Latent Variable - Items with different scales

Question

I want to measure the latent variable risk tolerance. Therefore, I use a total of 6 items. Afterward, I would like to use the latent variable in a linear regression model, however, I don't know how to summarize the 6 items to come up with the variable that I can use in the regression model.

The problem is that the 6 items have different scales. More precisely:

• First item has a scale from 1 to 5
• Second item has a scale from 1 to 7
• Third item has a scale from 1 to 6
• Fourth item has a scale from 1 to 3
• Fifth item has a scale from 1 to 2
• Sixth item has a scale from 1 to 2

Can I just sum up all the scores and take the sum as the input variable for my regression model? Or can I use factor analysis for that purpose? Or what are the best practices to solve that problem?

EDIT: The item responses are ordinal

Many thanks in advance :)

Answer 1

Yes, taking the sum could be one approach. However, if your sample is sufficiently large, you have many options. If you search for structural equation modeling (SEM) with categorical variables, you should find the best practices you are looking for (e.g., check this tutorial; also see Cai, 2013; and Edwards, Wirth, & Houts, 2012).

References

Cai, L. (2013). Factor analysis of tests and items.

Edwards, M. C., Wirth, R. J., Houts, C. R., & Xi, N. (2012). Categorical data in the structural equation modeling framework.