Kálmán's filtering technique in structural equation modeling

Abstract

Structural equation modeling finds linear relations between exogenous and endogenous latent and observable random vectors. In this paper, the model equations are considered as a linear dynamical system to which the celebrated R. E. Kálmán’s filtering technique is applicable. An artificial intelligence is developed, where the partial least squares algorithm of H. Wold and the block Cholesky decomposition of H. Kiiveri et al. are combined to estimate the parameter matrices from a training sample. Then the filtering technique introduced is capable to predict the latent variable case values along with the prediction error covariance matrices in the test sample. The recursion goes from case to case along the test sample, without having to reestimate the parameter matrices. The algorithm is illustrated on real life sociological data.