Structural Equation Modeling Approaches for Analyzing Partially Nested Data

REFERENCES

• Achenbach , T. and Rescorla , L. 2001 . Manual for ASEBA School-Age Forms and Profiles. , Burlington , VT : University of Vermont, Research Center for Children, Youth, and Families .
   Google Scholar
• Asparouhov , T. and Muthén , B. 2007 . Constructing covariates in multilevel regression (Web Note 11) Retrieved from http://www.statmodel.com
   Google Scholar
• Baldwin , S. , Bauer , D. , Stice , E. and Rohde , P. 2011 . Evaluating models for partially clustered designs . Psychological Methods , 16 : 149 – 165 .
   PubMed Web of Science ®Google Scholar
• Bauer , D. J. 2003 . Estimating multilevel linear models as structural equation models . Journal of Educational and Behavioral Statistics , 28 : 135 – 167 .
   Web of Science ®Google Scholar
• Bauer , D. J. , Preacher , K. J. and Gil , K. M. 2006 . Conceptualizing and testing random indirect effects and moderated mediation in multilevel models: New procedures and recommendations . Psychological Methods , 11 : 142 – 163 .
   PubMed Web of Science ®Google Scholar
• Bauer , D. J. , Sterba , S. K. and Hallfors , D. D. 2008 . Evaluating group-based interventions when control participants are ungrouped . Multivariate Behavioral Research , 43 : 210 – 236 .
   PubMed Web of Science ®Google Scholar
• Becker , S. , Mlay , R. and Schwandt , H. 2010 . Comparing couples’ and individual voluntary counseling and testing for HIV at antenatal clinics in Tanzania: A randomized trial . AIDS Behavior , 14 : 558 – 566 .
   PubMed Web of Science ®Google Scholar
• Beran , T. and Violato , C. 2010 . Structural equation modeling in medical research: A primer . BMC Research Notes , 3 : 1 – 10 .
   PubMedGoogle Scholar
• Candel , M. and van Breukelen , G. 2009 . Varying cluster sizes in trials with clusters in one treatment arm: Sample size adjustments when testing treatment effects with linear mixed models . Statistics in Medicine , 28 : 2307 – 2324 .
   PubMed Web of Science ®Google Scholar
• Candel , M. and van Breukelen , G. 2010 . D-optimality of unequal versus equal cluster sizes for mixed effects linear regression analysis of randomized trials with clusters in one treatment arm . Computational Statistics and Data Analysis , 54 : 1906 – 1920 .
   Web of Science ®Google Scholar
• Coatsworth , J. , Duncan , L. , Greenberg , M. and Nix , R. 2010 . Changing parent's mindfulness, child management skills and relationship quality with their youth: Results from a randomized pilot intervention trial . Journal of Child and Family Studies , 19 : 203 – 217 .
   PubMed Web of Science ®Google Scholar
• Cole , D. A. , Maxwell , S. E. , Arvey , R. and Salas , E. 1993 . Multivariate group comparisons of variable systems: MANOVA and structural equation modeling . Psychological Bulletin , 114 : 174 – 184 .
   Web of Science ®Google Scholar
• Compas , B. E. , Champion , J. E. , Forehand , R. , Cole , D. A. , Reeslund , K. L. , Fear , J. and … Roberts , L. 2010 . Coping and parenting: mediators of 12-month outcomes of a family group cognitive-behavioral preventive intervention with families of depressed parents . Journal of Consulting and Clinical Psychology , 78 : 623 – 634 .
   PubMed Web of Science ®Google Scholar
• Compas , B. E. , Forehand , R. , Keller , G. , Champion , A. , Reeslund , K. L. , McKee , L. and … Cole , D. A. 2009 . Randomized clinical trial of a family cognitive-behavioral preventive intervention for children of depressed parents . Journal of Consulting and Clinical Psychology , 77 : 1009 – 1020 .
   Web of Science ®Google Scholar
• Compas , B. E. , Forehand , R. , Thigpen , J. C. , Keller , G. , Hardcastle , E. J. , Cole , D. A. and … Roberts , L. 2011 . Family group cognitive-behavioral preventive intervention for families of depressed parents: 18- and 24-month outcomes . Journal of Consulting and Clinical Psychology , 79 : 488 – 499 .
   PubMed Web of Science ®Google Scholar
• Connor-Smith , J. , Compas , B. , Wadsworth , M. , Thomsen , A. and Saltzman , H. 2000 . Responses to stress in adolescence: Measurement of coping and involuntary responses to stress . Journal of Consulting and Clinical Psychology , 68 : 976 – 992 .
   PubMed Web of Science ®Google Scholar
• Croon , M. A. and van Veldhoven , J. P. 2007 . Predicting group-level outcome variables from variables measured at the individual level: A latent variable multilevel model . Psychological Methods , 12 : 45 – 57 .
   PubMed Web of Science ®Google Scholar
• Curran , P. J. 2003 . Have multilevel models been structural equation models all along? . Multivariate Behavioral Research , 38 : 529 – 569 .
   PubMed Web of Science ®Google Scholar
• Curran , P. J. and Bauer , D. J. 2011 . The disaggregation of within-person and between-person effects in longitudinal models of change . Annual Review of Psychology , 62 : 583 – 619 .
   PubMed Web of Science ®Google Scholar
• Curran , P. J. , Lee , T. , Howard , A. , Lane , S. and MacCallum , R. 2012 . “ Disaggregating within-person and between-person effects in multilevel and structural equation growth models ” . In Advances in longitudinal methods in the social and behavioral sciences , Edited by: Harring , J. and Hancock , G. 217 – 253 . Charlotte , NC : Information Age .
   Google Scholar
• Dannon , P. , Gon-Usishkin , M. , Gelbert , A. , Lowengrub , K. and Grunhaus , L. 2004 . Cognitive behavioral group therapy in panic disorder patients: The efficacy of CBGT versus drug treatment . Annals of Clinical Psychiatry , 16 : 41 – 46 .
   PubMedGoogle Scholar
• Enders , C. and Tofighi , D. 2007 . Centering predictors in cross-sectional multilevel models: A new look at an old issue . Psychological Methods , 12 : 121 – 138 .
   PubMed Web of Science ®Google Scholar
• Goldstein , H. 1995 . Multilevel statistical models (2nd ed.) , New York , NY : Wiley .
   Google Scholar
• Goldstein , H. 2003 . Multilevel statistical models (3rd ed.) , New York , NY : Oxford .
   Google Scholar
• Haugli , L. , Steen , E. , Laerum , E. , Nygard , R. and Finset , A. 2001 . Learning to have less pain: Is it possible? A one-year follow-up study of the effects of a personal construct group learning program on patients with chronic musculoskeletal pain . Patient Education and Counseling , 45 : 111 – 118 .
   PubMed Web of Science ®Google Scholar
• Hedeker , D. and Gibbons , R. D. 2006 . Longitudinal data analysis. , Hoboken , NJ : Wiley .
   Google Scholar
• Heller-Boersma , J. , Schmidt , U. and Edmonds , D. 2007 . A randomized controlled trial of a cognitive-behavioural group intervention versus waiting-list control for women with uterovaginal agenesis (Mayer–Rokitansky–Kuster–Hauser syndrome: MRKH) . Human Reproduction , 22 : 2296 – 2301 .
   PubMed Web of Science ®Google Scholar
• Hofmann , D. and Gavin , M. 1998 . Centering decisions in hierarchical linear models: Implications for research in organizations . Journal of Management , 24 : 623 – 641 .
   Web of Science ®Google Scholar
• Hoyle , R. and Smith , G. 1994 . Formulating clinical research hypotheses as structural equation models: A conceptual overview . Journal of Consulting and Clinical Psychology , 62 : 429 – 440 .
   PubMed Web of Science ®Google Scholar
• Jarrett , R. , Schaffer , M. , McIntire , D. , Witt-Browder , A. , Kraft , D. and Risser , R. 1999 . Treatment of atypical depression with cognitive therapy or phenelzine: A double-blind, placebo-controlled trial . Archives of General Psychiatry , 56 : 431 – 437 .
   PubMed Web of Science ®Google Scholar
• Jöreskog , K. 1971 . Simultaneous factor analysis in several populations . Psychometrika , 36 : 409 – 426 .
   Web of Science ®Google Scholar
• Jöreskog , K. and Sörbom , D. 2006 . LISREL 8.8 for Windows [Computer software] , Lincolnwood , IL : Scientific Software International .
   Google Scholar
• Kaplan , D. 2009 . Structural equation modeling: Foundations and extensions (2nd ed.) , Newbury Park , CA : Sage .
   Google Scholar
• Kim , S.-Y. , Mun , E.-Y. and Smith , S. in press . Using mixture models with known class membership to address incomplete covariance structures in multiple-group growth models . British Journal of Mathematical and Statistical Psychology , doi: 10.1111/bmsp.12008
   Web of Science ®Google Scholar
• Kirschner , F. , Paas , F. , Kirschner , P. and Janssen , J. 2011 . Differential effects of problem-solving demands on individual and collaborative learning outcomes . Learning and Instruction , 21 : 587 – 599 .
   Web of Science ®Google Scholar
• Korendijk , E. , Maas , C. , Hox , J. and Moerbeek , M. 2012 . “ The robustness of the parameter and standard error estimates in trials with partially nested data: A simulation study ” . In Robustness and optimal design issues for cluster randomized trials , Edited by: Korendijk , E. 59 – 94 . Dissertation, Utrecht University .
   Google Scholar
• Kreft , I. G. , de Leeuw , J. and Aiken , L. S. 1995 . The effects of different forms of centering in hierarchical linear models . Multivariate Behavioral Research , 30 : 1 – 21 .
   PubMed Web of Science ®Google Scholar
• Ladouceur , R. , Dugas , M. , Freeston , M. , Leger , E. , Gagnon , F. and Thibodeau , N. 2000 . Efficacy of a cognitive-behavioral treatment for generalized anxiety disorder: Evaluation in a controlled trial . Journal of Consulting and Clinical Psychology , 68 : 957 – 964 .
   PubMed Web of Science ®Google Scholar
• Lee , K. J. and Thompson , S. G. 2005 . The use of random effects models to allow for clustering in individually randomized trials . Clinical Trials , 2 : 163 – 173 .
   PubMed Web of Science ®Google Scholar
• Leyland , A. and Goldstein , H. 2001 . Multilevel modeling of health statistics. , New York , NY : Wiley .
   Google Scholar
• Liang , J. and Bentler , P. 2004 . An EM Algorithm for fitting two-level structural equation models . Psychometrika , 69 : 101 – 122 .
   Web of Science ®Google Scholar
• Lüdtke , O. , Marsh , H. , Robitzsch , A. , Trautwein , U. , Asparouhov , T. and Muthén , B. 2008 . The multilevel latent covariate model: A new, more reliable approach to group-level effects in contextual studies . Psychological Methods , 13 : 203 – 229 .
   PubMed Web of Science ®Google Scholar
• MacKinnon , D. P. , Lockwood , C. M. and Williams , J. 2004 . Confidence limits for the indirect effect: Distribution of the product and resampling methods . Multivariate Behavioral Research , 39 : 99 – 128 .
   PubMed Web of Science ®Google Scholar
• McDonald , R. 1994 . The bilevel reticular action model for path analysis with latent variables . Sociological Methods and Research , 22 : 399 – 413 .
   Web of Science ®Google Scholar
• McDonald , R. and Goldstein , H. 1989 . Balanced versus unbalanced designs for linear structural relations in two-level data . British Journal of Mathematical and Statistical Psychology , 42 : 215 – 232 .
   Web of Science ®Google Scholar
• Mehta , P. D. and Neale , M. C. 2005 . People are variables too: Multilevel structural equation modeling . Psychological Methods , 10 : 259 – 284 .
   PubMed Web of Science ®Google Scholar
• Moerbeek , M. and Wong , W. 2008 . Sample size formulae for trials comparing group and individual treatments in a multilevel model . Statistics in Medicine , 27 : 2850 – 2864 .
   PubMed Web of Science ®Google Scholar
• Muthén , B. O. 1987 . LISCOMP: Analysis of linear structural equations with a comprehensive measurement model. Theoretical integration and user's guide , Mooresville , IN : SSI .
   Google Scholar
• Muthén , B. O. Mean and covariance structure analysis of hierarchical data . Presentation given at the annual meeting of the Psychometric Society, Princeton, NJ ,
   Google Scholar
• Muthén , B. O. 2002 . Beyond SEM: General latent variable modeling . Behaviormetrika , 29 : 81 – 117 .
   Google Scholar
• Muthén , B. O. and Asparouhov , T. 2002 . Modeling of heteroscedastic measurement errors (Mplus Web Note 3) Retrieved from www.statmodel.com
   Google Scholar
• Muthén , B. O. and Asparouhov , T. 2009 . “ Growth mixture modeling: Analysis with non-Gaussian random effects ” . In Longitudinal data analysis , Edited by: Davidian , F. G. , Verbeke , M. G. and Molenberghs , G. 143 – 165 . Boca Raton , FL : Chapman & Hall/CRC Press .
   Google Scholar
• Muthén , L. K. and Muthén , B. O. 1998 . Mplus users’ guide. (7th ed.) , Los Angeles , CA : Author . –2013
   Google Scholar
• Neuhaus , J. and Kalbfleisch , J. 1998 . Between- and within-cluster covariate effects in the analysis of clustered data . Biometrics , 54 : 638 – 645 .
   PubMed Web of Science ®Google Scholar
• Pisinger , C. , Vestbø , J. , Borch-Johnsen , K. and Jørgensen , T. 2005 . Smoking cessation intervention in a large randomised population-based study: The Inter99 study . Preventive Medicine , 40 : 285 – 292 .
   PubMed Web of Science ®Google Scholar
• Preacher , K. J. and Selig , J. P. 2012 . Advantages of Monte Carlo confidence intervals for indirect effects . Communication Methods and Measures , 6 : 77 – 98 .
   Google Scholar
• Preacher , K. J. , Zyphur , M. J. and Zhang , Z. 2010 . A general multilevel SEM framework for assessing multilevel mediation . Psychological Methods , 15 : 209 – 233 .
   PubMed Web of Science ®Google Scholar
• Price , M. and Anderson , P. 2011 . The impact of cognitive behavioral therapy on post event processing among those with social anxiety disorder . Behaviour Research and Therapy , 49 : 132 – 137 .
   PubMed Web of Science ®Google Scholar
• Raudenbush , S. W. and Bryk , A. S. 2002 . Hierarchical linear models: Applications and data analysis methods (2nd ed.) , Newbury Park , CA : Sage .
   Google Scholar
• Roberts , C. and Roberts , S. A. 2005 . Design and analysis of clinical trials with clustering effects due to treatment . Clinical Trials , 2 : 152 – 162 .
   PubMed Web of Science ®Google Scholar
• Russell , D. , Kahn , J. , Spoth , R. and Altmaier , E. 1998 . Analyzing data from experimental studies: A latent variable structural equation modeling approach . Journal of Consulting Psychology , 45 : 18 – 29 .
   Google Scholar
• Sanders , E. 2011 . Multilevel analysis methods for partially nested cluster randomized trials (Unpublished doctoral dissertation) , Seattle: University of Washington .
   Google Scholar
• Snijders , T. and Bosker , R. 1999 . Multilevel analysis: An introduction to basic and advanced multilevel modeling , London , UK : Sage .
   Google Scholar
• Thomas , P. , Thomas , S. , Kersten , P. , Jones , R. , Nock , A. , Slingsby , V. and … Hillier , C. 2010 . Multi-centre parallel arm randomised controlled trial to assess the effectiveness and cost-effectiveness of a group-based cognitive behavioral approach to managing fatigue in people with multiple sclerosis . BMC Neurology , 10 : 1 – 12 .
   PubMed Web of Science ®Google Scholar
• Thompson , L. , Gallagher , D. and Breckenridge , J. 1987 . Comparative effectiveness of psychotherapies for depressed elders . Journal of Consulting and Clinical Psychology , 55 : 385 – 390 .
   PubMed Web of Science ®Google Scholar
• Tomarken , A. and Waller , N. 2005 . Structural equation modeling: Strengths, limitations, and misconceptions . Annual Review of Clinical Psychology , 1 : 31 – 65 .
   PubMed Web of Science ®Google Scholar
• Vadasy , P. F. and Sanders , E. A. 2008 . Benefits of repeated reading intervention for low achieving fourth- and fifth-grade students . Remedial and Special Education , 29 : 235 – 249 .
   Web of Science ®Google Scholar
• Van Minnen , A. , Hoogduin , K. , Keijsers , G. , Hellenbrand , I. and Hendriks , G. 2003 . Treatment of trichotillomania with behavioral therapy or fluoxetine . Archives of General Psychiatry , 60 : 517 – 522 .
   PubMed Web of Science ®Google Scholar
• Widaman , K. , Grimm , K. , Early , D. , Robins , R. and Conger , R. 2013 . Investigating factorial invariance of latent variables across populations when manifest variables are missing completely . Structural Equation Modeling , 20 : 384 – 408 .
   PubMed Web of Science ®Google Scholar