A State Space Modeling Approach to Mediation Analysis

Journal of Educational and Behavioral Statistics

Volumn 39, Issue 2, 2014, Pages 117-143

  Gu, Fei ^a   Preacher, Kristopher J ^b   Ferrer, Emilio ^c  

^a MCGILL UNIVERSITY   (Canada)

^b VANDERBILT UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

mediation; state space model

Indexed keywords

EID: 84898897601     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/1076998614524823     Document Type: Article

References (112)

1. Albert J. M.Mediation analysis via potential outcomes models.Statistics in Medicine. 2008;27:1282-1304.
2. Allport G. W.Personality: A psychological interpretation. New York, NY: Holt, Rinehart, and Winston; 1937:.
3. Aoki M.State space modeling of time series. Berlin, Germany: Springer; 1987:.
4. Baron R. M.,Kenny D. A.The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations.Journal of Personality & Social Psychology. 1986;51:1173-1182.
5. Bhattacharya S.,Ho M.-H. R.,Purkayastha S.A Bayesian approach to modeling dynamic effective connectivity with fMRI data.NeuroImage. 2006;30:794-812.
6. Bhattacharya S.,Maitra R.A nonstationary nonparametric Bayesian approach to dynamically modeling effective connectivity in functional magnetic resonance imaging experiments.The Annals of Applied Statistics. 2011;5:1183-1206.
7. Bollen K. A.,Stine R.Direct and indirect effects: Classical and bootstrap estimates of variability.Sociological Methodology. 1990;20:115-140.
8. Brose A.,Ram N.Handbook of research methods for studying daily life. Mehl M. R.Conner T. S., ed. New York, NY: The Guilford Press; 2012:43-61.
9. Browne M. W.,Nesselroade J. R.Contemporary psychometrics. Maydeu-Olivares A.McArdle J. J., ed. New York, NY: Routledge; 2005:415-452.
10. Card N. A.Handbook of research methods for studying daily life. Mehl M. R.Conner T. S., ed. New York, NY: The Guilford Press; 2012:479-494.
11. Cattell R. B.Problems in measuring change. Harris C. W., ed. Madison: University of Wisconsin Press; 1963:167-198.
12. Cattell R. B.,Cattell A. K. S.,Rhymer R. M.P-technique demonstrated in determining psychophysical source traits in a normal individual.Psychometrika. 1947;12:267-288.
13. Cheong J.,MacKinnon D. P.,Khoo S. T.Investigation of mediational processes using parallel process latent growth curve modeling.Structural Equation Modeling. 2003;10:238-262.
14. Chow S.-M.,Hamaker E. L.,Allaire J. C.Using innovative outliers to detect discrete shifts in dynamics in group-based state-space models.Multivariate Behavioral Research. 2009;44:465-496.
15. Chow S.-M.,Hamaker E. L.,Fujita F.,Boker S. M.Representing time-varying cyclic dynamics using multiple-subject state-space models.British Journal of Mathematical and Statistical Psychology. 2009;62:683-716.
16. Chow S.-M.,Ho M.-H. R.,Hamaker E. L.,Dolan C. V.Equivalence and differences between structural equation modeling and state-space modeling techniques.Structural Equation Modeling. 2010;17:303-332.
17. Chow S.-M.,Nesselroade J. R.,Shifren K.,McArdle J. J.Dynamic structure of emotions among individuals with Parkinson's disease.Structural Equation Modeling. 2004;11:560-582.
18. Chow S.-M.,Tang N.,Yuan Y.,Song X.,Zhu H.Bayesian estimation of semiparametric nonlinear dynamic factor analysis models using the Dirichlet process prior.British Journal of Mathematical and Statistical Psychology. 2011;64:69-106.
19. Chow S.-M.,Zu J.,Shifren K.,Zhang G.Dynamic factor analysis models with time-varying parameters.Multivariate Behavioral Research. 2011;46:303-339.
20. Cole D. A.,Maxwell S. E.Testing meditational models with longitudinal data: Questions and tips in the use of structural equation modeling.Journal of Abnormal Psychology. 2003;112:558-577.
21. Collins M. L.,Graham J. W.The effect of timing and spacing of observations in longitudinal studies of tobacco and other drug use: Temporal design considerations.Drug and Alcohol Dependence. 2002;68:85-96.
22. Collins M. L.,Graham J. W.,Flaherty B. P.An alternative framework for defining mediation.Multivariate Behavioral Research. 1998;33:295-312.
23. Commandeur J. J. F.,Koopman S. J.An introduction to state space time series analysis. New York, NY: Oxford University Press; 2007:.
24. DolanC. V. (2005). MKFM6: Multi-group, multi-subject stationary time series modeling based on the Kalman filter. Retrieved December 1, 2004, fromhttp://users.fmg.uva.nl/cdoman/.
25. Durbin J.,Koopman S. J.Time series analysis by state space methods. New York, NY: Oxford University Press; 2001:.
26. Ferrer E.,Nesselroade J. R.Modeling affective processes in dyadic relations via dynamic factor analysis.Emotion. 2003;3:344-360.
27. Ferrer E.,Steele J.,Hsieh F.Analyzing dynamics of affective dyadic interactions using patterns of intra- and inter-individual variability.Multivariate Behavioral Research. 2012;47:136-171.
28. Ferrer E.,Widaman K. F.Modeling dyadic and interdependent data in the developmental and behavioral sciences. Card N. A.Selig J. P.Little T. D., ed. Hillsdale, NJ: Psychology Press; 2008:107-137.
29. Gollob H. F.,Reichardt C. S.Best methods for the analysis of change: Recent advances, unanswered questions, future directions. Collins L. M.Horn J. L., ed. Washington, DC: American Psychological Association; 1991:243-259.
30. Gu F.,Yung Y.-F.A SAS/IML program using the Kalman filter for estimating state space model.Behavior Research Methods. 2013;45:38-53.
31. Hamagami F.,McArdle J. J.Data analytic techniques for dynamical systems. Boker S. M.Wegner M. L., ed. Mahwah, NJ: Lawrence Erlbaum; 2007:47-85.
32. Hamaker E. L.Handbook of research methods for studying daily life. Mehl M. R.Conner T. S., ed. New York, NY: The Guilford Press; 2012:43-61.
33. Hamaker E. L.,Dolan C. V.,Molenaar P. C. M.Statistical modeling of the individual: Rational and application of multivariate stationary time series analysis.Multivariate Behavioral Research. 2005;40:207-233.
34. Harvey A. C.Forecasting, structural time series models and the Kalman filter. Princeton, NJ: Princeton University Press; 1989:.
35. Hayes A. F.Beyond Baron and Kenny: Statistical mediation analysis in the new millennium.Communication Monographs. 2009;76:408-420.
36. Hershberger S. L.,Corneal S. E.,Molenaar P. C. M.Dynamic factor analysis: An application to emotional response patterns underlying daughter/father and stepdaughter/stepfather relationships.Structural Equation Modeling. 1994;2:31-52.
37. Ho M.-H. R.,Ombao H.,Shumway R.A state-space approach to modelling brain dynamics.Statistica Sinica. 2005;15:407-425.
38. Ho M.-H. R.,Shumway R.,Ombao H.Models for intensive longitudinal data. Walls T. A.Schafer J. L., ed. New York, NY: Oxford University Press; 2006:148-170.
39. Imai K.,Keele L.,Tingley D.A general approach to causal mediation analysis.Psychological Methods. 2010;15:309-334.
40. Judd C. M.,Kenny D. A.Process analysis: Estimating mediation in treatment evaluations.Evaluation Review. 1981;5:602-619.
41. Judd C. M.,Kenny D. A.,McClelland G. H.Estimating and testing mediation and moderation in within-participant designs.Psychological Methods. 2001;6:115-134.
42. Kalman R. E.A new approach to linear filtering and prediction problems.Transactions of the ASME-Journal of Basic Engineering (Series D). 1960;82:35-45.
43. Kelderman H.,Molenaar P. C. M.The effect of individual differences in factor loadings on the standard factor model.Multivariate Behavioral Research. 2007;42:435-456.
44. Kenny D. A.Correlation and causality. New York, NY: John Wiley; 1979:.
45. Lamiell J. T.Toward an idiothetic psychology of personality.American Psychologist. 1981;36:276-289.
46. Lamiell J. T.Once more into the breach: Why individual differences research cannot advance personality theory. August, Atlanta, GA: Paper presented at the annual meeting of the American Psychological Association; 1988:.
47. Lütkepohl H.New introduction to multiple time series analysis. Berlin, Germany: Springer; 2005:.
48. MacCallum R. C.,Ashby G. F.Relationships between linear systems theory and covariance structure modeling.Journal of Mathematical Psychology. 1986;30:1-27.
49. MacKinnon D. P.Introduction to statistical mediation analysis. New York, NY: Lawrence Erlbaum; 2008:.
50. MacKinnon D. P.,Lockwood C. M.,Williams J.Confidence limits for the indirect effect: Distribution of the product and resampling methods.Multivariate Behavioral Research. 2004;39:99-128.
51. Maxwell S. E.,Cole D. A.Bias in cross-sectional analyses of longitudinal mediation.Psychological Methods. 2007;12:23-44.
52. Maxwell S. E.,Cole D. A.,Mitchell M. A.Bias in cross-sectional analyses of longitudinal mediation: Partial and complete mediation under an autoregressive model.Multivariate Behavioral Research. 2011;46:816-841.
53. McArdle J. J.Structural equation modeling: Present and future. Cudeck R.du Toit S.Sorbom D., ed. Lincolnwood, IL: Scientific Software International; 2001:341-380.
54. McArdle J. J.,Nesselroade J. R.Life-span developmental psychology: Methodological contributions. Cohen S. H.Reese H. W., ed. Hillsdale, NJ: Lawrence Erlbaum; 1994:223-267.
55. Mitteness L. S.,Nesselroade J. R.Attachment in adulthood: Longitudinal investigation of mother-daughter affective interdependencies by p-technique factor analysis.The Southern Psychologist. 1987;3:37-44.
56. Molenaar P. C. M.A dynamic factor model for the analysis of multivariate time series.Psychometrika. 1985;50:181-202.
57. Molenaar P. C. M.Latent variable analysis. van Eye A.Clogg C. C., ed. Thousand Oaks, CA: Sage; 1994:155-180.
58. Molenaar P. C. M.A manifesto on psychology as idiographic science: Bring the person back into scientific psychology, this time forever.Measurement. 2004;2:201-218.
59. Molenaar P. C. M.On the implications of the classical ergodic theorems: Analysis of developmental processes has to focus on intra-individual variation.Developmental Psychobiology. 2008a;50:60-69.
60. Molenaar P. C. M.Handbook of cognitive aging: Interdisciplinary perspectives. Hofer S. M.Alwin D. F., ed. Thousand Oaks, CA: Sage; 2008b:90-104.
61. Molenaar P. C. M.Note on optimization of individual psychotherapeutic processes.Journal of Mathematical Psychology. 2010a;54:208-213.
62. Molenaar P. C. M.Testing all six person-oriented principles in dynamic factor analysis.Development and Psychopathology. 2010b;22:255-259.
63. Molenaar P. C. M.,Boomsma D. I.,Dolan C. V.A third source of developmental differences.Behavior Genetics. 1993;23:519-524.
64. Molenaar P. C. M.,Campbell C. G.The new person-specific paradigm in psychology.Current Directions in Psychological Science. 2009;18:112-117.
65. Molenaar P. C. M.,de Gooijer J. G.,Schmitz B.Dynamic factor analysis of nonstationary multivariate time series.Psychometrika. 1992;57:333-349.
66. Molenaar P. C. M.,Ram N.Dynamic process methodology in the social and developmental sciences. Valsiner J.Molenaar P. C. M.Lyra M. C. D. P.Chaudhary N., ed. Dordrecht, the Netherlands: Springer Science; 2009:255-268.
67. Molenaar P. C. M.,Ram N.Statistical methods for modeling human dynamics: An interdisciplinary dialogue. Chow S.-M.Ferrer E.Hsieh F., ed. New York, NY: Routledge; 2010:13-37.
68. Molenaar P. C. M.,Sinclair K. O.,Rovine M. J.,Ram N.,Corneal S. E.Analyzing developmental processes on an individual level using nonstationary time series modeling.Developmental Psychology. 2009;45:260-271.
69. Nesselroade J. R.Best methods for the analysis of change. Collins L. M.Horn J. L., ed. Washington, DC: American Psychological Association; 1991:92-105.
70. Nesselroade J. R.Individual pathway of change: Statistical models for analyzing learning and development. Molenaar P. C. M.Newell K. M., ed. Washington, DC: American Psychological Association; 2010:209-218.
71. Nesselroade J. R.,Boker S. M.Can personality change?. Heatherton T. F.Weinberger J. L., ed. Washington, DC: American Psychological Association; 1994:121-147.
72. Nesselroade J. R.,Gerstorf D.,Hardy S. A.,Ram N.Idiographic filters for psychological constructs.Measurement. 2007;5:217-235.
73. Nesselroade J. R.,Jones C. J.Multi-model selection effects in the study of adult development: A perspective on multivariate, replicated, single-subject, repeated measures designs.Experimental Aging Research. 1991;17:21-27.
74. Nesselroade J. R.,McArdle J. J.,Aggen S. H.,Meyers J. M.Modeling intraindividual variability with repeated measures data: Advances and techniques. Moskowitz D. M.Hershberger S. L., ed. Mahwah, NJ: Lawrence Erlbaum; 2002:235-265.
75. Nesselroade J. R.,Molenaar P. C. M.Statistical strategies for small sample research. Hoyle R. H., ed. Thousand Oaks, CA: Sage; 1999:223-250.
76. Otter P.Dynamic structure systems under indirect observation: Identifiability and estimation aspects from a system theoretic perspective.Psychometrika. 1986;51:415-428.
77. Pearl J.The foundations of causal inference.Sociological Methodology. 2010;40:75-149.
78. Pearl J.The causal mediation formula-A guide to the assessment of pathways and mechanisms.Prevention Science. 2012;13:426-436.
79. Preacher K. J.,Hayes A. F.SPSS and SAS procedures for estimating indirect effects in simple mediation models.Behavior Research Methods. 2004;36:717-731.
80. Preacher K. J.,Hayes A. F.Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models.Behavior Research Methods. 2008a;40:879-891.
81. Preacher K. J.,Hayes A. F.The Sage sourcebook of advanced data analysis methods for communication research. Hayes A. F.Slater M. D.Snyder L. B., ed. Thousand Oaks, CA: Sage; 2008b:13-54.
82. Preacher K. J.,Rucker D. D.,Hayes A. F.Addressing moderated mediation hypothesis: Theory, methods, and prescriptions.Multivariate Behavioral Research. 2007;42:185-227.
83. Roe R.What is wrong with mediators and moderators?.The European Health Psychologist. 2012;14:4-10.
84. Rosenzweig S.The place of the individual and of idiodynamics in psychology: A dialogue.Journal of Individual Psychology. 1958;14:3-20.
85. Sbarra D. A.,Ferrer E.The structure and process of emotional experience following nonmarital relationship dissolution: Dynamic factor analyses of love, anger, and sadness.Emotion. 2006;2:224-238.
86. Schmitz B.Advantages of studying processes in educational research.Learning and Instruction. 2006;16:433-449.
87. Schweppe F.Evaluation of likelihood functions for Gaussian signals.IEEE Transactions on Information Theory. 1965;11:61-70.
88. Selig J. P.,Preacher K. J.Mediation models for longitudinal data in developmental research.Research in Human Development. 2009;6:144-164.
89. Shifren K.,Hooker K.,Wood P.,Nesselroade J. R.Structure and variation of mood in individuals with Parkinson's disease: A dynamic factor analysis.Psychology and Aging. 1997;12:328-339.
90. Shrout P. E.,Bolger N.Mediation in experimental and nonexperimental studies: New procedures and recommendations.Psychological Methods. 2002;7:422-445.
91. Shumway R. H.,Stoffer D. S.Time series analysis and its applications: With R examples. New York, NY: Springer; 2011:.
92. Sinclair K. O.,Molenaar P. C. M.Optimal control of psychological processes: A new computational paradigm.Bulletin de la Societe des Sciences Medicales Luxembourg. 2008;:13-33.
93. Sliwinski M.,Mogle J.Handbook of cognitive aging: Interdisciplinary perspectives. Hofer S. M.Alwin D. F., ed. Thousand Oaks, CA: Sage; 2008:477-491.
94. Snijders T. A. B.,Bosker R. J.Multilevel analysis: An introduction to basic and advanced multilevel modeling. Thousand Oaks, CA: Sage; 2011:.
95. Song H.,Ferrer E.State-space modeling of dynamic psychological processes via the Kalman smoother algorithm: Rationale, finite sample properties, and applications.Structural Equation Modeling. 2009;16:338-363.
96. Song H.,Ferrer E.Bayesian estimation of random coefficient dynamic factor models.Multivariate Behavioral Research. 2012;47:26-60.
97. Stoffer D. S.,Wall K. D.Bootstrapping state-space models: Gaussian maximum likelihood estimation and the Kalman filter.Journal of the American Statistical Association. 1991;86:1024-1033.
98. Stoffer D. S.,Wall K. D.State space and unobserved component models: Theory and applications. Harvey A.Koopman S. J.Shephar N., ed. New York, NY: Cambridge University Press; 2004:171-202.
99. Ten Have T. R.,Joffe M. M.A review of causal estimation of effects in mediation analyses.Statistical Methods in Medical Research. 2010;21:77-107.
100. VanderWeele T. J.,Vansteelandt S.Conceptual issues concerning mediation, interventions and composition.Statistics and Its Interface. 2009;2:457-468.
101. van Kampen V.Idiographic complexity and the common personality dimensions of insensitivity, extraversion, neuroticism, and orderliness.European Journal of Personality. 2000;14:217-243.
102. Watson D.,Clark L. A.,Tellegen A.Development and validation of brief measures of positive and negative affect: The PANAS scales.Journal of Personality and Social Psychology. 1988;54:1063-1070.
103. Windle M.,Davies P. T.Psychological theories of drinking and alcoholism. 1999). Developmental research and theory. In LeonardK. E.BlaneH. T. (Eds.), Psychological theories of drinking and alcoholism (2nd ed., pp. 164-202). New York, NY: Guilford.Leonard K. E.Blane H. T., ed. New York, NY: Guilford; 1999:164-202.
104. Winkelmann L.,Winkelmann R.Why are the unemployed so unhappy? Evidence from panel data. Econometrica. 1998;65:1-15.
105. Wood P.,Brown D.The study of intraindividual differences by means of dynamic factor models: Rationale, implementation, and interpretation.Psychological Bulletin. 1994;116:166-186.
106. Yung Y.-F.,Chan W.Statistical strategies for small sample research. Hoyle R. H., ed. Thousand Oaks, CA: Sage; 1999:81-105.
107. Zevon M.,Tellegen A.The structure of mood change: Idiographic/nomothetic analysis.Journal of Personality and Social Psychology. 1982;43:111-122.
108. Zhang G.,Browne M. W.Bootstrap standard error estimates in dynamic factor analysis.Multivariate Behavioral Research. 2006;45:453-482.
109. Zhang G.,Chow S.-M.Individual pathway of change: Statistical models for analyzing learning and development. Molenaar P. C. M.Newell K. M., ed. Washington, DC: American Psychological Association; 2010:169-182.
110. Zhang Z.,Hamaker E. L.,Nesselroade J. R.Comparisons of four methods for estimating a dynamic factor model.Structural Equation Modeling. 2008;15:377-402.
111. Zhang Z.,Nesselroade J. R.Bayesian estimation of categorical dynamic factor models.Multivariate Behavioral Research. 2007;42:729-756.
112. Zu J.Examining nonlinear changes of coefficients in time-varying dynamic factor models. South Bend, IN: Unpublished master's thesis). University of Notre Dame; 2008:.