lavaan.survey: An R Package for Complex Survey Analysis of Structural Equation Models

This paper introduces the R package lavaan.survey, a user-friendly interface to design-based complex survey analysis of structural equation models (SEMs). By leveraging existing code in the lavaan and survey packages, the lavaan.survey package allows for SEM analyses of stratified, clustered, and weighted data, as well as multiply imputed complex survey data. lavaan.survey provides several features such as SEMs with replicate weights, a variety of resampling techniques for complex samples, and finite population corrections, features that should prove useful for SEM practitioners faced with the common situation of a sample that is not iid.

[1]  Sonya K Sterba,et al.  Alternative Model-Based and Design-Based Frameworks for Inference From Samples to Populations: From Polarization to Integration , 2009, Multivariate behavioral research.

[2]  Chris J. Skinner,et al.  Estimating models for panel survey data under complex sampling , 2008 .

[3]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics , 2019, Wiley Series in Probability and Statistics.

[4]  A. Satorra,et al.  Corrections to test statistics and standard errors in covariance structure analysis. , 1994 .

[5]  John Fox,et al.  TEACHER'S CORNER: Structural Equation Modeling With the sem Package in R , 2006 .

[6]  Albert Satorra,et al.  Asymptotic robust inferences in the analysis of mean and covariance structures , 1992 .

[7]  Daniel L. Oberski.  Conditional Design Effects for Structural Equation Model estimates , 2013 .

[8]  John W. Graham,et al.  Multiple imputation in multivariate research. , 2000 .

[9]  H. Marsh,et al.  Explaining Paradoxical Relations Between Academic Self-Concepts and Achievements: Cross-Cultural Generalizability of the Internal/External Frame of Reference Predictions Across 26 Countries. , 2004 .

[10]  A. Scherpenzeel,et al.  Data Collection in a Probability-Based Internet Panel: How the LISS Panel Was Built and How It Can Be Used , 2011 .

[11]  Laura M. Stapleton,et al.  An Assessment of Practical Solutions for Structural Equation Modeling with Complex Sample Data , 2006 .

[12]  Thomas Lumley,et al.  Complex Surveys: A Guide to Analysis Using R , 2010 .

[13]  Stephen Tueller,et al.  Issues in the Structural Equation Modeling of Complex Survey Data , 2013 .

[14]  Albert Satorra,et al.  Linear structural relations: Gradient and Hessian of the fitting function , 1991 .

[15]  StataCorp.  Stata structural equation modeling reference manual , 2011 .

[16]  Gary King,et al.  Amelia II: A Program for Missing Data , 2011 .

[17]  Tihomir Asparouhov,et al.  General Multi-Level Modeling with Sampling Weights , 2006 .

[18]  A. Satorra.  Alternative test criteria in covariance structure analysis: A unified approach , 1989 .

[19]  Y Kano,et al.  Can test statistics in covariance structure analysis be trusted? , 1992, Psychological bulletin.

[20]  J. Magnus,et al.  Matrix Differential Calculus with Applications in Statistics and Econometrics (Revised Edition) , 1999 .

[21]  D. Rubin,et al.  Statistical Analysis with Missing Data , 1988 .

[22]  William G. Cochran,et al.  Sampling Techniques, 3rd Edition , 1963 .

[23]  Daniel L. Oberski.  Measurement error in comparative surveys , 2011 .

[24]  Robert E. Fay,et al.  THEORY AND APPLICATION OF REPLICATE WEIGHTING FOR VARIANCE CALCULATIONS , 2002 .

[25]  Stef van Buuren,et al.  MICE: Multivariate Imputation by Chained Equations in R , 2011 .

[26]  Lynne Stokes,et al.  Introduction to Variance Estimation (2nd ed.) , 2008 .

[27]  Kyle C. Cavanaugh,et al.  Climate-driven increases in storm frequency simplify kelp forest food webs , 2011 .

[28]  Karl G. Jöreskog.  ESTIMATION AND TESTING OF SIMPLEX MODELS , 1970 .

[29]  Bjorn Roelstraete,et al.  FIAR: An R Package for Analyzing Functional Integration in the Brain , 2011 .

[30]  Martin Valcke,et al.  Academic self-efficacy and academic self-concept: Reconsidering structural relationships , 2009 .

[31]  Chris J. Skinner,et al.  Analysis of complex surveys , 1991 .

[32]  Peter M. Bentler,et al.  EQS : structural equations program manual , 1989 .

[33]  P M Bentler,et al.  Normal theory based test statistics in structural equation modelling. , 1998, The British journal of mathematical and statistical psychology.

[34]  Ferla John,et al.  ACADEMIC SELF-EFFICACY AND ACADEMIC SELF-CONCEPT , 2009 .

[35]  Joseph L Schafer,et al.  Analysis of Incomplete Multivariate Data , 1997 .

[36]  Chris J. Skinner,et al.  Variance estimation in the analysis of clustered longitudinal survey data , 2007 .

[37]  Aaron J. Ferguson,et al.  On the Utilization of Sample Weights in Latent Variable Models. , 1999 .

[38]  F. E. Satterthwaite.  Synthesis of variance , 1941 .

[39]  J. Rao,et al.  Small-Sample Comparisons of Level and Power for Simple Goodness-of-Fit Statistics under Cluster Sampling , 1987 .

[40]  A. Satorra,et al.  Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: a Monte Carlo study. , 1991, The British journal of mathematical and statistical psychology.

[41]  Laura M. Stapleton.  Variance Estimation Using Replication Methods in Structural Equation Modeling With Complex Sample Data , 2008 .

[42]  Tihomir Asparouhov,et al.  Multivariate Statistical Modeling with Survey Data , 2005 .

[43]  A. Gelman,et al.  Multiple Imputation with Diagnostics (mi) in R: Opening Windows into the Black Box , 2011 .

[44]  R. Kline.  Principles and practice of structural equation modeling, 3rd ed. , 2011 .

[45]  O. D. Duncan,et al.  Introduction to Structural Equation Models. , 1977 .

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

[47]  Wayne A. Fuller,et al.  On the bias of the multiple‐imputation variance estimator in survey sampling , 2006 .

[48]  John Fox,et al.  OpenMx: An Open Source Extended Structural Equation Modeling Framework , 2011, Psychometrika.

[49]  John Gelissen,et al.  The Multidimensionality of Welfare State Attitudes: A European Cross-National Study , 2012, Social Indicators Research.

[50]  R. P. McDonald,et al.  Structural Equations with Latent Variables , 1989 .

[51]  Tihomir Asparouhov,et al.  Sampling Weights in Latent Variable Modeling , 2005 .

[52]  D. Kaplan.  Structural Equation Modeling: Foundations and Extensions , 2000 .

[53]  Bengt Muthén,et al.  Simple Second Order Chi-Square Correction , 2010 .

[54]  Rex B. Kline,et al.  Principles and Practice of Structural Equation Modeling , 1998 .

[55]  Duane F. Alwin,et al.  Evaluating the Reliability and Validity of Survey Interview Data Using the MTMM Approach , 2011 .

[56]  James B. Grace,et al.  Structural Equation Modeling and Natural Systems , 2006 .

[57]  Richard G. Lomax,et al.  Utilization of Sample Weights in Single-Level Structural Equation Modeling , 2006 .

[58]  Willem E. Saris,et al.  Causal modelling in nonexperimental research : an introduction to the LISREL approach , 1985, American Political Science Review.

[59]  C. Stein,et al.  Structural equation modeling. , 2012, Methods in molecular biology.

[60]  Andrew Thomas,et al.  WinBUGS - A Bayesian modelling framework: Concepts, structure, and extensibility , 2000, Stat. Comput..

[61]  A. Scott,et al.  On Chi-Squared Tests for Multiway Contingency Tables with Cell Proportions Estimated from Survey Data , 1984 .

[62]  Yves Rosseel,et al.  lavaan: An R Package for Structural Equation Modeling , 2012 .

[63]  Roger A. Sugden,et al.  Multiple Imputation for Nonresponse in Surveys , 1988 .

[64]  Laura M. Stapleton,et al.  The Incorporation of Sample Weights Into Multilevel Structural Equation Models , 2002 .

[65]  K. Yuan,et al.  Structural Equation Modeling with Small Samples: Test Statistics. , 1999, Multivariate behavioral research.

[66]  J LunnDavid,et al.  WinBUGS A Bayesian modelling framework , 2000 .

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

[68]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[69]  Hadley Wickham,et al.  The Split-Apply-Combine Strategy for Data Analysis , 2011 .

[70]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[71]  A. Satorra,et al.  Measurement Error Models , 1988 .

[72]  Kevin Gross,et al.  Does productivity drive diversity or vice versa? A test of the multivariate productivity-diversity hypothesis in streams. , 2009, Ecology.

[73]  Thomas Lumley,et al.  Analysis of Complex Survey Samples , 2004 .