An item response theory approach to longitudinal analysis with application to summer setback in preschool language/literacy

Gregory Camilli,Sunhee Kim

doi:10.1186/2196-0739-1-8

Abstract

An item response theory approach to longitudinal analysis with application to summer setback in preschool language/literacy

Highlights

As the popularity of classroom observations has increased, they have been implemented in many longitudinal studies with large probability samples
We demonstrate that statistical estimates describing longitudinal growth can be obtained using a classroom-based set of items tapping cognitive skills while at the same time analyzing the psychometric properties of this instrument
We include an analysis of growth in language and literacy achievement for preschool children in a large-scale data set obtained as a national probability sample

Summary

Introduction

As the popularity of classroom observations has increased, they have been implemented in many longitudinal studies with large probability samples. Given the complexity of longitudinal measurements, there is a need for tools to investigate both growth and the properties of the measurement scale. Measurement framework Most IRT models contain two types of parameters: those for items, and those for person abilities. In the language of IRT, the probability of correct response on an item depends on person’s ability and characteristics of an item such as difficulty. In the IRT framework, Rasch models (Rasch, 1960), known as one-parameter logistic (1PL) models, provide the probability of a correct answer of person i on item j (IRT models are adapted to polytomous assessment items as shown below). Let Pij represent the true probability of a correct answer on a test question, the parameters of interest are the person’s latent score θi and item difficulty bj such that

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