The minimum number of indicators for a single factor measurement model in CFA is 3. This follows from k(k+1)/2 where 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?


The three factor model will have perfect fit. And therefore you haven't confirmed anything in your confirmatory factor analysis (CFA). You've just transformed the covariance (or correlation) matrix.

The nice thing about confirmatory factor analysis is that it tells you if you are wrong. If it doesn't tell you that you're wrong, you're more likely to be right (it doesn't mean you're right). If you don't want to be told that you're wrong, do CFA with three variables, or don't do CFA.

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  • $\begingroup$ By three factor model, I take it you mean 3 item model. I understand the model has a perfect fit. If I understand you correctly, you imply that a 3-item model with 1 factor isn't very meaningful? $\endgroup$ – Amonet Mar 5 '18 at 11:17
  • $\begingroup$ Sorry, perhaps a bit confusing on my part: when I say 'item' I mean manifest variable. I use the 2 interchangeably. $\endgroup$ – Amonet Mar 5 '18 at 11:18
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    $\begingroup$ (I also use them interchangeable). Yes, a 3 item model doesn't tell you anything about the underlying construct, which is what you're interested in. It just tells you if the three variables are related, and you can find that out by looking at the correlation matrix. $\endgroup$ – Jeremy Miles Mar 5 '18 at 17:10

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