Conferences

Item response models play an important role when studying position (aka order, sequence) effects, i.e. the fact that an item’s difficulty is altered depending on its position within an instrument. The LLTM plays an outstanding role for that purpose as it allows for the differentiation between “true” item difficulty and an additional “position parameter”. This model usually incorporates CML as the standard estimation method. Rijmen et al. (2003) have shown that the LLTM can be reformulated in terms of a mixed logistic regression model. The current contribution elaborates on the benefits and limitations of this methodological approach: Along with a gentle introduction of the essential idea, several feasible parametrizations and possible extensions (eg. introducing a discrimination parameter sensu 2PL, cross-level-interactions, and quantitative as well as categorical predictors) compared to the “classical” LLTM are discussed. By means of a simulation study parameter recovery are explicated, different kinds of ordering effects are considered and the question of necessary sample sizes is being discussed.

References

Rijmen, F., Tuerlinckx, F., De Boeck, P., & Kuppens, P. (2003). A Nonlinear Mixed Model Framework for Item Response Theory. Psychological Methods, 8, 185–205.