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.

This is the first paper in a series of two that synthesizes, compares, and extends methods for causal inference with longitudinal panel data in a structural equation modeling (SEM) framework. Starting with a cross-lagged approach, this paper builds a general cross-lagged panel model (GCLM) with parameters to account for stable factors while increasing the range of dynamic processes that can be modeled. We illustrate the GCLM by examining the relationship between national income and subjective well-being (SWB), showing how to examine hypotheses about short-run (via Granger-Sims tests) versus long-run effects (via impulse responses). When controlling for stable factors, we find no short-run or long-run effects among these variables, showing national SWB to be relatively stable, whereas income is less so. Our second paper addresses the differences between the GCLM and other methods. Online Supplementary Materials offer an Excel file automating GCLM input for Mplus (with an example also for Lavaan in R) and analyses using additional data sets and all program input/output. We also offer an introductory GCLM presentation at https://youtu.be/tHnnaRNPbXs . We conclude with a discussion of issues surrounding causal inference.

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.

Perceptions of age influence how we evaluate, approach, and interact with other people. Based on a paramorphic human judgment model, the present study investigates possible determinants of accuracy and bias in age estimation across the adult life span. For this purpose, 154 young, middle-aged, and older participants of both genders estimated the age of 171 faces of young, middle-aged, and older men and women, portrayed on a total of 2,052 photographs. Each face displayed either an angry, fearful, disgusted, happy, sad, or neutral expression (FACES database;Ebner, Riediger, & Lindenberger, 2010). We found that age estimation ability decreased with age. Older and young adults, however, were more accurate and less biased in estimating the age of members of their own as compared with those of the other age group. In contrast, no reliable own-gender advantage was observed. Generally, the age of older faces was more difficult to estimate than the age of younger faces. Furthermore, facial expressions had a substantial impact on accuracy and bias of age estimation. Relative to other facial expressions, the age of neutral faces was estimated most accurately, while the age of faces displaying happy expressions was most likely underestimated. Results are discussed in terms of methodological and practical implications for research on age estimation.