Item Response Theory

11Multiple Group Item Response Models

We may at once admit that any inference from the particular to the general must be attended with some degree of uncertainty, but this is not the same as to admit that such inference cannot be absolutely rigorous, for the nature and degree of the uncertainty may itself be capable of rigorous expression.

(Source: Sir Ronald Fisher)

11.1 Introduction

To this point, our primary focus has been on the analysis of data arising from a single population, with two notable exceptions. In Chapter 9, we discuss differential item functioning (DIF) where the item parameters are compared between a reference group and a focal group, and in Section 10.2.7 where we accommodate non‐normality of the underlying latent distribution by empirically estimating the prior distribution. This non‐normality could be produced by the mixing of different populations in the calibration sample. As we move beyond the single sample case, there are numerous different applications of item response theory (IRT) where the data are clustered within different manifest or latent subpopulations, or cases in which the sample may be stratified in terms of characteristics of the respondents. In these cases, there may be several different goals. In the case of DIF, we are interested in determining whether the item parameters may be different in the different populations. In the case of an empirical prior distribution, we are interested in obtaining unbiased estimates of item parameters ...