For testing national culture theory for example, there are four dimensions with each a set of related items. From the sample we get, I would think it better to analyze each dimension for its own set of reliability, KMO, and bartlett's test, and not for the overall (all four dimensions together) since it clearly a multidimensional instrument and not unidimensional. Please advise?
Ideally, you should analyze each dimension. In addition, you could analyze the correlation between the four dimensions, and if all four dimensions correlated positively, then you could also measure those four dimensions as a single construct.
In fact, the report of KMO and Barlett's tests independently will be fine, if they adequately reach the point of cut-off point ( the required score). As I understand you are doing factor analysis, EFA -Exploratory Factor Analysis - item reduction. Hope partially helps.
Is there any references for KMO being done partially (by dimension) to be refered?
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