Longitudinal factor score estimation using the Kalman filter

The advantages of the Kalman filter as a factorscore estimator in the presence of longitudinal dataare described. Because the Kalman filter presupposesthe availability of a dynamic state spacemodel, the state space model is reviewed first, andit is shown to be translatable into the LISRELmodel. Several extensions of the LISREL modelspecification are discussed in order to enhance theapplicability of the Kalman filter for behavioralresearch data. The Kalman filter and its mainproperties are summarized. Relationships areshown between the Kalman filter and two well-knowncross-sectional factor score estimators: theregression estimator, and the Bartlett estimator.The indeterminacy problem of factor scores is alsodiscussed in the context of Kalman filtering, andthe differences are described between Kalmanfiltering on the basis of a zero-means and astructured-means LISREL model. By using astructured-means LISREL model, the Kalman filteris capable of estimating absolute latent developmentalcurves. An educational research example ispresented. Index terms: factor score estimation,indeterminacy of factor scores, Kalman filter, L,ISRELlongitudinal LISREL modeling, longitudinal factor analysis,state space modeling.