Diagnosis and the residuals
An item’s global statistics (those with just the i subscript) are useful for flagging items, but any diagnosis or understanding means looking at finer detail, i.e., things that require two or more subscripts. Beginning with the items with the most disturbing values, examine them from every angle and keep reviewing, revising, and rejecting until you are chasing noise, the item pool is depleted, or the client runs out of money.
The choice of a favorite strategy may be based on unpleasant experiences from your youth or it may be based on deeply held philosophical principles. My deeply held philosophical principles are:
- Some notion of what might go wrong is more important than how you do the arithmetic.
- Contemplation of raw observations with an empty mind, even when it is possible, is often hardly more beneficial than not studying them at all. (Martin Wilk)
- If your data have something to tell you, your statistics won’t stop them. (G. Box)
- No single fit statistic is either necessary or sufficient. (David Andrich).
Continue . . . Control after Infit, Outfit