Hello, everyone. My goal is to create a factor (latent variable) from four questions in a questionnaire, each of a different type. Two are rated on a scale of 0-10 and so can be thought of as interval, one is on a scale of 1-5 and so is ordinal but could be thought of as interval (according to the literature) and the last is on a scale of 0-3 and so has only four categories and is ordinal.
I am wondering how should I go about the correct methodology if I want to create a factor from these variables? Respectively, what estimation and calculation methods should I apply, e.g. in EFA, CFA, IRT. Alternatively, should I convert all the variables to the same scale through transformation?
Thank you all very much for your answers, advice and tips.
Transforming or rescaling categorical/ordinal variables would not make them interval level, and I would definitely not recommend discretizing continuous (interval level) variables because you would loose information.
The best approach is probably to use an EFA/CFA/SEM/IRT software program that can handle a mix of categorical (binary or ordinal) and continuous variables such as Mplus. In Mplus, the default estimator for factor models (EFA & CFA) with such mixed indicator types is WLSMV based on a probit link function. WLSMV appears to work well across a range of conditions. Mplus also allows you to run IRT models for ordinal variables using a logistic link function and maximum likelihood (ML) estimation.
Thank you Christian Geiser .
I completely agree with you that it would be ideal not to modify (tranform/recode) the variables in any way. However, I have also found studies where it is a common formula to convert everything to the same scale, e.g. with five categories. I use Mplus, however IRT analysis is not good in it. Anyway, applying IRT to discrete variables is not appropriate either, so variables with fewer categories would be more appropriate.
I don't think that it is necessary or useful to convert everything to the same scale (i.e., the same number of categories). This would mean that you would loose information for variables that have more categories than others.
Also, I don't understand what you mean by "Anyway, applying IRT to discrete variables is not appropriate either, so variables with fewer categories would be more appropriate." Most IRT models are designed for discrete data (i.e., binary or ordinal variables), for example, the polytomous Rasch model (e.g., https://en.wikipedia.org/wiki/Polytomous_Rasch_model).
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