I have a CFA that has estimated one factor to have zero variance. (I fixed one loading to 1 for all factors & left variance free). I don't see how this could be possible, and would appreciate some input.

The overall model has 6 basic factors. The items from each of these factors also load on one of two subgeneral factors, and all items load onto a general factor. (This model is based on bifactor modelling, but is in fact a TRIfactor model). It is not shown in the figure below, but the basic(specific) factors are allowed to correlate:


So, even though the item that load onto the relevant factor each load onto two other factors (the relevant subgeneral factor and the general factor), I still don't know how it is possible that here could be actually ZERO variance for a factor.



The latent variable is doing no work - there is no variance left for it to explain. You can delete the latent variable and the model should be no worse.

In the diagram you show, I would not be surprised if any of the variables on the left hand side (confession, etc) had zero variance.


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