The separation of between-person and within-person components of individual change over time: A latent curve model with structured residuals

Journal of Consulting and Clinical Psychology

Volumn 82, Issue 5, 2014, Pages 879-894

  Curran, Patrick J ^a   Howard, Andrea L ^b   Bainter, Sierra A ^a   Lane, Stephanie T ^a   McGinley, James S ^a  

^a University of North Carolina at Chapel Hill   (United States)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Disaggregation of effects; Growth models; Latent curve models; Structural equation modeling

Indexed keywords

ALCOHOL CONSUMPTION; ANXIETY DISORDER; ARTICLE; AUTOREGRESSIVE LATENT TRAJECTORY MODEL; BEHAVIOR CHANGE; COVARIANCE; DEPRESSION; GROWTH; HUMAN; LATENT CURVE MODEL; MODEL; PSYCHOLOGICAL THEORY; STATISTICAL MODEL; TIME; TIME VARYING COVARIATE; INDIVIDUALITY; MENTAL DISEASE; METHODOLOGY; PROSPECTIVE STUDY; PSYCHOLOGY;

HUMANS; INDIVIDUALITY; MENTAL DISORDERS; MODELS, STATISTICAL; PROSPECTIVE STUDIES; PSYCHOLOGICAL THEORY; RESEARCH DESIGN;

EID: 84925868941     PISSN: 0022006X     EISSN: 19392117     Source Type: Journal    
DOI: 10.1037/a0035297     Document Type: Article

References (70)

1. Baltes, P. B., Reese, H. W., & Nesselroade, J. R. (1977). Life-span developmental psychology: Introduction to research methods. Oxford, England: Brooks/Cole.
2. Bauer, D. J., & Hussong, A. M. (2009). Psychometric approaches for developing commensurate measures across independent studies: Traditional and new models. Psychological Methods, 14, 101-125. doi: 10.1037/a0015583
3. Biesanz, J. C., Deeb-Sossa, N., Papadakis, A. A., Bollen, K. A., & Curran, P. J. (2004). The role of coding time in estimating and interpreting growth curve models. Psychological Methods, 9, 30-52. doi:10.1037/1082-989X.9.1.30
4. Bolger, N., Davis, A., & Rafaeli, E. (2003). Diary methods: Capturing life as it is lived. Annual Review of Psychology, 54, 579-616. doi:10.1146/annurev.psych.54.101601.145030
5. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
6. Bollen, K. A. (2007). On the origins of latent curve models. In R. Cudeck & R. MacCallum (Eds.), Factor analysis at 100 (pp. 79-98). Mahwah, NJ: Erlbaum.
7. Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods & Research, 32, 336-383. doi:10.1177/0049124103260222
8. Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation approach. Hoboken, NJ: Wiley.
9. Bollen, K. A., & Zimmer, C. (2010). An overview of the autoregressive latent trajectory (ALT) model. In K. van Montfort, J. H. L. Oud, & A. Satorra (Eds.), Longitudinal research with latent variables (pp. 153-176). Berlin, Germany: Springer-Verlag. doi:10.1007/978-3-642-11760-2-5
10. Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis: Forecasting and control. San Francisco, CA: Holden-Day.
11. Browne, M. W. (1993). Structured latent curve models. In C. M. Cuadras & C. R. Rao (Eds.), Multivariate analysis: Future directions 2 (pp. 171-198). Amsterdam, the Netherlands: North-Holland.
12. Browne, M. W., & du Toit, S. H. C. (1991). Models for learning data. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change (pp. 47-68). Washington, DC: American Psychological Association.
13. Chi, E. M., & Reinsel, G. C. (1989). Models for longitudinal data with random effects and AR(1) errors. Journal of the American Statistical Association, 79, 125-131.
14. Cole, D. A., Martin, N. C., & Steiger, J. H. (2005). Empirical and conceptual problems with longitudinal trait-state models: Introducing a trait-state-occasion model. Psychological Methods, 10, 3-20. doi: 10.1037/1082-989X.10.1.3
15. Curran, P. J., & 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. doi:10.1146/annurev.psych.093008.100356
16. Curran, P. J., Bauer, D. J., & Willoughby, M. T. (2004). Testing and probing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237. doi:10.1037/1082-989X.9.2.220
17. Curran, P. J., & Bollen, K. A. (2001). The best of both worlds: Combining autoregressive and latent curve models. In L. M. Collins & A. G. Sayer (Eds.), New methods for the analysis of change (pp. 107-135). Washington, DC: American Psychological Association Press. doi:10.1037/10409-004
18. Curran, P. J., & Hussong, A. M. (2003). The use of latent trajectory models in psychopathology research. Journal of Abnormal Psychology, 112, 526-544. doi:10.1037/0021-843X.112.4.526
19. Curran, P. J., Lee, T. H., Howard, A. H., Lane, S. T., & MacCallum, R. C. (2012). Disaggregating within-person and between-person effects in multilevel and structural equation growth models. In G. Hancock (Ed.), Advances in longitudinal methods in the social and behavioral sciences (pp. 217-253). Charlotte, NC: Information Age.
20. Curran, P. J., Muthén, B. O., & Harford, T. C. (1998). The influence of changes in marital status on developmental trajectories of alcohol use in young adults. Journal of Studies on Alcohol, 59, 647-658.
21. Curran, P. J., Stice, E., & Chassin, L. (1997). The relation between adolescent and peer alcohol use: A longitudinal random coefficients model. Journal of Consulting and Clinical Psychology, 65, 130-140. doi:10.1037/0022-006X.65.1.130
22. Curran, P. J., & Willoughby, M. J. (2003). Reconciling theoretical and statistical models of developmental processes. Development and Psychopathology, 15, 581-612.
23. Delsing, M. J. M. H., & Oud, J. H. L. (2008). Analyzing reciprocal relationships by means of the continuous-time autoregressive latent trajectory model. Statistica Neerlandica, 62, 58-82. doi:10.1111/j.1467-9574.2007.00386.x
24. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of American Statistical Association, 74, 427-431.
25. Diggle, P. J. (1988). An approach to the analysis of repeated measures. Biometrics, 44, 959-971. doi:10.2307/2531727
26. Ferrer, E., & McArdle, J. J. (2010). Longitudinal modeling of developmental changes in psychological research. Current Directions in Psychological Science, 19, 149-154. doi:10.1177/0963721410370300
27. Goldstein, H., Healy, M. J. R., & Rasbash, J. (1994). Multilevel time series models with applications to repeated measures data. Statistics in Medicine, 13, 1643-1655. doi:10.1002/sim.4780131605
28. Grimm, K. J., & Widaman, K. F. (2010). Residual structures in latent growth curve modeling. Structural Equation Modeling, 17, 424-442. doi:10.1080/10705511.2010.489006
29. Hamaker, E. L. (2005). Conditions for the equivalence of the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances. Sociological Methods & Research, 33, 404-416. doi:10.1177/0049124104270220
30. Hamaker, E. L., Dolan, C. V., & Molenaar, P. (2002). On the nature of SEM estimates of ARMA parameters. Structural Equation Modeling, 9, 347-368. doi:10.1207/S15328007SEM0903-3
31. Hartup, W. (1978). Perspectives on child and family interaction: Past, present, and future. In R. M. Lerner & G. B. Spanier (Eds.), Child influences on marital and family interaction: A life-span perspective (pp. 23-46). San Francisco, CA: Academic Press.
32. Hedeker, D., & Gibbons, R. D. (2006). Longitudinal data analysis. New York, NY: Wiley.
33. Hussong, A. M., Cai, L., Curran, P. J., Flora, D. B., Chassin, L., & Zucker, R. A. (2008). Disaggregating the distal, proximal, and time-varying effects of parent alcoholism on children's internalizing symptoms. Journal of Abnormal Child Psychology, 36, 335-346. doi:10.1007/s10802-007-9181-9
34. Hussong, A. M., Hicks, R. E., Levy, S. A., & Curran, P. J. (2001). Specifying the relations between affect and heavy alcohol use among young adults. Journal of Abnormal Psychology, 110, 449-461. doi: 10.1037/0021-843X.110.3.449
35. Hussong, A. M., Jones, D. J., Stein, G. L., Baucom, D. H., & Boeding, S. (2011). An internalizing pathway to alcohol use and disorder. Psychology of Addictive Behaviors, 25, 390-404. doi:10.1037/a0024519
36. Jongerling, J., & Hamaker, E. L. (2011). On the trajectories of the predetermined ALT model: What are we really modeling? Structural Equation Modeling, 18, 370-382. doi:10.1080/10705511.2011.582004
37. Kenny, D. A., & Zautra, A. J. (1995). The trait-state-error model for multiwave data. Journal of Consulting and Clinical Psychology, 63, 52-59. doi:10.1037/0022-006X.63.1.52
38. Kenny, D. A., & Zautra, A. J. (2001). Trait-state models for longitudinal data. In A. Sayer & L. Collins (Eds.), New methods for the analysis of change (pp. 243-263). Washington, DC: American Psychological Association. doi:10.1037/10409-008
39. Kwok, O., West, S. G., & Green, S. B. (2007). The impact of misspecifying the within-subject covariance structure in multiwave longitudinal multilevel models: A Monte Carlo study. Multivariate Behavioral Research, 42, 557-592. doi:10.1080/00273170701540537
40. Lutkepohl, H., & Saikkonen, P. (2000). Testing for the cointegrating rank of a VAR process with a time trend. Journal of Econometrics, 95, 177-198. doi:10.1016/S0304-4076(99)00035-4
41. McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In J. R. Nesselroade & R. B. Cattell (Eds.), Handbook of multivariate experimental psychology (pp. 561-614). New York, NY: Plenum Press. doi:10.1007/978-1-4613-0893-5-17
42. McArdle, J. J. (1989). Structural modeling experiments using multiple growth functions. In P. Ackerman, R. Kanfer, & R. Cudeck (Eds.), Learning and individual differences: Abilities, motivation, and methodology (pp. 71-117). Hillsdale, NJ: Erlbaum.
43. McArdle, J. J. (2009). Latent variable modeling of differences and changes with longitudinal data. Annual Review of Psychology, 60, 577-605. doi:10.1146/annurev.psych.60.110707.163612
44. McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110-133. doi:10.2307/1130295
45. McArdle, J. J., & Hamagami, F. (2001). Linear dynamic analyses of incomplete longitudinal data. In L. Collins & A. Sayer (Eds.), Methods for the analysis of change (pp. 139-175). Washington, DC: American Psychological Association. doi:10.1037/10409-005
46. Meredith, W., & Tisak, J. (1984, July). "Tuckerizing" curves. Paper presented at the annual meeting of the Psychometric Society, Santa Barbara, CA.
47. Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107-122. doi:10.1007/BF02294746
48. Morin, A. J. S., Maïano, C., Marsh, H. W., Janosz, M., & Nagengast, B. (2011). The longitudinal interplay of adolescents' self-esteem and body image: A conditional autoregressive latent trajectory analysis. Multivar-iate Behavioral Research, 46, 157-201. doi:10.1080/00273171.2010.546731
49. Muthén, B. O. (2001). Latent variable mixture modeling. In G. Marcoulides & R. Schumacker (Eds.), New developments and techniques in structural equation modeling (pp. 1-33). Mahwah, NJ: Erlbaum.
50. Muthén, B. O. (2002). Beyond SEM: General latent variable modeling. Behaviormetrika, 29, 81-117. doi:10.2333/bhmk.29.81
51. Muthén, B. O., & Curran, P. J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2, 371-402. doi:10.1037/1082-989X.2.4.371
52. Patterson, G. R., Reid, J. B., & Dishion, T. J. (1992). Antisocial boys. Eugene, OR: Castalia.
53. Patterson, G. R., & Yoerger, K. (2002). A developmental model for earlyand late-onset antisocial behavior. In J. B. Reid, J. Snyder, & G. R. Patterson (Eds.), Antisocial behavior in children and adolescents: A developmental analysis and model for intervention (pp. 147-172). Washington, DC: American Psychological Association. doi:10.1037/10468-007
54. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Thousand Oaks, CA: Sage.
55. Rindskopf, D. (1984). Using phantom and imaginary latent variables to parameterize constraints in linear structural models. Psychometrika, 49, 37-47. doi:10.1007/BF02294204
56. Rodebaugh, T. L., Curran, P. J., & Chambless, D. L. (2002). Expectancy of panic in the maintenance of daily anxiety in panic disorder with agoraphobia: A longitudinal test of competing models. Behavior Therapy, 33, 315-336. doi:10.1016/S0005-7894(02)80031-4
57. Rovine, M. J., & Molenaar, P. C. M. (2000). A structural modeling approach to a multilevel random coefficients model. Multivariate Behavioral Research, 35, 51-88. doi:10.1207/S15327906MBR3501-3
58. Saikkonen, P., & Lutkepohl, H. (2000). Trend adjustment prior to testing for the cointegrating rank of a vector autoregressive process. Journal of Time Series Analysis, 21, 435-456. doi:10.1111/1467-9892.00192
59. Scarr, S., & McCartney, K. (1983). How people make their own environments: A theory of genotype greater than environment effects. Child Development, 54, 424-435.
60. Sivo, S. (2001). Multiple indicator stationary time series models. Structural Equation Modeling, 8, 599-612. doi:10.1207/S15328007SEM0804-05
61. Sivo, S., & Fan, X. (2008). The latent curve ARMA (p, q) panel model: Longitudinal data analysis in educational research and evaluation. Educational Research and Evaluation, 14, 363-376. doi:10.1080/13803610802249670
62. Sivo, S., Fan, X., & Witta, L. (2005). The biasing effects of unmodeled ARMA time series processes on latent growth curve model estimates. Structural Equation Modeling, 12, 215-231. doi:10.1207/s15328007sem1202-2
63. Sivo, S., & Wilson, V. L. (2000). Modeling causal error structures in longitudinal panel data: A Monte Carlo study. Structural Equation Modeling, 7, 174-205. doi:10.1207/S15328007SEM0702-3
64. Stice, E., Marti, N., Rohde, P., & Shaw, H. (2011). Testing mediators hypothesized to account for the effects of a dissonance-based eating disorder prevention program over longer term follow-up. Journal of Consulting and Clinical Psychology, 79, 398-405. doi:10.1037/a0023321
65. Teachman, B. A., Marker, C. D., & Smith-Janik, S. B. (2008). Automatic associations and panic disorder: Trajectories of change over the course of treatment. Journal of Consulting and Clinical Psychology, 76, 988-1002. doi:10.1037/a0013113
66. van Buuren, S. (1997). Fitting ARMA time series by structural equation models. Psychometrika, 62, 215-236. doi:10.1007/BF02295276
67. Voelkle, M. C. (2008). Reconsidering the use of autoregressive latent trajectory (ALT) models. Multivariate Behavioral Research, 43, 564-591. doi:10.1080/00273170802490665
68. Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: Current approaches and future directions. Psychological Methods, 12, 58-79. doi:10.1037/1082-989X.12.1.58
69. Wohlwill, J. F. (1991). Relations between method and theory in developmental research: A partial-isomorphism view. Annals of Theoretical Psychology, 7, 91-138. doi:10.1007/978-1-4615-3842-4-5
70. Zyphur, M. J., Chaturvedi, S., & Arvey, R. D. (2008). Job performance over time is a function of latent trajectories and previous performance. Journal of Applied Psychology, 93, 217-224. doi:10.1037/0021-9010.93.1.217