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Abstract
Measuring academic growth, or change in aptitude, relies on longitudinal data collected across multiple measurements. The National Educational Longitudinal Study (NELS:88) is among the earliest, large-scale, educational surveys tracking students’ performance on cognitive batteries over 3 years. Notable features of the NELS:88 data set, and of almost all repeated measures educational assessments, are (a) the outcome variables are binary or at least categorical in nature; and (b) a set of different items is given at each measurement occasion with a few anchor items to fix the measurement scale. This study focuses on the challenges related to specifying and fitting a second-order longitudinal model for binary outcomes, within both the item response theory and structural equation modeling frameworks. The distinctions between and commonalities shared between these two frameworks are discussed. A real data analysis using the NELS:88 data set is presented for illustration purposes.
Notes
1 The reader should bear in mind that the following is merely an account of some of the more popular and better known longitudinal IRT models that appear in the empirical examples, and this list is by no means exhaustive.
2 The appendix can be found at http://www.psych.umn.edu/people/profile.php?UID=wang4066
3 Readers who are interested in the performance of two estimation methods can read our online supplementary material (http://www.psych.umn.edu/people/profile.php?UID=wang4066) for details regarding a small-scale simulation study and results.