12.1 Introduction

• All CDMs (general and specific) require a Q-matrix to identify the specific subset of attributes measured by each item

• In most CDM applications, constructing a Q-matrix tends to be subjective in nature, and has raised serious validity concerns among researchers

• Misspecifications in the Q-matrix severely affect estimation of model parameters, and ultimately, the accuracy of the examinee attribute classifications

• However, many model fit analyses in cognitive diagnosis assume that a Q-matrix is correct after it has been constructed

• This is largely due to the fact that, at present, little well-established method is available to detect misspecifications in the Q-matrix

• Without verifying its appropriateness, any model misfit attributable to the Q-matrix cannot be addressed and remedied

• Thus, a model fit analysis that does not include verification of the correctness of the Q-matrix is partial and incomplete