If I did proceed as you suggest, constraining the factors loadings onto the specific factor to 1 and setting the covariance between the specific and the common factor to 0, what would be left to estimate that would tell me the proportion of the variance accounted for by the specific and the common factor, respectively?
Thanks, as always
Marcel
Marcel Grieger The squared standardized factor loadings (e.g., STDYX in Mplus) give the proportion of observed score variance that is accounted for by the factors, respectively. For a given variable, the squared standardized loadings add up to the overall R^2 (reliability) estimate.
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