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.
Tom Booth posted on Thursday, September 27, 2012 - 4:32 am
Thanks Linda, will do. I am in the process of upgrading to version 7 and getting a new help license so will have to send once this is sorted.
jiesi G posted on Wednesday, December 18, 2013 - 3:36 am
Hello, I am running a 4-factor CFA using continuous and only one binary indicator. Three of the latent factors have continuous indicators, while the binary indicator was correlated with these 3 factors. The CFA model is set up as follows; usevariable = x1-x9 u1 ; categorical = u1 ; ANALYSIS: estimator=WLSMV; model: f1 by x1* x2 x3; f1@1 ; f2 by x4* x5 x6 ; f2@1 ; f3 by x7* x8 x9; f3@1 ; u1 with f1 f2 f3;
in the following up SEM analysis, f1 and f2 -> f3 -> u1, I want to treat the binary indicator as the outcome variable, and use MLR and link=logit to test indirect effect from f1 to u1.
my question is whether I can report the correlation matrix in my paper based on this set-up CFA input.
I don't know why you want to report a correlation matrix when your analysis estimates parameters of a path model. The model is sufficient. If you ask for TECH4, Mplus will give you correlations among your 3 factors. I don't think you want a correlation with the binary outcome.