Estimating Multilevel Linear Models as Structural Equation Models

Multilevel linear models (MLMs) provide a powerful framework for analyzing data collected at nested or non-nested levels, such as students within classrooms. The current article draws on recent analytical and software advances to demonstrate that a broad class of MLMs may be estimated as structural equation models (SEMs). Moreover, within the SEM approach it is possible to include measurement models for predictors or outcomes, and to estimate the mediational pathways among predictors explicitly, tasks which are currently difficult with the conventional approach to multilevel modeling. The equivalency of the SEM approach with conventional methods for estimating MLMs is illustrated using empirical examples, including an example involving both multiple indicator latent factors for the outcomes and a causal chain for the predictors. The limitations of this approach for estimating MLMs are discussed and alternative approaches are considered.

[1]  Stephen W. Raudenbush,et al.  A Multilevel, Multivariate Model for Studying School Climate With Estimation Via the EM Algorithm and Application to U.S. High-School Data , 1991 .

[2]  Stephen W. Raudenbush,et al.  Toward a coherent framework for comparing trajectories of individual change. , 2001 .

[3]  Peter C. M. Molenaar,et al.  A structural equations modeling approach to the general linear mixed model , 2001 .

[4]  S G West,et al.  Putting the individual back into individual growth curves. , 2000, Psychological methods.

[5]  James L. Arbuckle,et al.  Full Information Estimation in the Presence of Incomplete Data , 1996 .

[6]  Andrew Gelman,et al.  Let's Practice What We Preach , 2002 .

[7]  S. Raudenbush,et al.  Assessing Direct and Indirect Effects in Multilevel Designs with Latent Variables , 1999 .

[8]  M. Browne.  Asymptotically distribution-free methods for the analysis of covariance structures. , 1984, The British journal of mathematical and statistical psychology.

[9]  John B. Willett,et al.  Using covariance structure analysis to detect correlates and predictors of individual change over time , 1994 .

[10]  G. Molenberghs,et al.  Linear Mixed Models for Longitudinal Data , 2001 .

[11]  M J Rovine,et al.  A Structural Modeling Approach to a Multilevel Random Coefficients Model , 2000, Multivariate behavioral research.

[12]  W. DeSarbo,et al.  Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity , 1997 .

[13]  Pickles A SkrondalA. Rabe-HeskethS.  GLLAMM: A general class of multilevel models and a STATA programme , 2001 .

[14]  Kenneth A. Bollen,et al.  Structural Equations with Latent Variables , 1989 .

[15]  S. Rabe-Hesketh,et al.  Generalized linear latent and mixed models , 2000 .

[16]  H. Goldstein.  Multilevel Statistical Models , 2006 .

[17]  Patricio Cumsille,et al.  Second-order latent growth models. , 2001 .

[18]  B. Muthén,et al.  Finite Mixture Modeling with Mixture Outcomes Using the EM Algorithm , 1999, Biometrics.

[19]  B. Muthén,et al.  Multilevel Covariance Structure Analysis , 1994 .

[20]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[21]  D P MacKinnon,et al.  Multilevel Mediation Modeling in Group-Based Intervention Studies , 1999, Evaluation review.

[22]  K. Jöreskog.  Simultaneous factor analysis in several populations , 1971 .

[23]  Harvey Goldstein,et al.  A general model for the analysis of multilevel data , 1988 .

[24]  S. Rabe-Hesketh,et al.  Generalized multilevel structural equation modeling , 2004 .

[25]  D. Mackinnon,et al.  Multilevel Modeling of Individual and Group Level Mediated Effects , 2001, Multivariate behavioral research.

[26]  Aaron M. Pallas.  School Climate in American High Schools , 1988, Teachers College Record: The Voice of Scholarship in Education.

[27]  A. Satorra,et al.  Complex Sample Data in Structural Equation Modeling , 1995 .

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

[29]  R. MacCallum,et al.  Studying Multivariate Change Using Multilevel Models and Latent Curve Models. , 1997, Multivariate behavioral research.

[30]  Jürgen Baumert,et al.  Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples. , 2000 .

[31]  Peter M. Bentler,et al.  Comparisons of Two Statistical Approaches to Study Growth Curves: The Multilevel Model and the Latent Curve Analysis. , 1998 .

[32]  Naihua Duan,et al.  Multilevel Modeling : Methodological Advances, Issues, and Applications , 2003 .

[33]  Jason T. Newsom,et al.  A Multilevel Structural Equation Model for Dyadic Data , 2002 .

[34]  Peter C. M. Molenaar,et al.  A Nonstandard Method for Estimating a Linear G rowth Model in LISREL , 1998 .

[35]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[36]  Linda M. Collins,et al.  New methods for the analysis of change , 2001 .

[37]  Gerhard Arminger,et al.  Finite Mixtures of Covariance Structure Models with Regressors , 1997 .

[38]  William Meredith,et al.  Latent curve analysis , 1990 .