Beyond the Mean: A Flexible Framework for Studying Causal Effects Using Linear Models

Graph-based causal models are a flexible tool for causal inference from observational data. In this paper, we develop a comprehensive framework to define, identify, and estimate a broad class of causal quantities in linearly parametrized graph-basedmodels. The proposed method extends the literature, which mainly focuses on causal effects on the mean level and the variance of an outcome variable. For example, we show how to compute the probability that an outcome variable realizes within a target range of values given an intervention, a causal quantity we refer to as the probability of treatment success. We link graphbased causal quantities defined via the do-operator to parameters of the model implied distribution of the observed variables using so-called causal effect functions. Based on these causal effect functions, we propose estimators for causal quantities and show that these estimators are consistent and converge at a rate of N−1/2 under standard assumptions. Thus, causal quantities can be estimated based on sample sizes that are typically available in the social and behavioral sciences. In case of maximum likelihood estimation, the estimators are asymptotically efficient. We illustrate the proposed method with an example based on empirical data, placing special emphasis on the difference between the interventional and conditional distribution.Humboldt-Universität zu Berlin (1034)Peer Reviewe

Continuous Time Structural Equation Modeling with R Package ctsem

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

Psychopathological networks:Theory, methods and practice

In recent years, network approaches to psychopathology have sparked much debate and have had a significant impact on how mental disorders are perceived in the field of clinical psychology. However, there are many important challenges in moving from theory to empirical research and clinical practice and vice versa. Therefore, in this article, we bring together different points of view on psychological networks by methodologists and clinicians to give a critical overview on these challenges, and to present an agenda for addressing these challenges. In contrast to previous reviews, we especially focus on methodological issues related to temporal networks. This includes topics such as selecting and assessing the quality of the nodes in the network, distinguishing between- and within-person effects in networks, relating items that are measured at different time scales, and dealing with changes in network structures. These issues are not only important for researchers using network models on empirical data, but also for clinicians, who are increasingly likely to encounter (person-specific) networks in the consulting room

From Data to Causes III: Bayesian Priors for General Cross-Lagged Panel Models (GCLM)

This article describes some potential uses of Bayesian estimation for time-series and panel data models by incorporating information from prior probabilities (i.e., priors) in addition to observed data. Drawing on econometrics and other literatures we illustrate the use of informative “shrinkage” or “small variance” priors (including so-called “Minnesota priors”) while extending prior work on the general cross-lagged panel model (GCLM). Using a panel dataset of national income and subjective well-being (SWB) we describe three key benefits of these priors. First, they shrink parameter estimates toward zero or toward each other for time-varying parameters, which lends additional support for an income → SWB effect that is not supported with maximum likelihood (ML). This is useful because, second, these priors increase model parsimony and the stability of estimates (keeping them within more reasonable bounds) and thus improve out-of-sample predictions and interpretability, which means estimated effect should also be more trustworthy than under ML. Third, these priors allow estimating otherwise under-identified models under ML, allowing higher-order lagged effects and time-varying parameters that are otherwise impossible to estimate using observed data alone. In conclusion we note some of the responsibilities that come with the use of priors which, departing from typical commentaries on their scientific applications, we describe as involving reflection on how best to apply modeling tools to address matters of worldly concern

Continuous-time modeling in prevention research: An illustration

The analysis of cross-lagged relationships is a popular approach in prevention research to explore the dynamics between constructs over time. However, a limitation of commonly used cross-lagged models is the requirement of equally spaced measurement occasions that prevents the usage of flexible longitudinal designs and complicates cross-study comparisons. Continuous-time modeling overcomes these limitations. In this article, we illustrate the use of continuous-time models using Bayesian and frequentist approaches to model estimation. As an empirical example, we study the dynamic interplay of physical activity and health, a classic research topic in prevention science, using data from the “Midlife in the United States (MIDUS 2): Daily Stress Project, 2004–2009.” To help prevention researchers in adopting the approach, we provide annotated R scripts and a simulated data set based on the results from analyzing the MIDUS 2 data.Peer Reviewe

Robustness of Individual Score Methods against Model Misspecification in Autoregressive Panel Models

Different methods to obtain individual scores from multiple item latent variable models exist, but their performance under realistic conditions is currently underresearched. We investigate the performance of the regression method, the Bartlett method, the Kalman filter, and the mean score under misspecification in autoregressive panel models. Results from three simulations show different patterns of findings for the mean absolute error, for the correlations between individual scores and the true scores (correlation criterion), and for the coverage in our settings: a) all individual score methods are generally quite robust against the chosen misspecification in the loadings, b) all methods are similarly sensitive to positively skewed as well as leptokurtic response distributions with regard to the correlation criterion, c) only the mean score is not robust against an integrated trend component, and d) coverage for the mean score is consistently below the nominal value.Peer Reviewe

State-of-the-art presentation: The role of time in dynamic models of change

Content: What are dynamic continuous time models?; Why use dynamic continuous time models?; How to estimate and interpret dynamic continuous time models?; Recent extensions; Current limitations and future research direction

Ergodic Subspace Analysis

Properties of psychological variables at the mean or variance level can differ between persons and within persons across multiple time points. For example, cross-sectional findings between persons of different ages do not necessarily reflect the development of a single person over time. Recently, there has been an increased interest in the difference between covariance structures, expressed by covariance matrices, that evolve between persons and within a single person over multiple time points. If these structures are identical at the population level, the structure is called ergodic. However, recent data confirms that ergodicity is not generally given, particularly not for cognitive variables. For example, the g factor that is dominant for cognitive abilities between persons seems to explain far less variance when concentrating on a single person's data. However, other subdimensions of cognitive abilities seem to appear both between and within persons; that is, there seems to be a lower-dimensional subspace of cognitive abilities in which cognitive abilities are in fact ergodic. In this article, we present ergodic subspace analysis (ESA), a mathematical method to identify, for a given set of variables, which subspace is most important within persons, which is most important between person, and which is ergodic. Similar to the common spatial patterns method, the ESA method first whitens a joint distribution from both the between and the within variance structure and then performs a principle component analysis (PCA) on the between distribution, which then automatically acts as an inverse PCA on the within distribution. The difference of the eigenvalues allows a separation of the rotated dimensions into the three subspaces corresponding to within, between, and ergodic substructures. We apply the method to simulated data and to data from the COGITO study to exemplify its usage.Peer Reviewe

Toward a unified framework for the study of between-person and within-person structures. Building a bridge between two research paradigms

The vast majority of empirical research in the behavioral sciences is based on the analysis of between-person variation. In contrast, much of applied psychology is concerned with the analysis of variation within individuals. Furthermore, the mechanisms specified by psychological theories generally operate within, rather than across, individuals. This disconnect between research practice, applied demands, and psychological theories constitutes a major threat to the conceptual integrity of the field. Following groundbreaking earlier work, we propose a conceptual framework that distinguishes within-person (WP) and between-person (BP) sources of variation in psychological constructs. By simultaneously considering both sources of variation, it is shown how to identify possible reasons for nonequivalence of BP and WP structures as well as establishing areas of convergence. For this purpose, we first introduce the concept of conditional equivalence as a way to study partial structural equivalence of BP and WP structures in the presence of unconditional nonequivalence. Second, we demonstrate the construction of likelihood planes to explore the causes of structural nonequivalence. Third, we examine 4 common causes for unconditional nonequivalence autoregression, subgroup differences, linear trends, and cyclic trends-and demonstrate how to account for them. Fourth, we provide an empirical example on BP and WP differences in attentiveness