An SEM Approach to Continuous Time Modeling of Panel Data: Relating Authoritarianism and Anomia

• Published in: Psychological methods Vol. 17; no. 2; pp. 176 - 192
• Main Authors: Voelkle, Manuel C, Oud, Johan H. L, Davidov, Eldad, Schmidt, Peter
• Format: Journal Article
• Language: English
• Published: Washington, DC American Psychological Association 01-06-2012
• Subjects: Anomia; Anomie; Authoritarianism; Biological and medical sciences; Correlation; Data Analysis; Data Interpretation, Statistical; Discrete time; Empirical Research; Fundamental and applied biological sciences. Psychology; Humans; Intervals; Longitudinal Studies; Longitudinal Studies - statistics & numerical data; Models, Statistical; Notices; Observation; Panel studies; Parameters; Psychology - statistics & numerical data; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Social Change; Statistical Analysis; Statistical Regression; Statistics. Mathematics; Stochastic Modeling; Stochastic Processes; Structural Equation Modeling; Structural Equation Models; Time; Time Factors; Human; autoregressive cross-lagged model; Data analysis; Structural equation modeling; panel design; continuous time modeling; Continuous time; Autoregressive model; Modeling; Anomia; Authoritarianism; Statistical method; Panel data; Follow up study; Experimental design; longitudinal data analysis
• ISSN: 1082-989X; 1939-1463
• DOI: 10.1037/a0027543

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. (Contains 3 figures, 3 footnotes and 3 tables.)