Monitoring pupil development by means of the Kalman filter and smoother based upon SEM state space modeling

Abstract

If test scores are collected from an individual pupil at different points in time and a state-space model is available for describing latent ability development over time, the Kalman filter and smoother turn out to be the optimal procedures for estimating the pupil's latent curves. The Kalman filter is implemented in the Nijmegen Pupil Monitoring System, LISKAL. The essentials of Kalman filtering and smoothing in comparison to traditional cross-sectional factor score estimators are explained, stressing unbiasedness considerations and the initialization problem. The state-space model is represented as an SEM (structural equation model) and estimated by means of an SEM program. The value of the Kalman filter and smoother in pupil monitoring is enhanced by specifying a “structured means” instead of the traditional “zero means” SEM model and by introducing random subject effects.