"stacking" Cronbach alpha's on combined variables

[Sem vanWesten]

This is less of a technical question and more statistics in general. I tried to find information about this on the internet but I believe that I don't have the wording right in order to find what I'm looking for.
I received a dataset from a researcher and he works with main dimensions and sub dimensions. It looks as follows:

He calculated Cronbach alpha's for the sub-dimensions and, since they were above his cutoff value of 0.67, both sub-dimensions received a single variable by combining the question scores through the use of

egen sub_dimension1 = rowmean(Question1 Question2)

He then used these two sub dimension variables to calculate a new Cronbach alpha for the main dimension. In other words, he calculated a Cronbach alpha over two variables that were already combined variables.

My question is, did he do the right thing? In my eyes, by "stacking" these alpha's, the internal consistency is reduced further then reflected in the second Alpha and you are therefore not allowed to do it. However, this data comes from an official research agency and I would assume that they are doing it right.

[wbuchanan]

How were the "sub-dimensions" created? Are they sum scores of the item responses, scaled from some procedure, etc...? There isn't a sufficient number of items to determine whether there are higher order constructs without imposing some fairly reaching assumptions on the data (more so than I would feel comfortable with at least). It may have been the best solution given the context, but without knowing anything more about the data it would be fairly difficult for anyone to comment about the correctness of the approach.

[Sem vanWesten]

Thank you for your reply, I am sorry for my late response. The sub dimensions were created according to the code I have written in my post. They are means from the two questions. Nothing more and nothing less. I myself also believe that you need more then two variables to accurately measure a latent theory, but this is the data that I have and they used two questions per latent concept so i'll have to take that as given. My question relates more to the correctness of stacking Cronbach Alpha in general. Can you measure (and accept) a cronbach alpha that is measured over variables that are already combined variables on itself?