In the modeling of standardized testing data, it is often desirable to assume that the underlying ability being measured is unidimensional and that the responses to the test questions are conditionally (locally) independent given the examinee's ability. Many papers in the field deal with the case where the data is multidimensional, but where the researcher still conditions on a unidimensional composite ability. However, there is confusion that arises from not being clear about exactly which unidimensional ability is being conditioned on. This talk will show that when conditioning on a "reasonable" unidimensional ability that positive local item dependencies imply that there must also be negative local item dependencies. This result is discussed in relation to several foundational theoretical articles, to the simulation of multidimensional testing data, and to the use of testlet scoring for the removal of local item dependencies.