Item response theory posits "local independence," or conditional independence of item responses given item parameters and examinee proficiency parameters. The usual definition of local independence, however, addresses the context of fixed tests and initially appears to yield incorrect response-pattern probabilities in the context of adaptive testing. The paradox is resolved by introducing additional notation to deal with the item selection mechanism. The probability of a response vector can then be expressed as the product of two factors. One concerns item selection and does not depend on the examinee ability parameter. The other concerns item response given item selection and can be written as a product over items in a manner analogous to the expression for local independence in fixed tests.
