Can it be useful to run a factor analysis for only two items? I have a data set with two items that potentially measure the same latent variable: personal well-being. Can it be useful to run a factor analysis (Principal Axis Factoring Analysis) on them, or does a factor analysis require more items?

I have difficulty seeing how factor analysis of two items would tell you anything new, above and beyond the correlation (or covariance) between the two variables.
The factor model will perfectly reproduce the correlation (or covariance) between the items, because with two indicators you have to specify the loadings to be equal. Then you can identify the scale of the latent factor in one of two ways:

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*Fix the variance of the latent factor to 1. The loadings will equal the square root of the correlation between x1 and x2. So no need to perform factor analysis, you can just compute the correlation between x1 and x2 and you're done.


*Fix loadings to 1. The variance of the factor will now equal the squared correlation between x1 and x2. So no need to perform factor analysis, you can just compute the correlation between x1 and x2 and you're done.
A similar result applies when you choose to factor analyse the (co)variances, save for multiplication of the loadings or factor variance by the standard deviations of the item scores, and you will reproduce the covariance instead of the correlation between x1 and x2.
