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.

Continuous time dynamic models are similar to popular discrete time models such as autoregressive cross-lagged models, but through use of stochastic differential equations can accurately account for differences in time intervals between measurements, and more parsimoniously specify complex dynamics. As such they offer powerful and flexible approaches to understand ongoing psychological processes and interventions, and allow for measurements to be taken a variable number of times, and at irregular intervals. However, limited developments have taken place regarding the use of continuous time models in a fully hierarchical context, in which all model parameters are allowed to vary over individuals. This has meant that questions regarding individual differences in parameters have had to rely on single-subject time series approaches, which require far more measurement occasions per individual. We present a hierarchical Bayesian approach to estimating continuous time dynamic models, allowing for individual variation in all model parameters. We also describe an extension to the ctsem package for R, which interfaces to the Stan software and allows simple specification and fitting of such models. To demonstrate the approach, we use a subsample from the German socioeconomic panel and relate overall life satisfaction and satisfaction with health. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

The lead-lag structure of multivariate time-ordered observations and the possibility to disentangle between-person (BP) from within-person (WP) sources of variance are major assets of longitudinal (panel) data. Hence, psychologists are making increasing use of such data, often with the intent to delineate the dynamic properties of psychological mechanisms, understood as a sequence of causal effects that govern psychological functioning. However, even with longitudinal data, psychological mechanisms are not easily identified. In this article, we show how an adequate representation of time may enhance the tenability of causal interpretations in the context of multivariate longitudinal data analysis. We anchor our considerations with an example that illustrates some of the main problems and questions faced by applied researchers and practitioners. We distinguish between static versus dynamic and discrete versus continuous time modeling approaches and discuss their advantages and disadvantages. We place particular emphasis on different ways of addressing BP differences and stress their dual role as potential confounds versus valuable sources of information for improving estimation and aiding causal inference. We conclude by outlining an approach that offers the potential of better integration of information on BP differences and WP changes in the search for causal mechanisms along with a discussion of current problems and limitations.

The pursuit of social rank pervades all human societies and the position that an individual occupies within a hierarchy has important effects on their social and reproductive success. Whilst recent research has indicated that there are two distinct routes to rank attainmentdominance (through the induction of fear) and prestige (through respect and admiration)this empirical evidence has generally provided only a cross-sectional snapshot of how the two processes operate in human hierarchy. Whether dominance and prestige are potentially viable long-term strategies, rather than more effective short-term tactics, for acquiring rank in groups remains an open question. The current research addresses this gap by examining the temporal dynamics between prestige, dominance and social rank using a dynamic, evolutionary approach to understanding human social hierarchy, and thus supplies the first longitudinal empirical assessment of these variables' relationships. Using naturalistic student project groups comprised of 3-5 teammates, the present research tracks the temporal relationships between prestige, dominance and social rank-provided through round-robin teammate-ratings-from the initial formation of collaborative task groups through to the end of a 16-week long academic semester. Results indicate that, whilst dominance and prestige both promoted social rank in unacquainted groups initially and were distinct processes throughout the period examined, only prestige had a positive effect on social rank over time. Further results reveal that the temporal relationship between prestige and social rank was bidirectional, such that acquiring social rank further perpetuates future prestige. Overall, findings present a framework for the longitudinal distinction between prestige and dominance.

Continuous-time modeling offers a flexible approach to analyze longitudinal data from designs with unequally spaced measurement occasions. Measurement models are popular tools in psychological research to control for measurement error. The objective of the present article is to introduce the continuous-time Rasch model, a combination of the Rasch model and a continuous-time dynamic model. In a series of simulations we demonstrate the performance of the proposed model and that ignoring individual unequal time interval lengths, choosing a wrong measurement model, and selecting a wrong analysis strategy results in poor parameter estimates. The newly proposed continuous-time Rasch model overcomes these problems and offers a powerful new approach to longitudinal analysis with dichotomous items. A step-by-step tutorial on how to run a continuous-time Rasch model with the R package ctsem and an illustrative empirical example is given.