Could you please tell me why a second-order factor model cannot be identified when there are only two constructs for one second-order factor. I know there are estimation methods that are able to fit the model, but is it appropriate to employ these in such a situation? I should also note Iím working with ordinal indicators? Also, could you just correlate the two first-order constructs?
For a factor with two indicators, the parameters that need to be estimated are one factor loading, two residual variances, and one factor variance. With two continuous items, you have two sample variances and one sample covariance. So you have more parameters to estimate that you have information from the data. Thus the model is not identified. You can apply this same reasoning to a second-order factor with two first-order factors.
Even if you can find a method that will give you estimates for all parameters in the model, this is not proper.
You can estimate a covariance or correlation for the two first-order factors.