I have only ever used similarly scaled items in my PLS models. Logically, I can see that would be possible to rescale items with more categories to smaller scales, but with some loss of information - say to convert items in a 5 point Likert having Strongly Disagree, Disagree, Neutral, Agree, Strongly Agree to a 3 point Likert scale of Disagree, Neutral, Agree. I am less convinced that one could go the other direction without adding information that isn't there, or that one could standardize dichotomous variables alongside likert scale variables - but I am not a mathematical statistician. Hence, my question is about mixing indicators in the model...
Suppose we want to create a latent reflective construct using 4 items from a recently administered survey, as follows:
Item 1 - Y or N answers
Item 2 - 3 point likert answers
Item 3 - 5 point likert answers
Item 4 - Continuous variable that can be binned into several categories
Is this advisable or is it ill advised? Please include your rationale.