AMOS Configural Invariance / three indicator single factor model

[J911]

I'm running a multigroup CFA (groups indicate time points) to assess metric invariance. My baseline model has three indicators loading on one single factor. The first step in ME/I testing is to establish configural invariance by constraining one of the factorloadings to one for each group. However with only three indicators I do not have any df's left so no model fit. Several articles suggest to set the intercept value of this particular indicator to 0 (for each group) for identification purposes. My model still won't fit this way.
However if I set the the error variance of the indicator to 0 (or 1) my model fits perfectly (non sig chi square, and perfect RMSEA, CFI values). Is this a legitimate way to establish configural invariance?
I would be very happy if anyone can shed some light on this!

[CowboyBear]

I think this would depend on whether you have a legitimate substantial reason for why you think the error variance of that item is actually at the given value. Zero error variance sounds especially worrisome - in this case you are saying that the item is a perfect errorless indicator for the latent! (in which case, why would we need any other indicators?)

My personal feeling is that CFA isn't very meaningful with a single latent and three indicators - even with fiddling around fixing error variances and so on to get an overidentified model, the degrees of freedom will be so low that the model will inevitably fit "well". In such a situation you are reproducing the terms in the original covariance matrix with a model that is only very slightly less complex than the original covariance matrix, so it's easy for the model to "predict" the covariance matrix with small residuals. Also note that statistical power for fit statistics reduces dramatically when model df is lower.

EDIT: Just to expand on this a little:

However with only three indicators I do not have any df's left so no model fit.

In this case the reason you don't get fit statistics is not that the model doesn't fit well, but rather that the model is just as complex as the covariance matrix it is intended to explain, and as such fit is perfect (but meaningless, and therefore not reported).

[J911]

Thank you very much for your reply and the link you provided. It motivated me to jump to a LMACS model (multiple occasions with single factors in one model) to solve the df problem.

Ps. My idea to constrain the error variance was precisely for the reason stated by you. Having a perfect indicator should allow me to evaluate the less perfect indicators in this particular context although i do not know whether this endeavor is statistically sound.