title: Analyzing Longitudinal Item Response Data via the Pairwise Fitting Method.
abstract: Multidimensional item response theory (MIRT) models can be applied to longitudinal educational surveys where a group of individuals are administered different tests over time with some common items. However, computational problems typically arise as the dimension of the latent variables increases. This is especially true when the latent variable distribution cannot be integrated out analytically, as with MIRT models for binary data. In this article, based on the pseudolikelihood theory, we propose a pairwise modeling strategy to estimate item and population parameters in longitudinal studies. Our pairwise method effectively reduces the dimensionality of the problem and hence is applicable to longitudinal IRT data with high-dimensional latent variables, which are challenging for classical methods. And in the low-dimensional case, our simulation study shows that it performs comparably with the classical methods. We further illustrate the implementation of the pairwise method using a development study of mathematics levels of junior high school students in which the response data are collected from 65 classes of 8 schools from 4 different school districts in China.
authors.affiliation: a Department of Statistics and School of Mathematics and System Science , Shenyang Normal University.
authors.forename: Zhi-Hui
authors.initials: ZH
authors.lastname: Fu
authors.affiliation: b Key Laboratory of Applied Statistics of MOE and School of Mathematics and Statistics and School of Education Science Northeast Normal University.
authors.forename: Jian
authors.initials: J
authors.lastname: Tao
authors.affiliation: b Key Laboratory of Applied Statistics of MOE and School of Mathematics and Statistics and School of Education Science Northeast Normal University.
authors.forename: Ning-Zhong
authors.initials: NZ
authors.lastname: Shi
authors.affiliation: b Key Laboratory of Applied Statistics of MOE and School of Mathematics and Statistics and School of Education Science Northeast Normal University.
authors.forename: Ming
authors.initials: M
authors.lastname: Zhang
authors.affiliation: c Department of Mathematics , Washington University in Saint Louis.
authors.forename: Nan
authors.initials: N
authors.lastname: Lin