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

If test scores are collected from an individual pupil at different points i n time and a state-space model is available for describing latent ability d evelopment over time, the Kalman filter and smoother turn out to be the opt imal procedures for estimating the pupil's latent curves. The Kalman filter is implemented in the Nijmegen Pupil Monitoring System, LISKAL. The essent ials of Kalman filtering and smoothing in comparison to traditional cross-s ectional factor score estimators are explained, stressing unbiasedness cons iderations and the initialization problem. The state-space model is represe nted 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 i s enhanced by specifying a "structured means" instead of the traditional "z ero means" SEM model and by introducing random subject effects.