Tom Booth posted on Monday, September 24, 2012 - 6:57 am
Is it possible to create a single indicator latent variable based on a binary indicator?
I am trying to develop a measurement model where my primary interest is in a second-order construct. However, my indicator set is sub-optimal for estimating a second order construct as I only have two well measured latent factors(>3 indicators with reasonable loadings >0.40). In addition I have a single observed binary variable which could act as a third indicator.
I want to discuss and demonstrate/estimate the alternatives whilst acknowledging the problems. I am comfortable describing the issues in the 2 first order factor model (non-identification at the 2nd order without additional constraints), and can present a bi-factor model as an alternative way to get at the general construct (with its different assumptions about the nature of the construct).
But it is the estimation and discussion of a model with two first order latent factors and, potentially, a single indicator latent variable from a binary observed indicator with which I am struggling.