How do I calculate a latent variable using questions with different measurement scales and data types? I want to calculate risk perception using survey responses to questions about risk to health, employment and finances. There are 10 questions in total, 3 with responses on a 5 point Likert scale, 3 with Yes/No, 3 with Yes/Maybe/No and 1 with Yes/No/I don't know. How do I normalize and calculate the risk perception variable?
 A: This is something you should really know before you ask people the questions. There are two options when measuring latent constructs this way:

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*Either you use established questions that have been validated in prior studies. Then you also have to weigh them together in roughly the same way that was validated before.


*Or you have come up with a new set, and this is your pilot study you use to validate the questions in the first place. If this is the case, there are various tests for convergent and discriminant validity that would be a good starting point.
There's no definitive way to weigh items together -- it just has to be done in a way that preserves the validity of the instrument and is clinically useful. Sometimes that's a plain sum. Sometimes the responses are rescaled to the 0-1 range and then summed. Sometimes it's using custom weights to make more reliable responses contribute more, thus reducing the variance of the result.
It is very common to create items that are supposed to measure a latent construct but upon testing for convergent validity it is revealed that they don't measure the same thing at all!
A: You could use item response theory (IRT) to scale your latent variable. IRT can accommodate ordinal items with different numbers of response options easily.
