Katja Soyez posted on Thursday, September 29, 2011 - 10:33 am
Dear Professor Muthen I would like to test the invariance of mymeasurement model which includes single and multi-item constructs. Since for single item constructs factor loadings are restrained to 1 and the error to 0, does it make sense to include these constructs in the invariance test? Thank you very much in advance!
A factor with one indicator that has a residual variance of zero is equivalent to the indicator. Testing measurement invariance is not relevant. It is basically an observed variable and using the observed variable in the analysis will yield the same results.
Katja Soyez posted on Tuesday, October 04, 2011 - 7:05 am
Thank you Linda! Please allow me one more question. What's your opinion on applying single-item constructs in a cross-national comparison? Thank you!
When the single-indicator factor is identical to the observed variable (residual variance equal to zero), I would use the observed variable in the analysis not the factor. Using the factor is misleading since uninformed people might not know that it is the same as the observed variable.