The minimum number of indicators for a single factor measurement model in CFA is 3. This follows from
k = # indicators. In such a model we'd need to estimate 6 parameters, hence the model is
just-identified with 0 DF left.
I was wondering the following: what is the practical use of this model? I am currently running a CFA and my 4-item model (over-identified) shows good overall fit indices and quite good local fit (i.e. low residual correlations and low modification indices). There is however 1 item that has a standardized factor loading of 0.5, which is much lower than the others: 0.69, 0.72, 0.93. Hence I was curious whether the 3-item model would still provide a good fit.
The problem however is that I cannot use the overall goodness of fit indices (such as
rsmea, tli, cfi, ...). Therefore my question: what is the practical (or theoretical) use of a 3-item model if I cannot be sure of the overall goodness of fit?