Do we need to rescale items that have different categories for a latent variable in SEM? For instance, I have three items measured on a 1-5 scale, one measured on 1-4 scale, and one measured on a 1-6 scale. I have put them all together to create a latent variable and running an SEM analysis. I had the impression that categories of items do not matter to form a latent variable in SEM. But, a reviewer has asked to justify the method with citation of relevant reference, and I am needing a reference for this approach.
Ramesh Paudyal, The indicators of a latent variable do not have to be measured using the same scale. If you need an example illustrating this, see page 94 in James B. Grace's book titled "Structural Equation Modelling and Natural Systems". Here, Grace models Body Size as a latent variable using body mass, wing length, and beak length as indicators.
I don't think the scale needs to be the same. That said, since the reviewer is primarily concerned about reliability, I suggest doing two things. First, calculate the Cronbach alpha of all measured variables to ensure that measurement variables are closely related as a group. Second, calculate the composite reliability of the loadings ex-post SEM.
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