That’s Still a State Space Model

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State space models (SSMs) have seen heavier use in the last few decades within the social and behavioral sciences, due at least in part to the more ready availability of intensive longitudinal data. However, long methodological traditions in these sciences have used structural equation models (SEMs), and various special cases of them, to study both longitudinal processes and contemporaneous structures. This presentation unites SSM and SEM by showing that all continuous-variable SEMs are a special case of SSMs. Moreover, for SEMs that model change processes over time the SSM framework has both conceptual and computational advantages. We explore several example models in their SSM and SEM form to show their identical likelihood functions and parameter estimates while noticing the differences in their specification, interpretation, and computational time. With the firm footing that SEMs have provided and the link between SEMs and SSMs, methodological researchers can take the next step forward to extend their models in time.