FIGURE 4–7 Item response model with two observation model facets—raters (ρ1and ρ2), and item type (τ1and τ2).

Similar to ways in which G-theory has extended CTT, elements of the observations, such as raters and item features, can be added to the basic item response framework (see Figure 4–7) in what might be called faceted IRMs. Examples of facets are (1) different raters, (2) different testing conditions, and (3) different ways to communicate the items. One foundational difference is that in IRMs the items are generally considered fixed, whereas in G-theory they are most often considered random. That is, in G-theory the items are considered random samples from the universe of all possible similarly generated items measuring the particular construct. In practice very few tests are constructed in a way that would allow the items to be truly considered a random sampling from an item population.

Latent Class Models

In the measurement approaches described thus far, the latent construct has been assumed to be a continuous variable. In contrast, some of the research on learning described in Chapter 3 suggests that achievement in certain domains of the curriculum might better be characterized in the form of discrete classes or types of understanding. That is, rather than assuming



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