SEM modeling with singular moment matrices : Part I: ML-Estimation of time series
A structural equation model (SEM) with deterministic intercepts is introduced. The gaussian likelihood function does not contain determi- nants of sample moment matrices and is thus well de ned for only one statistical unit. The SEM is applied to the dynamic state space model and compared with the Kalman lter (KF) approach. The likelihoods of both methods are shown to be equivalent, but for long time series numerical problems occur in the SEM approach, which are traced to the inversion of the latent state covariance matrix. Both approaches are compared on several aspects. The SEM approach is now open for idiographic analysis and estimation of panel data with correlated units.
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