Continuous Time Structural Equation Modeling with R Package ctsem

Abstract

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.

Developmental cognitive neuroscience using Latent Change Score models: A tutorial and applications

“…As the autoregressive parameter between COGT2 and COGT1 is fixed to unity, we implicitly assume that the intervals are equidistant across individuals. Deviations from this assumption can be dealt with by rescaling scores (Ferrer & McArdle, 2004, p. 941) or, ideally, by using definition variables (Mehta & West, 2000) or continuous-time modelling approaches (Driver et al, 2016), which yield parameters that more easily generalize across different longitudinal designs. The model shown in Figure 2 is just identified, that is, there are as many unique pieces of information that enter the model (two variances, two means and a covariance) as parameters to be estimated (one observed variance, one latent variance, one observed Figure 1: Basic path model notation mean score, one latent mean score and one regression parameter).…”

“…(Schermelleh-Engel et al, 2003). Recommended sources for a wide range of (longitudinal) SEM topics include McArdle, (2009), Newsom (2015), Hoyle (2014), Little, (2013), (Voelkle & Oud, 2015), Driver et al (2016) and Voelkle (2007), as well as the tutorials cited above. Other useful resources are SEM-oriented email groups such as SEMNET (http://www2.gsu.edu/~mkteer/semnet.html) or package focused help groups (e.g.…”

“…(McArdle, 2009, p. 579). Alternative longitudinal SEM approaches that address specific questions with differing strengths and weaknesses include the autoregressive latent trajectory (ALT) model (Bollen & Curran, 2004), survival models (Newsom, 2015, chapter 12), continuous time models (Driver et al, 2016), simplex models (Newsom, 2015), the incorporation of definition variables (Mehta & West, 2000), regime switching LCS models (Chow, Grimm, Filteau, Dolan, & McArdle, 2013), latent traitstate models (Steyer, Schmitt, & Eid, 1999), and extensions of latent curve models including structured residuals and time-varying covariates (Curran, Howard, Bainter, Lane, & McGinley, 2014). For a general introduction to longitudinal SEM approaches we recommend the recent book by Newsom (2015).…”

Ideology and Post‐Colonial Society

“…Oud (2002; see also Oud & Jansen, 2000;Voelkle, Oud, Davidov, & Schmidt, 2012) provided an elegant solution to this problem by employing stochastic differential equations that explicitly identify time as a parameter in longitudinal multiwave autoregressive models using Structural Equation Modelling (see also Singer, 1998). Their approach, known as Continuous Time Structural Equation Modelling, has also been recently implemented as a package in R (see Driver, Oud, & Voelkle, 2015).…”

Capturing Context-Related Change in Emotional Dynamics via Fixed Moderated Time Series Analysis

“…First, missing values on the moderator cannot be handled readily within the model. This also concerns attempts to take unequal measurement intervals into account by incorporating missing values or by taking a continuous time perspective (Driver, Oud, & Voelkle, 2017;Voelkle, Oud, Davidov, & Schmidt, 2012). Fortunately, as these are problems shared with a broad class of other modeling approaches that include fixed or exogenous variables (e.g., standard regression and multilevel modeling, VAR models with covariates), strategies to cope with this have been developed.…”