The advantages of the Kalman filter as a factor
score estimator in the presence of longitudinal data
are described. Because the Kalman filter presupposes
the availability of a dynamic state space
model, the state space model is reviewed first, and
it is shown to be translatable into the LISREL
model. Several extensions of the LISREL model
specification are discussed in order to enhance the
applicability of the Kalman filter for behavioral
research data. The Kalman filter and its main
properties are summarized. Relationships are
shown between the Kalman filter and two well-known
cross-sectional factor score estimators: the
regression estimator, and the Bartlett estimator.
The indeterminacy problem of factor scores is also
discussed in the context of Kalman filtering, and
the differences are described between Kalman
filtering on the basis of a zero-means and a
structured-means LISREL model. By using a
structured-means LISREL model, the Kalman filter
is capable of estimating absolute latent developmental
curves. An educational research example is
presented. Index terms: factor score estimation,
indeterminacy of factor scores, Kalman filter, L,ISREL
longitudinal LISREL modeling, longitudinal factor analysis,
state space modeling.
Oud, Johan H.; Van den Bercken, John H.; Essers, Raymond J..
Longitudinal factor score estimation using the Kalman filter.
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