This chapter offers an in-depth discussion of the three statistical assumptions of item response theory (IRT), namely unidimensionality, local independence, and correct model specification. Each of these assumptions is described more fully, with a focus on procedures for testing each assumption. For each assumption, a number of statistical tests is proposed and explored in the literature. In addition, three common methods for testing unidimensionality are discussed: analysis of the eigenvalues of the inter-item correlation matrix, Stout's test of essential unidimensionality, and indices based on the residuals from a unidimensional solution. Weaknesses of some common approaches and indices is noted, and newer alternative procedures are described. Unfortunately, some of these procedures are quite complex and not easily implemented.
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