This paper reviews a variety of definitions of local (conditional) independence presented in the testing literature. An attempt is made to clarify and differen tiate among conflicting conceptualizations of this fundamental measurement principle. In particular, it is argued that local independence, unidimension ality, and noninvasiveness are important but distinct concepts that may, but need not necessarily, overlap. Methods of testing for the presence of local independence in several of its conceptualizations are also presented.
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