An Examination of Initial Condition Specification in the Structural Equations Modeling Framework Public Deposited

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  • March 21, 2019
  • Losardo, Diane
    • Affiliation: College of Arts and Sciences, Department of Psychology and Neuroscience
  • A challenge when estimating time series models is deciding how to correctly specify an initial condition distribution, which describes the process prior to the first sampled observation. For example, the process may have started in the distant past, started exactly at the first observation point, or displayed a different structure before the first time point was collected. Time series models may be estimated within the structural equations modeling (SEM) framework (Browne & Nesselroade, 2005), and while some psychological research has focused on the issue of initial condition specification (e.g., Du Toit & Browne, 2007; Chow, Ho., Hamaker, & Dolan, 2010; Oud, Bercken, & Essers, 1990), a thorough examination of the consequences of using a misspecified initial condition distribution has not been conducted. As the number of time points increases, the consequences of a misspecified initial condition become less severe (i.e., parameter estimates and state estimates are not affected as noticeably, see Oud et al., 1990). If a process is not stationary (i.e., does not have the same mean and covariance structure over time), then conventional methods for initial condition specification may not be appropriate (De Jong, 1991; Harvey, 1991). Proper methods for such cases have been developed in the state-space literature (De Jong, 1991; Koopman, 1997). In this thesis I conducted a systematic examination comparing initial condition specifications for time series models estimated within the SEM framework. For stationary models, I considered three approaches, including (1) a model-implied initial condition, (2) a free-parameter condition, (3) and a null initial condition specification. For nonstationary models, I considered De Jong's augmented filtering approach (De Jong, 1991), which consists of augmenting the standard Kalman filter (KF) with computational products associated with nonstationary portions of the model, a modification by Koopman (1997), who developed an exact initial KF approach which removes the reliance of the filtering equations on the nonstationary portions, and a large κ approximation which is widely used in the time series literature but may lead to numerical inaccuracies. A Monte Carlo simulation was conducted to examine parameter and state estimate recovery given different types of initial condition specification for both intensive repeated measures data and panel data. Finally, each initial condition specification was estimated using an empirical data set. Results suggest that, when the process is nonstationary and true initial condition is diffuse, the de Jong initial condition approach leads to proper point and standard error estimates with fewer numerical difficulties when compared to the other approaches. However, the Koopman and free-parameter approaches also performed well, but exhibited more severe computational problems in the estimation process, leading to convergence problems and biased point estimates of the variance parameters. Furthermore, results illustrate how using different initial condition specifications with real data may lead to different point and standard error estimates and thus different substantive conclusions. Implications of results and recommendations for practice are highlighted in the discussion section.
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  • Chow, Sy-Miin
  • Doctor of Philosophy
Graduation year
  • 2012

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