A Model for Integrating Fixed-, Random-, and Mixed-Effects Meta-Analyses Into Structural Equation Modeling

Psychological Methods

Volumn 13, Issue 3, 2008, Pages 182-202

  Cheung, Mike W L ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

fixed effects model; meta analysis; mixed effects model; random effects model; structural equation model

Indexed keywords

ARTICLE; HUMAN; META ANALYSIS; PSYCHOLOGICAL MODEL;

HUMANS; META-ANALYSIS AS TOPIC; MODELS, PSYCHOLOGICAL;

EID: 54549116275     PISSN: 1082989X     EISSN: None     Source Type: Journal    
DOI: 10.1037/a0013163     Document Type: Article

References (120)

1. Adams D.C., Gurevitch J., and Rosenberg M.S. Resampling tests for meta-analysis of ecological data. Ecology 78 (1997) 1277-1283
2. Arbuckle J.L. Full information estimation in the presence of incomplete data. In: Marcoulides G.A., and Schumacker R.E. (Eds). Advanced structural equation modeling: Issues and techniques (1996), Erlbaum, Mahwah, NJ 243-277
3. Bauer D.J. Estimating multilevel linear models as structural equation models. Journal of Educational and Behavioral Statistics 28 (2003) 135-167
4. Becker B.J. Synthesizing standardized mean-change measures. British Journal of Mathematical and Statistical Psychology 41 (1988) 257-278
5. Becker B.J. Using results from replicated studies to estimate linear models. Journal of Educational Statistics 17 (1992) 341-362
6. Becker B.J. Corrections to "Using results from replicated studies to estimate linear models.". Journal of Educational Statistics 20 (1995) 100-102
7. Becker B.J. Multivariate meta-analysis. In: Tinsley H.E.A., and Brown S.D. (Eds). Handbook of applied multivariate statistics and mathematical modeling (2000), Academic Press, San Diego, CA 499-525
8. Becker B.J., and Schram C.M. Examining explanatory models through research synthesis. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 357-381
9. Bentler P.M. EQS 6 [Computer software] (2004), Multivariate Software, Encino, CA
10. Berkey C.S., Hoaglin D.C., Mostellar F., and Colditz G.A. A random effects regression model for meta-analysis. Statistics in Medicine 14 (1995) 395-411
11. Biggerstaff B.J., and Tweedie R.L. Incorporating variability in estimates of heterogeneity in the random effects model in meta-analysis. Statistics in Medicine 16 (1997) 753-768
12. Böhning D. Computer assisted analysis of mixtures and applications: Meta-analysis, disease mapping, and others (1999), Chapman & Hall/CRC, London
13. Böhning D. Meta-analysis: A unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality. Methods of Information in Medicine 44 (2005) 127-136
14. Bollen K.A. Structural equations with latent variables (1989), Wiley, New York
15. Bollen K.A., and Long J.S. Testing structural equation models (1993), Sage, Newbury Park, CA
16. Cheung M.W.L. Comparison of approaches to constructing confidence intervals for mediating effects using structural equation models. Structural Equation Modeling 14 (2007) 227-246
17. Cheung M.W.L. Comparison of methods of handling missing time-invariant covariates in latent growth models under the assumption of missing completely at random. Organizational Research Methods 10 (2007) 609-634
18. Cheung, M. W. L. (in press). Constructing approximate confidence intervals for parameters with structural equation models. Structural Equation Modeling
19. Cheung M.W.L., and Chan W. Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods 10 (2005) 40-64
20. Cheung, M. W. L., & Chan, W. (in press). A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling. Structural Equation Modeling
21. Cheung, S. F. (2000). Examining solutions to two practical issues in meta-analysis: Dependent correlations and missing data in correlation matrices. Unpublished doctoral dissertation, Chinese University of Hong Kong.
22. Cochran W.G. The combination of estimates from different experiments. Biometrics 10 (1954) 101-129
23. Cohen J. Multiple regression as a general data-analytic system. Psychological Bulletin 70 (1968) 426-443
24. Cohen J., and Cohen P. Applied multiple regression/correlation analysis for the behavioral sciences (1975), Erlbaum, Hillsdale, NJ
25. Cooper H.M., and Hedges L.V. The handbook of research synthesis (1994), Russell Sage Foundation, New York
26. Curran P.J. Have multilevel models been structural equation models all along?. Multivariate Behavioral Research 38 (2002) 529-569
27. Curran P.J., and Bauer D.J. Building path diagrams for multilevel models. Psychological Methods 12 (2007) 283-297
28. Davison A.C., and Hinkley D.V. Bootstrap methods and their application (1997), Cambridge University Press, New York
29. Demidenko E. Mixed models: Theory and applications (2004), Wiley-Interscience, Hoboken, NJ
30. DerSimonian R., and Laird N. Meta-analysis in clinical trials. Controlled Clinical Trials 7 (1986) 177-188
31. Enders C.K. The performance of the full information maximum likelihood estimator in multiple regression models with missing data. Educational and Psychological Measurement 61 (2001) 713-740
32. Enders C.K. A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling 8 (2001) 128-141
33. Enders C.K. A primer on the use of modern missing-data methods in psychosomatic medicine research. Psychosomatic Medicine 68 (2006) 427-436
34. Fleiss J.L. Measures of effect size for categorical data. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 245-260
35. Furlow C.F., and Beretvas S.N. Meta-analytic methods of pooling correlation matrices for structural equation modeling under different patterns of missing data. Psychological Methods 10 (2005) 227-254
36. Glass G.V. Primary, secondary, and meta-analysis of research. Educational Researcher 5 (1976) 3-8
37. Graham J.W., Olchowski A.E., and Gilreath T.D. How many imputations are really needed? Some practical clarifications of multiple imputation theory. Prevention Science 8 (2007) 206-213
38. Haddock C.K., Rindskopf D., and Shadish W.R. Using odds ratios as effect sizes for meta-analysis of dichotomous data: A primer on methods and issues. Psychological Methods 3 (1998) 339-353
39. Hafdahl, A. R. (2001). Multivariate meta-analysis for exploratory factor analytic research. Unpublished doctoral dissertation, University of North Carolina at Chapel Hill.
40. Hall D.B., and Wang L. Two-component mixtures of generalized linear mixed effects models for cluster correlated data. Statistical Modelling 5 (2005) 21-37
41. Hedges L.V. Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics 6 (1981) 107-128
42. Hedges L.V. Fitting categorical models to effect sizes from a series of experiments. Journal of Educational Statistics 7 (1982) 119-137
43. Hedges L.V. Fitting continuous models to effect size data. Journal of Educational Statistics 7 (1982) 245-270
44. Hedges L.V. A random effects model for effect sizes. Psychological Bulletin 93 (1983) 388-395
45. Hedges L.V. Fixed effects models. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 285-299
46. Hedges L.V. Meta-analysis. In: Rao C.R., and Sinharay S. (Eds). Handbook of statistics: Vol. 26. Psychometrics (2007), Russell Sage Foundation, New York 919-953
47. Hedges L.V., and Olkin I. Statistical methods for meta-analysis (1985), Academic Press, Orlando, FL
48. Hedges L.V., and Vevea J.L. Fixed- and random-effects models in meta-analysis. Psychological Methods 3 (1998) 486-504
49. Higgins J.P.T., and Thompson S.G. Quantifying heterogeneity in a meta-analysis. Statistics in Medicine 21 (2002) 1539-1558
50. Hox J.J. Multilevel analysis: Techniques and applications (2002), Erlbaum, Mahwah, NJ
51. Hox J.J., and de Leeuw E.D. Multilevel models for meta-analysis. In: Reise S.P., and Duan N. (Eds). Multilevel modeling: Methodological advances, issues, and applications (2003), Erlbaum, Mahwah, NJ 90-111
52. 2 index?. Psychological Methods 11 (2006) 193-206
53. Hunter J.E., and Schmidt F.L. Fixed effects vs. random effects meta-analysis models: Implications for cumulative research knowledge. International Journal of Selection and Assessment 8 (2000) 275-292
54. Hunter J.E., and Schmidt F.L. Methods of meta-analysis: Correcting error and bias in research findings. 2nd ed. (2004), Sage, Thousand Oaks, CA
55. Jamshidian M., and Bentler P.M. ML estimation of mean and covariance structures with missing data using complete data routines. Journal of Educational and Behavioral Statistics 24 (1999) 21-41
56. Jöreskog K.G., and Sörbom D. LISREL 8: A user's reference guide (1996), Scientific Software International, Chicago
57. Kalaian H.A., and Raudenbush S.W. A multivariate mixed linear model for meta-analysis. Psychological Methods 1 (1996) 227-235
58. Konstantopoulos S. An introduction to meta-analysis. In: Osborne J.W. (Ed). Best practices in quantitative methods (2008), Sage, Thousand Oaks, CA 177-194
59. Konstantopoulos S., and Hedges L.V. Meta-analysis. In: Kaplan M. (Ed). Handbook of quantitative methods in the social sciences (2004), Sage, Thousand Oaks, CA 281-297
60. Kutner M.H., Nachtsheim C.J., Neter J., and Li W. Applied linear statistical models. 5th ed. (2005), McGraw-Hill Irwin, Boston
61. Lipsey M.W., and Wilson D.B. Practical meta-analysis (2001), Sage, Thousand Oaks, CA
62. Little R.J.A. Regression with missing X's: A review. Journal of the American Statistical Association 87 (1992) 1227-1237
63. Lo Y., Mendell N., and Rubin D.B. Testing the number of components in a normal mixture. Biometrika 88 (2001) 767-778
64. Lubke G.H., and Muthén B.O. Investigating population heterogeneity with factor mixture models. Psychological Methods 10 (2005) 21-39
65. Lubke G., and Muthén B.O. Performance of factor mixture models as a function of model, size, covariate effects, and class-specific parameters. Structural Equation Modeling 14 (2007) 26-47
66. Lubke G., and Neale M.C. Distinguishing between latent classes and continuous factors: Resolution by maximum likelihood?. Multivariate Behavioral Research 41 (2006) 499-532
67. MacIntosh R., and Hashim S. Converting MIMIC model parameters to IRT parameters in DIF analysis. Applied Psychological Measurement 27 (2003) 372-379
68. McLachlan G.J., and Peel D. Finite mixture models (2000), Wiley, New York
69. Mehta P.D., and Neale M.C. People are variables too: Multilevel structural equation modeling. Psychological Methods 10 (2005) 259-284
70. Morris S.B., and DeShon R.P. Combining effect size estimates in meta-analysis with repeated measures and independent-groups designs. Psychological Methods 7 (2002) 105-125
71. Muthén B. Latent variable mixture modeling. In: Marcoulides G.A., and Schumacker R.E. (Eds). New developments and techniques in structural equation modeling (2001), Erlbaum, Mahwah, NJ 1-33
72. Muthén B. Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In: Kaplan D. (Ed). Handbook of quantitative methodology for the social sciences (2004), Sage, Newbury Park, CA 345-368
73. Muthén B. Mplus technical appendices (2004). http://www.statmodel.com/download/techappen.pdf Retrieved from http://www.statmodel.com/download/techappen.pdf
74. Muthén B., and Asparouhov T. Modeling of heteroscedastic measurement errors (2002). http://www.statmodel.com/download/webnotes/mc3.pdf Retrieved from http://www.statmodel.com/download/webnotes/mc3.pdf
75. Muthén B., and Asparouhov T. Modeling interactions between latent and observed continuous variables using maximum-likelihood estimation in Mplus (2003). http://www.statmodel.com/download/webnotes/webnote6.pdf Retrieved from http://www.statmodel.com/download/webnotes/webnote6.pdf
76. Muthén B., Kaplan D., and Hollis M. On structural equation modeling with data that are not missing completely at random. Psychometrika 52 (1987) 431-462
77. Muthén L.K., and Muthén B.O. Mplus user's guide. 5th ed. (2007), Muthén & Muthén, Los Angeles
78. National Research Council. Combining information: Statistical issues and opportunities for research (1992), National Academy Press, Washington, DC
79. Neale M.C. Individual fit, heterogeneity, and missing data in multigroup structural equation modeling. In: Little T.D., Schnabel K.U., and Baumert J. (Eds). Modeling longitudinal and multilevel data: Practical issues, applied approaches and specific examples (2000), Erlbaum, Hillsdale, NJ 249-267
80. Neale M.C., Boker S.M., Xie G., and Maes H.H. Mx: Statistical modeling (7th ed.) (2006) Available from Virginia Commonwealth University, Department of Psychiatry, Box 900126, Richmond, VA 23298.
81. Overton R.C. A comparison of fixed-effects and mixed (random-effects) models for meta-analysis tests of moderator variable effects. Psychological Methods 3 (1998) 354-379
82. Petticrew M., and Roberts H. Systematic reviews in the social sciences: A practical guide (2006), Blackwell, Malden, MA
83. Pigott T.D. Methods for handling missing data in research synthesis. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 163-175
84. Pigott T.D. Missing predictors in models of effect size. Evaluation & the Health Professions 24 (2001) 277-307
85. R Development Core Team. R: A language and environment for statistical computing (2008). http://www.r-project.org Available from http://www.r-project.org
86. Raudenbush S.W. Random effects models. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 301-321
87. Raudenbush S.W., Becker B.J., and Kalaian H. Modeling multivariate effect sizes. Psychological Bulletin 103 (1988) 111-120
88. Raudenbush S.W., and Bryk A.S. Hierarchical linear models: Applications and data analysis methods. 2nd ed. (2002), Sage, Thousand Oaks, CA
89. Rosenthal R. Parametric measures of effect size. In: Cooper H., and Hedges L.V. (Eds). The handbook of research synthesis (1994), Russell Sage Foundation, New York 231-244
90. Rothstein H.R., Sutton A.J., and Borenstein M. Publication bias in meta-analysis: Prevention, assessment and adjustments (2005), Wiley, Chichester, United Kingdom
91. Rovine M.J., and Molenaar P.C.M. A structural modeling approach to a multilevel random coefficients model. Multivariate Behavioral Research 35 (2000) 51-88
92. Rovine M.J., and Molenaar P.C.M. A structural equations modeling approach to the general linear mixed model. In: Collins L.M., and Sayer A.G. (Eds). New methods for the analysis of change (2001), American Psychological Association, Washington, DC 65-96
93. Rubin D.B. Multiple imputation for nonresponse in surveys (1987), Wiley, New York
94. Schafer J.L. Analysis of incomplete multivariate data (1997), Chapman & Hall, London
95. Schafer J.L., and Graham J.W. Missing data: Our view of the state of the art. Psychological Methods 7 (2002) 147-177
96. Schafer J.L., and Olsen M.K. Multiple imputation for multivariate missing data problems: A data analyst's perspective. Multivariate Behavioral Research 33 (1998) 545-571
97. Schwartz G. Estimating the dimension of a model. The Annals of Statistics 6 (1978) 461-464
98. Shadish W.R. Meta-analysis and the exploration of causal mediating processes: A primer of examples, methods, and issues. Psychological Methods 1 (1996) 47-65
99. Sidik K., and Jonkman J.N. Robust variance estimation for random effects meta-analysis. Computational Statistics & Data Analysis 50 (2006) 3681-3701
100. Skrondal A., and Rabe-Hesketh S. Generalized latent variable modeling: Multilevel, longitudinal, and structural equation models (2004), Chapman & Hall, Boca Raton, FL
101. Stapleton L.M., and Leite W.L. A review of syllabi for a sample of structural equation modeling courses. Structural Equation Modeling 12 (2005) 642-664
102. Stoel R.D., Galindo-Garre F., Dolan C., and van den Wittenboer G. On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints. Psychological Methods 11 (2006) 439-455
103. Sutton A.J., Abrams K.R., Jones D.R., Sheldon T.A., and Song F. Methods for meta-analysis in medical research (2000), Wiley, Chichester, United Kingdom
104. Sutton A.J., and Pigott T.D. Bias in meta-analysis: Induced by incompletely reported studies. In: Rothstein H.R., Sutton A.J., and Borenstein M. (Eds). Publication bias in meta-analysis: Prevention, assessment and adjustments (2005), Wiley, Chichester, United Kingdom 223-239
105. Takane Y., and de Leeuw J. On the relationship between item response theory and factor analysis of discretized variables. Psychometrika 52 (1987) 393-408
106. Takkouche B., Cadarso-Suarez C., and Spiegelman D. Evaluation of old and new tests of heterogeneity in epidemiologic meta-analysis. American Journal of Epidemiology 150 (1999) 206-215
107. Thomas H. A mixture model for distributions of correlation coefficients. Psychometrika 54 (1989) 523-530
108. Thompson S.G., and Higgins J.P.T. How should meta-regression analyses be undertaken and interpreted?. Statistics in Medicine 21 (2002) 1559-1573
109. Thompson S.G., and Sharp S.J. Explaining heterogeneity in meta-analysis: A comparison of methods. Statistics in Medicine 18 (1999) 2693-2708
110. Van den Noortgate W., and Onghena P. Parametric and nonparametric bootstrap methods for meta-analysis. Behavior Research Methods 37 (2005) 11-22
111. Verbeke G., and Lesaffre E. A linear mixed-effects model with heterogeneity in the random-effects population. Journal of the American Statistical Association 91 (1996) 217-221
112. Viechtbauer W. Bias and efficiency of meta-analytic variance estimators in the random-effects model. Journal of Educational and Behavioral Statistics 30 (2005) 261-293
113. Viechtbauer W. MiMa: An S-Plus/R function to fit meta-analytic mixed-, random-, and fixed-effects models [Computer software and manual] (2006). http://www.wvbauer.com/ Retrieved from http://www.wvbauer.com/
114. Viechtbauer W. Confidence intervals for the amount of heterogeneity in meta-analysis. Statistics in Medicine 26 (2007) 37-52
115. Viechtbauer W. Hypothesis tests for population heterogeneity in meta-analysis. British Journal of Mathematical and Statistical Psychology 60 (2007) 29-60
116. Viswesvaran C., and Ones D.S. Theory testing: Combining psychometric meta-analysis and structural equations modeling. Personnel Psychology 48 (1995) 865-885
117. Wang X., Schumitzky A., and D'Argenio D.Z. Nonlinear random effects mixture models: Maximum likelihood estimation via the EM algorithm. Computational Statistics & Data Analysis 51 (2007) 6614-6623
118. Xia Y., Weng S., Zhang C., and Li S. Mixture random effect model based meta-analysis for medical data mining. In: Perner P., and Imiya A. (Eds). Machine learning and data mining in pattern recognition (2005), Springer, Berlin 630-640
119. Yuan K.-H., and Bentler P.M. Robust procedures in structural equation modeling. In: Lee S.-Y. (Ed). Handbook of latent variable and related models (2007), Elsevier/North-Holland, Amsterdam 367-397
120. Yung Y.-F. Finite mixtures in confirmatory factor-analysis models. Psychometrika 62 (1997) 297-330