Dynamic Structural Equation Models

This article presents dynamic structural equation modeling (DSEM), which can be used to study the evolution of observed and latent variables as well as the structural equation models over time. DSEM is suitable for analyzing intensive longitudinal data where observations from multiple individuals are collected at many points in time. The modeling framework encompasses previously published DSEM models and is a comprehensive attempt to combine time-series modeling with structural equation modeling. DSEM is estimated with Bayesian methods using the Markov chain Monte Carlo Gibbs sampler and the Metropolis–Hastings sampler. We provide a detailed description of the estimation algorithm as implemented in the Mplus software package. DSEM can be used for longitudinal analysis of any duration and with any number of observations across time. Simulation studies are used to illustrate the framework and study the performance of the estimation method. Methods for evaluating model fit are also discussed.

[1]  William J. Browne,et al.  Bayesian and likelihood-based methods in multilevel modeling 1 A comparison of Bayesian and likelihood-based methods for fitting multilevel models , 2006 .

[2]  Ellen L. Hamaker,et al.  Incorporating measurement error in n = 1 psychological autoregressive modeling , 2015, Front. Psychol..

[3]  Ellen L. Hamaker,et al.  UvA-DARE ( Digital Academic Repository ) To center or not to center ? Investigating inertia with a multilevel autoregressive model , 2014 .

[4]  Ulrich Ebner-Priemer,et al.  The Role of Ambulatory Assessment in Psychological Science , 2014, Current directions in psychological science.

[5]  Kristopher J Preacher,et al.  No Need to be Discrete: A Method for Continuous Time Mediation Analysis , 2016 .

[6]  E L Hamaker,et al.  At the Frontiers of Modeling Intensive Longitudinal Data: Dynamic Structural Equation Models for the Affective Measurements from the COGITO Study , 2018, Multivariate behavioral research.

[7]  B. Muthén,et al.  A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the metropolis-hastings algorithm , 1998 .

[8]  Bradley P. Carlin,et al.  Bayesian measures of model complexity and fit , 2002 .

[9]  Clive W. J. Granger,et al.  Time Series Modelling and Interpretation , 1976 .

[10]  R. Tibshirani,et al.  Linear Smoothers and Additive Models , 1989 .

[11]  Peter C M Molenaar,et al.  Equivalent Dynamic Models , 2017, Multivariate behavioral research.

[12]  F. Vaida,et al.  Conditional Akaike information for mixed-effects models , 2005 .

[13]  N. Bolger,et al.  Intensive Longitudinal Methods: An Introduction to Diary and Experience Sampling Research , 2013 .

[14]  Francis Tuerlinckx,et al.  A hierarchical latent stochastic differential equation model for affective dynamics. , 2011, Psychological methods.

[15]  B. Muthén,et al.  The multilevel latent covariate model: a new, more reliable approach to group-level effects in contextual studies. , 2008, Psychological methods.

[16]  T. Asparouhov.  General Random Effect Latent Variable Modeling : Random Subjects , Items , Contexts , and Parameters , 2012 .

[17]  M. Nerlove,et al.  Biases in dynamic models with fixed effects , 1988 .

[18]  Sik-Yum Lee,et al.  Structural equation modelling: A Bayesian approach. , 2007 .

[19]  Jean-Philippe Laurenceau,et al.  A Multilevel AR(1) Model: Allowing for Inter-Individual Differences in Trait-Scores, Inertia, and Innovation Variance , 2015, Multivariate behavioral research.

[20]  J. Oud,et al.  Continuous time modelling with individually varying time intervals for oscillating and non-oscillating processes. , 2013, The British journal of mathematical and statistical psychology.

[21]  Peter C. M. Molenaar,et al.  A dynamic factor model for the analysis of multivariate time series , 1985 .

[22]  Ellen L. Hamaker,et al.  Conditions for the Equivalence of the Autoregressive Latent Trajectory Model and a Latent Growth Curve Model With Autoregressive Disturbances , 2005 .

[23]  Bengt Muthén,et al.  Bayesian Analysis Using Mplus: Technical Implementation , 2010 .

[24]  Anthony S. Bryk,et al.  Hierarchical Linear Models: Applications and Data Analysis Methods , 1992 .

[25]  Ellen L. Hamaker,et al.  Comparisons of Four Methods for Estimating a Dynamic Factor Model , 2008 .

[26]  Mary Kathryn Cowles,et al.  Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models , 1996, Stat. Comput..

[27]  T. Trull,et al.  Analysis of affective instability in ecological momentary assessment: Indices using successive difference and group comparison via multilevel modeling. , 2008, Psychological methods.

[28]  C. Robert,et al.  Deviance information criteria for missing data models , 2006 .

[29]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[30]  Zhiyong Zhang,et al.  Bayesian Estimation of Categorical Dynamic Factor Models , 2007 .