Modeling local dependence in longitudinal IRT models

Abstract

Measuring change in a latent variable over time is often done using the same instrument at several time points. This can lead to dependence between responses across time points for the same person yielding within person correlations that are stronger than what can be attributed to the latent variable. Ignoring this can lead to biased estimates of changes in the latent variable. In this paper we propose a method for modeling local dependence in the longitudinal 2PL model. It is based on the concept of item splitting, and makes it possible to correctly estimate change in the latent variable.

%lrasch_mml: ASASMacro for Marginal Maximum Likelihood Estimation in Longitudinal Polytomous Rasch Models

“…The macro can be used to test the assumption of item parameter invariance using likelihood ratio tests, thus adding to existing methods for detection of item parameter drift (Donoghue and Isham 1998;DeMars 2004;Galdin and Laurencelle 2010). The macro also makes it possible to study local dependence across time points, by splitting of the item at follow-up into new items according to the responses given at baseline (Olsbjerg and Christensen 2014). The macro %lrasch_mml makes it possible to include splitted items and to test the assumption of local independence across time points using likelihood ratio tests, thus adding to existing tests of this assumption (Olsbjerg and Christensen 2013).…”

“…Their method is based on splitting an item into two new ones according to the responses to another item. This method has been generalized to polytomous items and to other IRT models and can be used to overcome local response dependence across time points (Olsbjerg and Christensen 2014). The macro %lrasch_mml makes it possible to include splitted items and to test the assumption of local independence across time points using likelihood ratio tests.…”

“…In our implementation of the longitudinal Rasch model the latter of these approaches is used. A detailed account of how splitting an item at the second time point based on observed responses at the first time point is provided by Olsbjerg and Christensen (2014). Briefly, a model where local dependence across time points is modeled for an item i ∈ I can be formulated by defining m i + 1 time 2 items…”

SAS macros for longitudinal IRT models

“…The SAS macros also make it possible to study local dependence across time points, by splitting of the item at follow-up into new items according to the responses given at baseline (Olsbjerg & Christensen, 2013b). The macro %lrasch mml makes it possible include splitted items and to test the assumption local independence across time points using likelihood ratio tests, thus adding to existing tests of this assumption (Olsbjerg & Christensen, 2013a).…”

Use of the Ages and Stages Questionnaires to Establish Indicators of Child Development in Public Daycare Centers in Rio De Janeiro, Brazil

“…In MIRT, an Item Characteristic Surface (ICS) represents the probability that an examinee with a given ability ( ) composite will correctly answer an item. To deal with local independence, Item Splitting is a way for the estimation of item and person parameters (Olsbjerg & Christensen, 2015). In the same direction, the comparison between unidimensional and multidimensional models have shown that as the number of latent traits underlying item performance increase, item and ability parameters estimated under MIRT have less error scores and reach more precise measurement (Kose & Demirtasli, 2012).…”