Continuous Time State Space Modeling of Panel Data by Means of Sem

Oud, Johan H. L.; Jansen, Robert A.R.G.

doi:10.1007/bf02294374

Cited by 183 publications

(235 citation statements)

References 22 publications

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“…Continuous time models have already been implemented as structural equation models, using either non-linear algebraic constraints (Oud and Jansen 2000) or linear approximations of the matrix exponential (Oud 2002). Our formulation uses either the SEM RAM (reticular action model) specification as per McArdle and McDonald (1984), or the state space form recently added to OpenMx (Neale et al 2016;Hunter 2014).…”

Section: Continuous Time and Semmentioning

confidence: 99%

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Continuous Time Structural Equation Modeling with R Package ctsem

Driver¹,

Oud²,

Voelkle³

2017

J. Stat. Soft.

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204

253

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We introduce ctsem, an R package for continuous time structural equation modeling of panel (N > 1) and time series (N = 1) data, using full information maximum likelihood. Most dynamic models (e.g., cross-lagged panel models) in the social and behavioural sciences are discrete time models. An assumption of discrete time models is that time intervals between measurements are equal, and that all subjects were assessed at the same intervals. Violations of this assumption are often ignored due to the difficulty of accounting for varying time intervals, therefore parameter estimates can be biased and the time course of effects becomes ambiguous. By using stochastic differential equations to estimate an underlying continuous process, continuous time models allow for any pattern of measurement occasions. By interfacing to OpenMx, ctsem combines the flexible specification of structural equation models with the enhanced data gathering opportunities and improved estimation of continuous time models. ctsem can estimate relationships over time for multiple latent processes, measured by multiple noisy indicators with varying time intervals between observations. Within and between effects are estimated simultaneously by modeling both observed covariates and unobserved heterogeneity. Exogenous shocks with different shapes, group differences, higher order diffusion effects and oscillating processes can all be simply modeled. We first introduce and define continuous time models, then show how to specify and estimate a range of continuous time models using ctsem.

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Section: Continuous Time and Semmentioning

confidence: 99%

“…For a more general introduction to continuous time models by means of structural equation modeling (SEM), the reader is referred to Voelkle et al (2012). For additional information on the technical details we refer the reader to Oud and Jansen (2000).…”

Section: Introductionmentioning

confidence: 99%

Continuous Time Structural Equation Modeling with R Package ctsem

Driver¹,

Oud²,

Voelkle³

2017

J. Stat. Soft.

Self Cite

204

253

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show abstract

“…denotes the Kronecker product. Equations 10 and 11 are described in more detail in Appendix C, while we refer the reader to Arnold (1974, p. 128-134), Ruymgaart and Soong (1985, p. 80-99 ), Oud and Jansen (2000), or Singer (1990) for mathematical details. Because of the stochastic component of the error term, Equation 10 is called a stochastic differential equation.…”

Section: Continuous Time Modeling 18mentioning

confidence: 99%

“…As before, we assume that b and Bu do not vary across time (but see Oud & Jansen, 2000). Due to lack of space, however, group differences will not be considered any further in the present paper.…”

Section: Continuous Time Modeling 20mentioning

confidence: 99%

An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia.

Voelkle

Oud

Davidov

et al. 2012

Psychological Methods

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292

409

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Panel studies, in which the same subjects are repeatedly observed at multiple time points, are among the most popular longitudinal designs in psychology. Meanwhile, there exists a wide range of different methods to analyze such data, with autoregressive and cross-lagged models being 2 of the most well known representatives. Unfortunately, in these models time is only considered implicitly, making it difficult to account for unequally spaced measurement occasions or to compare parameter estimates across studies that are based on different time intervals. Stochastic differential equations offer a solution to this problem by relating the discrete time model to its underlying model in continuous time. It is the goal of the present article to introduce this approach to a broader psychological audience. A step-by-step review of the relationship between discrete and continuous time modeling is provided, and we demonstrate how continuous time parameters can be obtained via structural equation modeling. An empirical example on the relationship between authoritarianism and anomia is used to illustrate the approach. Person to ContactCorrespondence concerning this article should be addressed to Manuel C. Voelkle, anomia is used to illustrate the approach.

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“…The OU model's self-regulation parameter controls for the autocorrelation in the changes, and turned into a random effect. Besides the correspondence with the LMM framework, the OU model falls into the class of dynamical models termed as stochastic differential equations (SDEs; see e.g., Oud & Jansen, 2000;Oud, 2007;Molenaar & Newell, 2003;Chow, Ferrer, & Nesselroade, 2007), which extend ordinary differential equations (ODEs; e.g., the oscillator model; Chow, Ram, Boker, Fujita, & Clore, 2005; and the reservoir model; Deboeck & Bergeman, 2013) in allowing for process noises or uncertainties in how the latent processes change over time. When compared to oscillatory models of change, the OU model does not reinforce an oscillatory pattern on the dynamics itself, but can include cyclic changes in baseline levels (as TVCs), while at the same time capturing stochastic variation that is separate from measurement noise.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model

Oravecz

Tuerlinckx

Vandekerckhove

2016

Multivariate Behavioral Research

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In this paper, we propose a multilevel process modeling approach to describing individual differences in within-person changes over time. To characterize changes within an individual, repeated measurements over time are modeled in terms of three person-specific parameters: a baseline level, intra-individual variation around the baseline and regulatory mechanisms adjusting towards baseline. Variation due to measurement error is separated from meaningful intra-individual vari- can be studied in a one-stage analysis, meaning that model parameters and regression coefficients are estimated in the same step. Mathematical details of the approach, including a description of the core process model-the Ornstein-Uhlenbeck model-are provided. We also describe a user friendly, freely accessible software program that provides a straightforward graphical interface to carry out parameter estimation and inference. The proposed approach is illustrated by analyzing data collected via self-reports on affective states.

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Continuous Time State Space Modeling of Panel Data by Means of Sem

Abstract: continuous time state space modeling, exact discrete model, linear stochastic differential equations, longitudinal structural equation modeling, panel analysis,

Cited by 183 publications

References 22 publications

Continuous Time Structural Equation Modeling with R Package ctsem

Continuous Time Structural Equation Modeling with R Package ctsem

An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia.

Bayesian Data Analysis with the Bivariate Hierarchical Ornstein-Uhlenbeck Process Model

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