chapter  8
Applications of Measurement Models
Pages 24

A design can be represented in the form of a persons-by-items matrix. As an example, consider the design represented in Figure 8.1. This figure is a graphical representation of a design matrix with as entries the item administration variables dik (I = 1,…,N and k = 1,…,K) defined by Formula (3) in the previous chapter. The item administration variable dik was equal to 1 if person i responded to item k, and 0 otherwise. At this moment, it is not yet specified what caused the missing data. There may be no response because the item was not presented, or because the item was skipped, or because the item was not reached. In the sequel it will be discussed under which circumstances the design will interfere with the inferences. For the time being assume that the design was fixed by the test administrator and that the design does not depend on an a-priori estimate of the ability level of the respondents.