Extending Fit Indices from Structural Equation Models to State Space Models

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Abstract: 

Researchers are increasingly interested in modeling within-person processes over time using intensive longitudinal data. A longstanding method for analyzing such data, drawing from the econometrics, engineering, and time series analysis literature, is the discrete-time state space models (SSM). The SSM can be considered an extension of conventional structural equation models (SEM), enabling the recursive handling of large amounts of repeated measurements while allowing for both observed and latent variables. Accordingly, variations of the SSM have yielded fruitful applications in the social and behavioral sciences. However, traditional measures of model fit available for SEM do not exist for SSM. Thus, the present work aims to extend SEM fit indices to SSM. Through analytical work and a small simulation study, we evaluated the proposed method of obtaining fit indices for SSM by examining: (1) varying levels of model complexity, including both univariate and multivariate settings, and (2) different lags between observations. We conclude by discussing the implications for SSM fit assessment and model selection, as well as outlining future research directions.