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Full-Length Research Report

Multivariate Longitudinal Modeling of Cognitive Aging

Associations Among Change and Variation in Processing Speed and Visuospatial Ability

Published Online:https://doi.org/10.1024/1662-9647/a000051

We illustrate the use of the parallel latent growth curve model using data from OCTO-Twin. We found a significant intercept-intercept and slope-slope association between processing speed and visuospatial ability. Within-person correlations among the occasion-specific residuals were significant, suggesting that the occasion-specific fluctuations around individual’s trajectories, after controlling for intraindividual change, are related between both outcomes. Random and fixed effects for visuospatial ability are reduced when we include structural parameters (directional growth curve model) providing information about changes in visuospatial abilities after controlling for processing speed. We recommend this model to researchers interested in the analysis of multivariate longitudinal change, as it permits decomposition and directly interpretable estimates of association among initial levels, rates of change, and occasion-specific variation.

References

  • American Psychiatric Association . (1987). Diagnostic and Statistical Manual of Mental Disorders (DSM-III-R) (3rd ed. rev.). Washington, DC: Author. First citation in articleGoogle Scholar

  • Arbuckle, J. L. (1983–2007). Amos (Version 16.0) [Computer software]. Chicago, IL: SPSS. First citation in articleGoogle Scholar

  • Bentler, P. M., Wu, E. (2005). EQS (Version 6) [Computer software]. Encino, CA: Multivariate Software. First citation in articleGoogle Scholar

  • Blozis, S. A. (2007). On fitting nonlinear latent curve models to multiple variables measured longitudinally. Structural Equation Modeling, 14, 179–201. First citation in articleCrossrefGoogle Scholar

  • Blozis, S. A., Conger, K. J., Harring, J. R. (2007). Nonlinear latent curve models for longitudinal data. International Journal of Behavioral Development, 31, 340–346. First citation in articleCrossrefGoogle Scholar

  • Bollen, K. A., Curran, P. J. (2006). Latent curve models: A structural equation approach. Hoboken, NJ: Wiley. First citation in articleGoogle Scholar

  • Bryk, A. S., Raudenbush, S. W. (1987). Application of hierarchical linear models to assessing change. Psychological Bulletin, 101, 147–158. First citation in articleCrossrefGoogle Scholar

  • Bryk, A. S., Raudenbush, S. W. (1992). Hierarchical linear models in social and behavioral research: Applications and data analysis methods (1st ed.). Newbury Park, CA: Sage. First citation in articleGoogle Scholar

  • Cederlof, R., Lorich, U. (1978). The Swedish Twin Registry. In W. E. Nance G. Allen P. ParisiEds., Twin research: Biology and epidemiology (pp. 189–195). New York: Alan R. Riss. First citation in articleGoogle Scholar

  • 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. First citation in articleCrossrefGoogle Scholar

  • Curran, P. J., Harford, T. C., Muthén, B. O. (1996). The relation between heavy alcohol use and bar patronage: A latent growth model. Journal of Studies on Alcohol, 57, 410–418. First citation in articleCrossrefGoogle Scholar

  • Curran, P. J., Obeidat, K., Losardo, D. (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognition and Development, 11, 121–136. First citation in articleCrossrefGoogle Scholar

  • Curran, P. J., Stice, E., Chassin, L. (1997). The relation between adolescent alcohol use and peer alcohol use: A longitudinal random coefficients model. Journal of Consulting and Clinical Psychology, 65, 130–140. First citation in articleCrossrefGoogle Scholar

  • Curran, P. J., Willoughby, M. J. (2003). Implications of latent trajectory models for the study of developmental psychopathology. Development and Psychopathology, 15, 581–612. First citation in articleCrossrefGoogle Scholar

  • Dixon, R. A. (2011). Enduring theoretical themes in psychological aging: Derivation, functions, perspectives, and opportunities. In K. W. Schaie L. W. SherryEds., Handbook of the psychology of aging (7th ed., pp. 3–23). San Diego: Academic Press. First citation in articleCrossrefGoogle Scholar

  • Duncan, T. E., Duncan, S. C., Strycker, L. A. (2006). An introduction to latent variable growth curve modeling: Concepts, issues, and applications (2nd ed.). Mahwah, NJ: Erlbaum. First citation in articleGoogle Scholar

  • Dureman, I., Salde, H. (1959). Psykometriska och experimental-psykologiska metoderfor klinisk tillampning. Uppsala, Sweden: Almqvist & Wiksell. First citation in articleGoogle Scholar

  • Enders, C. K. (2006). Analyzing structural equation models with missing data. In G. R. Hancock R. O. MuellerEds., Structural equation modeling: A second course (pp. 313–342). Greenwich, CT: Information Age Publishing. First citation in articleGoogle Scholar

  • Ferrer, E., Ghisletta, P. (2011). Methodological and analytical issues in the psychology of aging. In K. W. Schaie L. W. SherryEds., Handbook of the psychology of aging (7th ed., pp. 25–39). San Diego: Academic Press. First citation in articleCrossrefGoogle Scholar

  • Fieuws, S., Verbeke, G. (2006). Pairwise fitting of mixed models for the joint modeling of multivariate longitudinal profiles. Biometrics, 62, 424–431. First citation in articleCrossrefGoogle Scholar

  • Fieuws, S., Verbeke, G., Molenberghs, G. (2007). Random-effects models for multivariate repeated measures. Statistical Methods in Medical Research, 16, 387–397. First citation in articleCrossrefGoogle Scholar

  • Gibbons, R. D., Hedeker, D., DuToit, S. (2010). Advances in analysis of longitudinal data. Annual Review of Clinical Psychology, 6, 79–107. First citation in articleCrossrefGoogle Scholar

  • Goldstein, H. (1987). Multilevel models in educational and social research. London: Griffin. First citation in articleGoogle Scholar

  • Goldstein, H. (1995). Multilevel statistical models. London: Edward Arnold. First citation in articleGoogle Scholar

  • Grimm, K. J. (2007). Multivariate longitudinal methods for studying developmental relationships between depression and academic achievement. International Journal of Behavioral Development, 31, 328–339. First citation in articleCrossrefGoogle Scholar

  • Grimm, K. J., Ram, N., Hamagami, F. (2011). Nonlinear growth curves in developmental research. Child Development, 82, 1357–1371. First citation in articleCrossrefGoogle Scholar

  • Harvey, D. J., Beckett, L. A., Mungas, D. M. (2003). Multivariate modeling of two associated cognitive outcomes in a longitudinal study. Journal of Alzheimer’s Disease, 5, 357–365. First citation in articleCrossrefGoogle Scholar

  • Hertzog, C. (1985). An individual differences perspective. Research on Aging, 7, 7–45. First citation in articleCrossrefGoogle Scholar

  • Hofer, S. M., Gray, K. M., Piccinin, A. M., Mackinnon, A., Bontempo, D. E., Einfeld, S. L. , ... Tonge, B. J. (2009). Correlated and coupled within-person change in emotional and behavior disturbance in individuals with intellectual disability. American Journal on Intellectual and Developmental Disabilities, 114, 307–321. First citation in articleCrossrefGoogle Scholar

  • Hofer, S. M., Sliwinski, M. J. (2006). Design and analysis of longitudinal studies of aging. In J. E. Birren K. W. SchaieEds., Handbook of the psychology of aging (6th ed., pp. 1537). San Diego: Academic Press. First citation in articleCrossrefGoogle Scholar

  • Hoffman, L. (in press). Considering alternative metrics of time: Does anybody really know what “time” is? In G. Hancock J. R. HarringEds., Advances in longitudinal methods in the social and behavioral sciences. Charlotte, NC: Information Age Publishing. First citation in articleGoogle Scholar

  • Hoffman, L., Stawski, R. (2009). Persons as contexts: Evaluating between-person and within-person effects in longitudinal analysis. Research in Human Development, 6, 97–100. First citation in articleCrossrefGoogle Scholar

  • Hultsch, D. F., Hertzog, C., Dixon, R. A., Small, B. J. (1998). Memory change in the aged. New York: Cambridge University Press. First citation in articleGoogle Scholar

  • Johansson, B., Hofer, S. M., Allaire, J. C., Maldonado-Molina, M., Piccinin, A. M., Berg, S. , ... McClearn, G. E. (2004). Change in memory and cognitive functioning in the oldest-old: The effects of proximity to death in genetically related individuals over a six-year period. Psychology and Aging, 19, 145–156. First citation in articleCrossrefGoogle Scholar

  • Johansson, B., McClearn, G. E. (1996). Aging, environment and genetics: The OCTO Twin study of twins 80 and older: Presentation and progress [Technical report]. Institute of Gerontology, University College of Health Science, Jönköping, Sweden. First citation in articleGoogle Scholar

  • Laird, N. M., Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963–974. First citation in articleCrossrefGoogle Scholar

  • Littell, R. C., Milliken, G. A., Stroup, W. W., Wolfinger, R. D. (1996). PROC MIXED in SAS [Computer software]. New York: SAS Institute. First citation in articleGoogle Scholar

  • Longford, N. T. (1987). A fast scoring algorithm for maximum likelihood estimation in unbalanced mixed models with nested random effects. Biometrika, 74, 817–827. First citation in articleCrossrefGoogle Scholar

  • MacCallum, R. C., Kim, C. (2000). Modeling multivariate change. In T. D. Little K. U. Schnabel U. LindenbergEds., Modeling longitudinal and multiple-group data: Practical issues, applied approaches, and specific examples. Mahwah, NJ: Erlbaum. First citation in articleGoogle Scholar

  • MacCallum, R. C., Kim, C., Malarkey, W. B., Kiecolt-Glaser, J. K. (1997). Studying multivariate change using multilevel models and latent curve models. Multivariate Behavioral Research, 32, 215–253. First citation in articleCrossrefGoogle Scholar

  • MacDonald, S. W. S., Hultsch, D. F., Dixon, R. A. (2003). Performance variability is related to change in cognition: Evidence from the Victoria Longitudinal Study. Psychology and Aging, 18, 510–523. First citation in articleCrossrefGoogle Scholar

  • MacDonald, S. W. S., Hultsch, D. F., Strauss, E., Dixon, R. A. (2003). Age-related slowing of Digit Symbol Substitution revisited: What do longitudinal age changes reflect? Journal of Gerontology: Psychological Sciences, 58B, 187–194. First citation in articleCrossrefGoogle Scholar

  • Martin, M., Hofer, S. M. (2004). Intraindividual variability, change, and aging: Conceptual and analytical issues. Gerontology, 50, 7–11. First citation in articleCrossrefGoogle Scholar

  • McArdle, J. J. (1986). Latent variable growth within behavior genetic models. Behavior Genetics, 16, 163–200. First citation in articleCrossrefGoogle Scholar

  • McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In R. B. Cattell J. NesselroadeEds., Handbook of experimental psychology (2nd ed., pp. 561–614). New York: Plenum. First citation in articleCrossrefGoogle Scholar

  • McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural equation analyses. In R. Cudeck S. DuToit D. SörbomEds., Structural equation modeling: Present and future (pp. 342–380). Lincolnwood, IL: Scientific Software International. First citation in articleGoogle Scholar

  • McArdle, J. J., Hamagami, F. (2001). Latent difference score structural models for linear dynamic analyses with incomplete longitudinal data. In L. M. Collins A. J. SayerEds., New methods for the analysis of change (pp. 139–175). Washington, DC: American Psychological Association. First citation in articleCrossrefGoogle Scholar

  • McKhann, G., Drachman, D., Folstein, M., Katzman, R., Price, D., Stadlan, E. M. (1984). Clinical diagnosis of Alzheimer’s disease: Report of the NINCDS-ADRDA Work Group under the auspices of Department of Health and Human Services Task Force on Alzheimer’s Disease. Neurology, 34, 939–944. First citation in articleGoogle Scholar

  • Meredith, W., Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122. First citation in articleCrossrefGoogle Scholar

  • Muthén, L. K., Muthén, B. O. (1998–2010a). Mplus (Version 6.11) [Computer software]. Los Angeles, CA: Muthén and Muthén. First citation in articleGoogle Scholar

  • Muthén, L. K., Muthén, B. O. (1998–2010b). Mplus user’s guide (6th ed.). Los Angeles, CA: Muthén and Muthén. First citation in articleGoogle Scholar

  • Piccinin, A. M., Rabbitt, P. M. A. (1999). Contribution of cognitive abilities to performance and improvement on a substitution coding task. Psychology and Aging, 14, 539–551. First citation in articleCrossrefGoogle Scholar

  • Rabbitt, P. (1993). Does it all go together when it goes? The nineteenth Bartlett memorial lecture. The Quarterly Journal of Experimental Psychology Section A, 46, 385–434. First citation in articleCrossrefGoogle Scholar

  • Raudenbush, S. W., Chan, W. S. (1993). Application of a hierarchical linear model to the study of adolescent deviance in an overlapping cohort design. Journal of Clinical and Consulting Psychology, 61, 941–951. First citation in articleCrossrefGoogle Scholar

  • Roman, G. C., Tatemichi, T. K., Erkinjuntti, T., Cummings, J. L., Masdeu, J. C., Garcia, J. H. , ... Hofman, A. (1993). Vascular dementia: Diagnostic criteria for research studies. Report of the NINDS-AIREN International Workshop. Neurology, 43, 250–260. First citation in articleGoogle Scholar

  • Rosenberg, B. (1973). Linear regression with randomly dispersed parameters. Biometrika, 60, 61–75. First citation in articleCrossrefGoogle Scholar

  • Salthouse, T. A. (1996). The processing speed theory of adult age differences in cognition. Psychological Review, 103, 403–428. First citation in articleCrossrefGoogle Scholar

  • Singer, J. D., Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press. First citation in articleCrossrefGoogle Scholar

  • Sliwinski, M., Buschke, H. (1999). Cross-sectional and longitudinal relationships among age, memory and processing speed. Psychology and Aging, 14, 18–33. First citation in articleCrossrefGoogle Scholar

  • Sliwinski, M., Buschke, H. (2004). Modeling intraindividual cognitive change in aging adults: Results from the Einstein Aging Studies. Aging, Neuropsychology and Cognition, 11, 196–211. First citation in articleGoogle Scholar

  • Sliwinski, M., Hofer, S., Hall, C. (2003). Correlated cognitive change in older adults with and without preclinical dementia. Psychology and Aging, 18, 672–683. First citation in articleCrossrefGoogle Scholar

  • Sliwinski, M., Hofer, S., Hall, C. B., Buschke, H., Lipton, R. (2003). Modeling memory decline in older adults: The importance of preclinical dementia, attrition and chronological age. Psychology and Aging, 18, 658–671. First citation in articleCrossrefGoogle Scholar

  • Sliwinski, M. J., Hoffman, L., Hofer, S. M. (2010). Evaluating convergence of within-person change and between-person age differences in age-heterogeneous longitudinal studies. Research in Human Development, 7, 45–60. First citation in articleCrossrefGoogle Scholar

  • Sliwinski, M., Mogle, J. (2008). Time-based and process-based approaches to analysis of longitudinal data. In S. M. Hofer D. F. AlwinEds., Handbook on cognitive aging: interdisciplinary perspectives (pp. 477–491). Thousand Oaks, CA: Sage. First citation in articleCrossrefGoogle Scholar

  • Stapleton, L. M. (2006). An assessment of practical solutions for structural equation modeling with complex sample data. Structural Equation Modeling, 13, 28–58. First citation in articleCrossrefGoogle Scholar

  • Stoel, R. D., Garre, F. G. (2011). Growth curve analysis using multilevel regression and structural equation modeling. In J. J. Hox J. K. RobertsEds., Handbook of advanced multilevel analysis (pp. 97–111). New York: Taylor & Francis Group. First citation in articleGoogle Scholar

  • Stoel, R. D., Van den Wittenboer, G., Hox, J. J. (2003). Analyzing longitudinal data using multilevel regression and latent growth curve analysis. Metodologia de las Ciencas del Comportamiento, 5, 21–42. First citation in articleGoogle Scholar

  • Stoolmiller, M. (1994). Antisocial behavior, delinquent peer association, and unsupervised wandering for boys: Growth and Change from childhood to early adolescence. Multivariate Behavioral Research, 29, 263–288. First citation in articleCrossrefGoogle Scholar

  • Tisak, J., Meredith, W. (1990). Descriptive and associative developmental models. In A. von, Eye (Ed.), Statistical methods in longitudinal research (pp. 387–406). San Diego, CA: Academic Press. First citation in articleGoogle Scholar

  • Verhaeghen, P., Salthouse, T. A. (1997). Meta-analyses of age-cognition relations in adulthood: Estimates of linear and nonlinear age effects and structural models. Psychological Bulletin, 122, 231–249. First citation in articleCrossrefGoogle Scholar

  • Wechsler, D. (1991). The Wechsler intelligence scale for children (3rd ed.). San Antonio, TX: The Psychological Corporation. First citation in articleGoogle Scholar

  • Willett, J. B., Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of change. Psychological Bulletin, 116, 363–381. First citation in articleCrossrefGoogle Scholar

  • Willett, J. B., Sayer, A. G. (1996). Cross-analyses of change over time: Combining growth modeling and covariance structure analysis. In G. A. Marcoulides R. E. SchumackerEds., Advanced structural equation modeling: Issues and techniques (pp. 125–157). Hillsdale, NJ: Erlbaum. First citation in articleGoogle Scholar

  • Yuan, K. H., Bentler, P. M. (2000). Three likelihood-based methods for mean and covariance structure analysis with nonnormal missing data. Sociological Methodology, 30, 165–200. First citation in articleCrossrefGoogle Scholar

  • Zimprich, D. (2002). Cross-sectionally and longitudinally balanced effects of processing speed on intellectual abilities. Experimental Aging Research, 28, 231–251. First citation in articleCrossrefGoogle Scholar