I am brand new to using MPlus and I just started the 1st online short course today(Thanks for that!). In the course, Bengt says, (not exact) "we see a lot of literature in which people build models with 2 indicator latent variables- we strongly discourage this because the factor must borrow [too much?] infomation from the rest of the model." I have a model in which three latent factors are made up of two continuous indicators each. They are all predicted by one continuous indicator and two of the factors predict the third (I am testing mediation of two of the factors). Model fits great. Questions: 1. Is this okay or am I making a big mistake by building these types of latents? 2. What did Bengt mean by "borrow" information? Much Thanks! Tasha Mendoza
1. It depends on how you have arrived at your 2 indicators per factor. If they are selected from a larger set of indicators by factor analysis and found to be good indicators for which the factor model holds, then fine. If not, there are risks of model mis-specification (see 2.)
2. A model with 2 indicators for a factor is not identified by itself. It becomes identified by having other indicators of other factors in the model - this is what "borrowing information" means. This implies that not only does this model part have to be correctly specified, but also the covariances with indicators in other parts of the model have to be correctly specified, or else the parameters of this part will be distorted. Also, if the 2 indicators of a factor have correlated residuals, you are not able to detect that in the model for that part alone, nor are you typically able to identify that residual correlation. A model can fit well and still have these possible distortions that you don't easly see with only 2 indicators.
Whew! Based on your explanation I think I am okay (I was just about to submit the abstract). Thank you for this and again, the MPlus courses are a gift! I am very grateful that you and your company offer them. I feel like I have discovered a hidden treasure. -Tasha