Latent factor scores following CFA

[Ferdi Botha]

Hi,
I have predicted factor scores for two latent variables following a CFA. The properties of each factor score are that they have a minimum value of around -2.5 and a maximum value of around 1.5. Does this sound correct? Are there any specific range of values that these factor scores are supposed to take, or does it not matter? Also, how can these factor scores be interpreted?

[Clyde Schechter]

There are no correct or incorrect ranges of values for the latent variables in a CFA. If you think about at the general CFA model:

sem (Factor -> indicator1 indicator2 indicator3 /*etc.*/)

you could, in principle, apply any arbitrary linear transformation to the latent Factor variable and you would get equivalent results, with some compensating linear transformations of the factor loadings and constant terms. In more technical language, the model is unidentified. To identify the model, Stata (and all other SEM programs I know of) impose the constraint that the loading on the first indicator is 1.0. As a result, the range of values of Factor will generally tend to be about the same as the range of values of indicator 1. But this is just an arbitrary way of identifying the model. One could, in principle (and in practice by specifying it in your command) constrain some other loading to some other value. So the point is that the values of the latent variable are an artifact of the particular identifying constraint used.

[wbuchanan]

If Ferdi Botha wanted additional information about what Clyde Schechter mentioned I'd suggest looking at Little, T. D., Slegers, D. W., & Card, N. A. (2006). A Non-arbitrary method of identifying and scaling latent variables in SEM and MACS models. Structural Equation Modeling, 13(1), pp. 59-72.

[Clyde Schechter]

wbuchanan That looks very interesting--I wasn't aware of this. Will definitely read this whole article later today.

[Ferdi Botha]

Thank you so much. The info has been immensely helpful