INVESTIGATING LOCAL DEPENDENCE WITH CONDITIONAL COVARIANCE FUNCTIONS

The local dependence of item pairs is investigated via a conditional c ovariance function estimation procedure. The conditioning variable use d in the procedure is obtained by a monotonic transformation of total score on the remaining items. Intuitively, the conditioning variable c orresponds to the unidimensional latent ability that is best measured by the test. The conditional covariance functions are estimated using kernel smoothing, and a standardization to adjust for the confounding effect of item difficulty is introduced. The particular standardizatio n chosen is an adaptation of Yule's coefficient of colligation. Severa l models of local dependence are discussed to explain special situatio ns, such as speededness and latent space multidimensionality, in which the assumptions of unidimensionality and local independence are viola ted.