Kline (2011) p249 writes:
To identify a hierarchical CFA model, there must be at least three first-order factors. Otherwise, the direct effects of the second-order factor on the first-order factors or the disturbance variances may be underidentified. Each first-order factor should have at least two indicators.
Kline presents this as a hard and fast rule. Are there any exceptions to this rule that could apply in a practical scenario (even if those exceptions are a bit farfetched)?
Why are 3+ first-order factors required? If we forget about hierarchical factor analysis for a moment, I know that in a regular factor analysis having two indicators per factor and two factors is a technical minimum. That is, with two indicators per factor and two factors we might have with empirical underidentification or nonconvergence of iterative estimation, but usually it more or less works. I figured that since the second-order factor has no indicators, the first-order factors were in a way acting like indicators for the second-order factor. So maybe a model with one second-order factor and two first-order factors was kinda like a factor analysis model with two indicators and only one factor, which doesn't work. Is that an appropriate analogy for why it doesn't work?
What should I do in a situation in which I 'want' to test a hierarchical factor model with a single second-order factor only two first-order factors? Are such models inherently untestable, or is there some way around this?
Kline, R. B. (2011). Principles and practice of structural equation modeling. Guilford publications.