An SEM approach to continuous time modeling of panel data: Relating authoritarianism and anomia.
Psychological MethodsPublished 1 January 2012Open access
Manuel C. Voelkle, Johan H. L. Oud, Eldad Davidov, Peter Schmidt
Citations322
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TL;DR
A step-by-step review of the relationship between discrete and continuous time modeling is provided, and it is demonstrated how continuous time parameters can be obtained via structural equation modeling.
Abstract
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.
Keywords
PsychologyDecision SciencesEconomics, Econometrics and Finance
Structural Equation Modeling A Multidisciplinary JournalCutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives
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EconometricaInvestigating Causal Relations by Econometric Models and Cross-spectral Methods
22,877 Citations1969Clive W. J. Granger
Contemporary Sociology A Journal of ReviewsStructural Equations with Latent Variables.
17,606 Citations1991Clifford C. Clogg, Kenneth A. Bollen
Journal of the American Statistical AssociationHierarchical Linear Models: Applications and Data Analysis Methods
13,908 Citations2003Marie Davidian
The authors give us a thorough accounting of the core of linear model theory while having it extend into more modern extensions in many directions, and there is little attempt at motivation for parameterizations of classi cation models.
Psychological MethodsFit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification.
11,435 Citations1998Li‐tze Hu, Peter M. Bentler
Social ForcesTesting Structural Equation Models.
8,255 Citations1995Clifford C. Clogg, Kenneth A. Bollen +1 more
Structural Equation Modeling A Multidisciplinary JournalIn Search of Golden Rules: Comment on Hypothesis-Testing Approaches to Setting Cutoff Values for Fit Indexes and Dangers in Overgeneralizing Hu and Bentler's (1999) Findings
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4,510 Citations1993William Meredith
Structural Equation Modeling With Lisrel, Prelis, and Simplis: Basic Concepts, Applications, and Programming
3,874 Citations1998Barbara M. Byrne
This paper presents a meta-modelling framework for testing the factorial Validity of a Theoretical Construct and the Invariant Factorial Structure of a theoretical construct using LISREL, PRELIS, and SIMPLIS through Windows.
Annual Review of PsychologyLatent Variable Modeling of Differences and Changes with Longitudinal Data
1,947 Citations2008John J. McArdle
This review considers a common question in data analysis: What is the most useful way to analyze longitudinal repeated measures data and presents several classic SEMs based on the inclusion of invariant common factors and why these are so important.
Wiley series in probability and statisticsLatent Curve Models
1,706 Citations2005Kenneth A. Bollen, Patrick J. Curran
Psychological BulletinCan test statistics in covariance structure analysis be trusted?
1,360 Citations1992Li‐tze Hu, Peter M. Bentler +1 more
Covariance structure analysis uses chi 2 goodness-of-fit test statistics whose adequacy is not known to evaluate the behavior of 6 test statistics, which perform dramatically differently under 7 distributional conditions at 6 sample sizes.
The authoritarian specter
1,267 Citations1996Bob Altemeyer
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1,202 Citations2011Steven M. Boker, Michael C. Neale +10 more
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Medical Entomology and ZoologyAn Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Application, Second Edition
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ETS Research Bulletin SeriesA GENERAL METHOD FOR ESTIMATING A LINEAR STRUCTURAL EQUATION SYSTEM*
1,098 Citations1970Karl G. Jöreskog
BehaviormetrikaBeyond SEM: General Latent Variable Modeling
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Different applications of latent variable applications are discussed in a unifying framework that brings together in one general model such different analysis types as factor models, growth curve models, multilevel models, latent class models and discrete-time survival models.
American Sociological ReviewSocial Integration and Certain Corollaries: An Exploratory Study
1,030 Citations1956Leo Srole
The Economic JournalStructural Equation Models in the Social Sciences.
813 Citations1974Mervyn King, Arthur S. Goldberger +1 more
PsychometrikaA Dynamic Factor Model for the Analysis of Multivariate Time Series
481 Citations1985Peter C. M. Molenaar
A new statistical technique, coined dynamic factor analysis, is proposed, which accounts for the entire lagged covariance function of an arbitrary second order stationary time series.
Organizational Research MethodsToward a Further Understanding of and Improvement in Measurement Invariance Methods and Procedures
453 Citations2002Robert J. Vandenberg
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449 Citations2004Kenneth A. Bollen, Patrick J. Curran
Tutorials in Quantitative Methods for PsychologyA short tutorial of GPower
400 Citations2007Susanne Mayr, Edgar Erdfelder +2 more
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384 Citations2002Sasha Cyganowski, Peter E. Kloeden +1 more
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365 Citations2017Kees van Montfort, Johan H. L. Oud +4 more
Psychology and AgingAssessing Psychological Change in Adulthood: An Overview of Methodological Issues.
279 Citations2003Christopher Hertzog, John R. Nesselroade
The current status of methods available for the analysis of psychological change in adulthood and aging is reviewed, as reflected in techniques such as latent growth curve models and multilevel (random-effects) models.
Psychometrika<i>P</i>-Technique Demonstrated in Determining Psychophysiological Source Traits in a Normal Individual
253 Citations1947Raymond B. Cattell, Alan Cattell +1 more
P-technique, a method employing intra-individual correlation, is tried out for the first time and definite factors are obtained among the psychological and physiological variables, which can be mutually matched.
Human Brain MappingUnified structural equation modeling approach for the analysis of multisubject, multivariate functional MRI data
249 Citations2006Jieun Kim, Wei Zhu +3 more
This work proposes a two‐stage unified SEM plus GLM (General Linear Model) approach for the analysis of multisubject, multivariate functional magnetic resonance imaging (fMRI) time series data with subject‐level covariates to examine the impact of these covariates on effective connectivity via a GLM.
PsychometrikaUsing Phantom and Imaginary Latent Variables to Parameterize Constraints in Linear Structural Models
237 Citations1984David Rindskopf
PsychometrikaContinuous Time State Space Modeling of Panel Data by Means of Sem
188 Citations2000Johan H. L. Oud, Robert A.R.G. Jansen
NeuroImageAutomatic search for fMRI connectivity mapping: An alternative to Granger causality testing using formal equivalences among SEM path modeling, VAR, and unified SEM
179 Citations2010Kathleen M. Gates, Peter C. M. Molenaar +3 more
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Journal of Mathematical SociologyProblems with the estimation of stochastic differential equations using structural equations models
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Social ForcesAuthoritarianism, Anomia, and Prejudice
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