State space techniques in structural equation modeling: Transformation of latent variables in and out of latent variable models

This book contains 3 chapters. The first chapter re-derives the equivalence between theregression estimator of factor scores and the Kalman filter, adding a proof of theequivalence of second-order moments. Chapter 2 is quite lengthy and derives the so-called Houdini transformation with which latent variables can be transformed out oflatent variable models, yielding equivalent models lacking these latent variables. Thetransformation is described in detail, involving technical elements from time seriesanalysis. Chapter 3 discusses the implications of ergodic theory for the relation betweenresults obtained in analyses of inter-individual variation with analogous results obtainedin analyses of intra-individual variation.

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