Identified Parameters, Parameters of Interest and Their Relationships

摘要

The goal of this commentary is to provide some additional results to the interesting and provocative paper of Maris and Bechger (this issue). More specifically, we have three aims. First, we want to distinguish between three fundamental concepts that are important in studying identification in statistical models: the statistical model, the identified parametrization, and the parameters of interest. Second, we want to take the analysis of Maris and Bechger (this issue) one step further by showing what restrictions are needed to identify the 3PL with discriminations equal to 1 (which, following San Martin, Del Pino, and De Boeck, 2006, we term 1PL-G) in a meaningful way. Third, we want to point to an implicit problem in the analysis of Maris and Bechger (this issue), but one that has much broader consequences than appear at first sight.