Explanatory Secondary Dimension Modeling of Latent Differential Item Functioning

Abstract

The models used in this article are secondary dimension mixture models with the potential to explain differential item functioning (DIF) between latent classes, called latent DIF. The focus is on models with a secondary dimension that is at the same time specific to the DIF latent class and linked to an item property. A description of the models is provided along with a means of estimating model parameters using easily available software and a description of how the models behave in two applications. One application concerns a test that is sensitive to speededness and the other is based on an arithmetic operations test where the division items show latent DIF.Keywords differential item functioning, dimensionality, item response model, latent class model For manifest groups, differential item functioning (DIF) means that, conditioning on the person trait (e.g., ability), one or more items function differently in a focal group in comparison with a reference group (Scheuneman, 1979). In other words, equal levels of the person trait lead to different response probabilities depending on the group one belongs to. The difference relates most commonly to the item location and more rarely to the slope or gradient of the item, which, in an item response context, are commonly called the difficulty and degree of discrimination of an item, respectively. Reviews and discussions of the topic can be found in Millsap and Everson (1993) and Holland and Wainer (1993) and more recently in Teresi and Fleishman (2007).It is common to view DIF as the consequence of one or more dimensions not accounted for and, consequently, as the failure to account for secondary dimensions, also called ''nuisance dimensions'' that can result in

Performance decline in low-stakes educational assessments: different mixture modeling approaches

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“…Therefore, in the decline class, items appear to be more difficult than in the no-decline class, resulting in lower item intercept parameter estimates after the switching point. In their original formulation of the 2PDM, Bolt et al (2002) suggested specifying the switching point i 0 in advance (see also De Boeck et al 2011;Wollack et al 2003), so that it refers to an item position up to which responses are expected to not be affected by PD. When put into the multigroup context, this specification implies that, in each group, the switching point is a dichotomous variable that can take two values, that is, δ p = i 0 for all test takers showing PD, and δ p = I for all test takers not showing PD.…”

Mixture Random-Effect IRT Models for Controlling Extreme Response Style on Rating Scales

“…Thus, this study can be compared to other studies. In addition, such a constraint implies that metric invariance is satisfied but scalar invariance is not (De Boeck et al, 2011). When appropriate, the assumption of equal discrimination parameters across latent classes can be easily relaxed and metric invariance can be evaluated.…”

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“…Augmenting this perspective, several IRT calibration approaches have been proposed in an attempt to improve the estimation of parameters for items at the end of tests in the presence of test speededness (e.g., Bolt, Cohen, & Wollack, 2002; Bolt, Mroch, and Kim, 2003; De Boeck, Cho, & Wilson, 2011; Mroch, Bolt, & Wollack, 2005; Wollack, Cohen, & Wells, 2003; Yamamoto & Everson, 1997). For example, Bolt et al (2002) proposed a two‐class mixture Rasch model and showed that the parameter estimates obtained for end‐of‐test items in the nonspeeded class were nearly identical to the estimates obtained when those same items were administered under nonspeeded conditions.…”