This dissertation is comprised of a set of four simulations investigating the model-building approach to assessing Q3 values. This method allows researchers to take a confirmatory approach to detecting violations of local item independence in item response theory (IRT) models. The first simulation deals with the 3 parameters logistic model and local item dependence of pairs. The second simulation identifies the usefulness of the approach for assessing item clusters. The third and fourth extends the previous work to polytomous data for pairs and for polytomous item clusters, respectively. The aim is to determine under what circumstances the model-building approach correctly identifies local item dependence.