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Longitudinal dynamic analyses of cognition in the health and retirement study panel

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Abstract

The purpose of this paper is to highlight some classic issues in the measurement of change and to show how contemporary solutions can be used to deal with some of these issues. Five classic issues will be raised here: (1) Separating individual changes from group differences; (2) options for incomplete longitudinal data over time, (3) options for nonlinear changes over time; (4) measurement invariance in studies of changes over time; and (5) new opportunities for modeling dynamic changes. For each issue we will describe the problem, and then review some contemporary solutions to these problems base on Structural Equation Models (SEM). We will fit these SEM to using existing panel data from the Health & Retirement Study (HRS) cognitive variables. This is not intended as an overly technical treatment, so only a few basic equations are presented, examples will be displayed graphically, and more complete references to the contemporary solutions will be given throughout.

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References

  • Allison, P.D.: Change scores as dependent variables in regression analysis. In: Clogg, C.C. (ed.) Sociological Methodology 1990, pp. 93–114. Jossey-Bass, San Francisco (1990)

    Google Scholar 

  • Baltagi, B.: Econometric Analysis of Panel Data. Wiley, New York (2005)

    Google Scholar 

  • Bayley, N.: Learning in adulthood: the role of intelligence. In: Klausmeier, H.J., Harris, C.W. (eds.) Analyses of Concept Learning, pp. 117–138. Academic Press, New York (1966)

    Google Scholar 

  • Boker, S.M.: Differential structural equation modeling of intra-individual variability. In: Collins, L., Sayer, A. (eds.) New Methods for the Analysis of Change, pp. 3–28. APA, Washington (2001)

    Google Scholar 

  • Boker, S., McArdle, J.J.: Vector field plots. In: Armitage, P., Colton, P. (eds.) Encyclopedia of Biostatistics, vol. 8, pp. 5700–5704, 2nd edn. Wiley, New York (2005)

    Google Scholar 

  • Bollen, K., Curran, P.J.: Latent Curve Models: A Structural Equation Perspective. Wiley, New York (2006)

    MATH  Google Scholar 

  • Bryk, A.S., Raudenbush, S.W.: Hierarchical Linear Models: Applications and Data Analysis Methods. Sage, Newbury Park (1992)

    Google Scholar 

  • Cagney, K.A., Lauderdale, D.S.: Education, wealth and cognitive function in later life. J. Geront., Ser. B Psychol. Sci. Soc. Sci. 57B, P163–P172 (2002)

    Article  Google Scholar 

  • Cattell, R.B.: The Handbook of Multivariate Experimental Psychology. Macmillan, New York (1966)

    Google Scholar 

  • Chow, S.-M., Ferrer, E., Nesselroade, J.R.: An unscented Kalman filter approach for the estimation of nonlinear dynamic systems models. Multivar. Behav. Res. 42(2), 283–321 (2007)

    Article  Google Scholar 

  • Cnaan, A., Laird, N.M., Slasor, P.: Using the general linear mixed model to analyze unbalanced repeated measures and longitudinal data. Stat. Med. 16, 2349–2380 (1997)

    Article  Google Scholar 

  • Collins, L., Sayer, A. (eds.): New Methods for the Analysis of Change. APA, Washington (2001)

    Google Scholar 

  • Cronbach, L.J., Furby, L.: How we should measure change—or should we? Psychol. Bull. 74, 68–80 (1970)

    Article  Google Scholar 

  • Cudeck, R., Klebe, K.J.: Multiphase mixed-effects models for repeated measures data. Psychol. Methods 7(1), 41–62 (2002)

    Article  Google Scholar 

  • Diggle, P.J., Liang, K.-Y., Zeger, S.L.: Analysis of Longitudinal Data. Oxford Press, New York (1994)

    Google Scholar 

  • Duncan, T.E., Duncan, S.C., Strycker, L.A., Li, F.: An Introduction to Latent Variable Growth Curve Modeling: Concepts, Issues, and Applications, 2nd edn. Erlbaum, Mahwah (2006)

    Google Scholar 

  • Ferrer, E., McArdle, J.J.: An experimental analysis of dynamic hypotheses about cognitive abilities and achievement from childhood to early adulthood. Dev. Psychol. 40, 935–952 (2004)

    Article  Google Scholar 

  • Ferrer, E., Hamagami, F., McArdle, J.J.: Modeling latent growth curves with incomplete data using different types of structural equation modeling and multilevel software. Struct. Equ. Model. 11(3), 452–483 (2004)

    Article  MathSciNet  Google Scholar 

  • Freedman, V.A., Aykan, H., Martin, L.G.: Another look at aggregate changes in severe cognitive impairment: cumulative effects of three survey design issues. J. Geront., Ser. B Psychol. Sci. Soc. Sci. 57B, S126–S131 (2002)

    Article  Google Scholar 

  • Ghisletta, P., Lindenberger, U.: Exploring the structural dynamics of the link between sensory and cognitive functioning in old age: longitudinal evidence from the Berlin Aging Study. Intelligence 33, 555–587 (2005)

    Article  Google Scholar 

  • Grimm, K.J., Hamagami, F., McArdle, J.J.: Nonlinear growth models in research on cognitive aging. In: Montfort, K.v., Oud, H., Satorra, A. (eds.) Longitudinal Models in the Behavioural and Related Sciences, pp. 267–294. Erlbaum, Mahwah (2007)

    Google Scholar 

  • Hamagami, F., McArdle, J.J.: Advanced studies of individual differences linear dynamic models for longitudinal data analysis. In: Marcoulides, G., Schumacker, R. (eds.) New Developments and Techniques in Structural Equations Modeling, pp. 203–246. Erlbaum, Mahwah (2000)

    Google Scholar 

  • Harris, C.W. (ed.): Problems in Measuring Change. University of Wisconsin Press, Madison (1963)

    Google Scholar 

  • Hedecker, D., Gibbons, R.: Longitudinal Data Analysis. Wiley, New York (2006)

    Google Scholar 

  • Herzog, A.R., Wallace, R.B.: Measures of cognitive functioning in the AHEAD study. J. Geront., Ser. B Psychol. Sci. Soc. Sci. 52B, 37–48 (1997) (Special Issue)

    Article  Google Scholar 

  • Horn, J.L.: State, trait, and change dimensions of intelligence. Br. J. Math. Stat. Psychol. 42(2), 159–185 (1972)

    MathSciNet  Google Scholar 

  • Horn, J.L., McArdle, J.J.: Understanding human intelligence since Spearman. In: Cudeck, R., MacCallum, R. (eds.) Factor Analysis at 100 Years, pp. 205–247. Lawrence Erlbaum Associates, Mahwah (2007)

    Google Scholar 

  • Hsiao, C.: Analysis of Panel Data. Cambridge University Press, New York (2003)

    Book  Google Scholar 

  • Jöreskog, K.G., Sörbom, D.: Advances in Factor Analysis and Structural Equation Models. Abt Books, Cambridge (1979)

    MATH  Google Scholar 

  • Juster, F.T., Suzman, R.: An overview of the health and retirement study. J. Hum. Resour. 30(Suppl), S7–S56 (1995)

    Article  Google Scholar 

  • Kenny, D.A., Zautra, A.: The trait-state model for longitudinal data. In: Collins, L., Sayer, A. (eds.) New Methods for the Analysis of Change, pp. 241–264. APA, Washington (2001)

    Google Scholar 

  • Kline, R.: Principles and Practices in Structural Equation Modeling. Guilford, New York (2005)

    Google Scholar 

  • Littell, R.C., Milliken, G.A., Stroup, W.W., Wolfinger, R.D., Schabenberger, O.: SAS System for Mixed Models, 2nd edn. SAS Institute, Cary (2006)

    Google Scholar 

  • Little, R.J.A.: Modeling the dropout mechanism in repeated-measures studies. J. Am. Stat. Assoc. 90, 1112–1121 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  • Lord, F.: Further problems in the measurement of growth. Educ. Psychol. Meas. 18, 437–454 (1958)

    Article  Google Scholar 

  • McArdle, J.J.: Latent variable growth within behavior genetic models. Behav. Genet. 16(1), 163–200 (1986)

    Article  Google Scholar 

  • McArdle, J.J.: Dynamic but structural equation modeling of repeated measures data. In: Nesselroade, J.R., Cattell, R.B. (eds.) The Handbook of Multivariate Experimental Psychology, vol. 2, pp. 561–614. Plenum, New York (1988)

    Chapter  Google Scholar 

  • McArdle, J.J.: Structural modeling experiments using multiple growth functions. In: Ackerman, P., Kanfer, R., Cudeck, R. (eds.) Learning and Individual Differences: Abilities, Motivation, and Methodology, pp. 71–117. Erlbaum, Hillsdale (1989)

    Google Scholar 

  • McArdle, J.J.: Structural factor analysis experiments with incomplete data. Multivar. Behav. Res. 29(4), 409–454 (1994)

    Article  Google Scholar 

  • McArdle, J.J.: A latent difference score approach to longitudinal dynamic structural analyses. In: Cudeck, R., du Toit, S., Sorbom, D. (eds.) Structural Equation Modeling: Present and Future, pp. 342–380. Scientific Software International, Lincolnwood (2001)

    Google Scholar 

  • McArdle, J.J.: Five steps in the structural factor analysis of longitudinal data. In: Cudeck, R., MacCallum, R. (eds.) Factor Analysis at 100 Years, pp. 99–130. Erlbaum Associates, Mahwah (2007)

    Google Scholar 

  • McArdle, J.J.: Latent variable modeling of differences and changes. Ann. Rev. Psychol. 60 (2008)

  • McArdle, J.J., Anderson, E.: Latent variable growth models for research on aging. In: Birren, J.E., Schaie, K.W. (eds.) The Handbook of the Psychology of Aging, pp. 21–43. Plenum Press, New York (1990)

    Google Scholar 

  • McArdle, J.J., Bell, R.Q.: An introduction to latent growth curve models for developmental data analysis. In: Little, T.D., Schnabel, K.U., Baumert, J. (eds.) Modeling Longitudinal and Multiple-Group Data: Practical Issues, Applied Approaches, and Scientific Examples, pp. 69–107. Erlbaum, Mahwah (2000)

    Google Scholar 

  • McArdle, J.J., Hamagami, F.: Modeling incomplete longitudinal and cross-sectional data using latent growth structural models. In: Collins, L., Horn, J.L. (eds.) Best Methods for the Analysis of Change, pp. 276–304. APA, Washington (1991)

    Google Scholar 

  • McArdle, J.J., Hamagami, F.: Multilevel models from a multiple group structural equation perspective. In: Marcoulides, G., Schumacker, R. (eds.) Advanced Structural Equation Modeling: Issues and Techniques, pp. 89–124. Erlbaum, Hillsdale (1996)

    Google Scholar 

  • McArdle, J.J., Hamagami, F.: Linear dynamic analyses of incomplete longitudinal data. In: Collins, L., Sayer, A. (eds.) Methods for the Analysis of Change, pp. 137–176. APA, Washington (2001)

    Google Scholar 

  • McArdle, J.J., Nesselroade, J.R.: Structuring data to study development and change. In: Cohen, S.H., Reese, H.W. (eds.) Life-Span Developmental Psychology: Methodological Innovations, pp. 223–267. Erlbaum, Hillsdale (1994)

    Google Scholar 

  • McArdle, J.J., Nesselroade, J.R.: Growth curve analyses in contemporary psychological research. In: Schinka, J., Velicer, W. (eds.) Comprehensive Handbook of Psychology, Volume Two: Research Methods in Psychology, pp. 447–480. Pergamon, New York (2003)

    Google Scholar 

  • McArdle, J.J., Woodcock, J.R.: Expanding test-rest designs to include developmental time-lag components. Psychol. Methods 2(4), 403–435 (1997)

    Article  Google Scholar 

  • McArdle, J.J., Hamagami, F., Meredith, W., Bradway, K.P.: Modeling the dynamic hypotheses of Gf-Gc theory using longitudinal life-span data. Learn. Individ. Differ. 12(2000), 53–79 (2001)

    Google Scholar 

  • McArdle, J.J., Ferrer-Caja, E., Hamagami, F., Woodcock, R.W.: Comparative longitudinal multilevel structural analyses of the growth and decline of multiple intellectual abilities over the life-span. Dev. Psychol. 38(1), 115–142 (2002)

    Article  Google Scholar 

  • McArdle, J.J., Hamagami, F., Jones, K., Jolesz, F., Kikinis, R., Spiro, A., Albert, M.S.: Structural modeling of dynamic changes in memory and brain structure using longitudinal data from the normative aging study. J. Geront., Psychol. Sci. 59B(6), P294–P304 (2004)

    Article  Google Scholar 

  • McArdle, J.J., Small, B.J., Backman, L., Fratiglioni, L.: Longitudinal models of growth and survival applied to the early detection of Alzheimer’s Disease. J. Geriatr. Psychiatry Neurol. 18(4), 234–241 (2005)

    Article  Google Scholar 

  • McArdle, J.J., Fisher, G.G., Kadlec, K.M.: Latent variable analysis of age trends in tests of cognitive ability in the health and retirement survey, 1992–2004. Psychol. Aging 22(3), 525–545 (2007)

    Article  Google Scholar 

  • McArdle, J.J., Hamagami, F., Kadlec, K., Fisher, G.: A dynamic structural analysis of dyadic cycles of depression in the Health and Retirement Study data. Unpublished Manuscript, Department of Psychology, University of Southern California (2009)

  • McArdle, J.J., Grimm, K., Hamagami, F., Bowles, R., Meredith, W.: A dynamic structural equation analysis of vocabulary abilities over the life-span. Psychol. Methods (2009, in press)

  • McDonald, R.P.: Test Theory: A Unified Treatment. Mahwah, Erlbaum (1999)

    Google Scholar 

  • Meredith, W.: Notes on factorial invariance. Psychometrika 29, 177–185 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  • Meredith, W., Horn, J.L.: The role of factorial invariance in measuring growth and change. In: Collins, L., Sayer, A. (eds.) New Methods for the Analysis of Change, pp. 201–240. APA, Washington (2001)

    Google Scholar 

  • Meredith, W., Tisak, J.: Latent curve analysis. Psychometrika 55, 107–122 (1990)

    Article  Google Scholar 

  • Miyazaki, Y., Raudenbush, S.W.: Tests for linkage of multiple cohorts in an accelerated longitudinal design. Psychol. Methods 5(1), 24–63 (2000)

    Article  Google Scholar 

  • Montfort, K., Oud, H., Satorra, A. (eds.): Longitudinal Models in the Behavioural and Related Sciences. Erlbaum, Mahwah (2007)

    Google Scholar 

  • Muller, K.E., Stewart, P.W.: Linear Model Theory. Wiley, New York (2006)

    MATH  Google Scholar 

  • Muthén, L.K., Muthén, B.O.: Mplus, the Comprehensive Modeling Program for Applied Researchers: 4th Edition User’s Guide. Muthen & Muthen, Los Angeles (2006)

    Google Scholar 

  • Nesselroade, J.R., Baltes, P.B. (eds.): Longitudinal Research in the Study of Behavior and Development. Academic Press, New York (1979)

    Google Scholar 

  • Nesselroade, J.R., Cable, D.G.: Sometimes it’s okay to factor difference scores—the separation of state and trait anxiety. Multivar. Behav. Res. 9, 273–282 (1974)

    Article  Google Scholar 

  • Orth, U., Berking, M., Walker, N., Meier, L.L., Znoj, H.: Forgiveness and psychological adjustment following interpersonal transgressions: a longitudinal analysis. J. Res. Pers. 42, 365–385 (2008)

    Article  Google Scholar 

  • Oud, J.H.L., Jansen, R.A.R.G.: Continuous time state space modeling of panel data by means of SEM. Psychometrika 65, 199–215 (2000)

    Article  MathSciNet  Google Scholar 

  • Rodgers, W.L., Ofstedal, M.B., Herzog, A.R.: Trends in scores on tests of cognitive ability in the elderly US population, 1993–2000. J. Geront., Ser. B Psychol. Sci. Soc. Sci. 58B, S338–S346 (2003)

    Article  Google Scholar 

  • Rogosa, D.: Causal models in longitudinal research: rationale, formulation, and interpretation. In: Nesselroade, J.R., Baltes, P.B. (eds.) Longitudinal Research in the Study of Behavior and Development, pp. 263–302. Academic Press, New York (1979)

    Google Scholar 

  • Rogosa, D., Willett, J.: Demonstrating the reliability of the difference score in the measurement of change. J. Educ. Meas. 20(4), 335–343 (1983)

    Article  Google Scholar 

  • Singer, J.D., Willett, J.: Applied Longitudinal Data Analysis. Oxford University Press, London (2003)

    Book  Google Scholar 

  • Steyer, R., Partchev, I., Shanahan, M.J.: Modeling true intraindividual change in structural equation models: the case of poverty and children’s psychological adjustment. In: Little, T.D., Schnabel, K.U., Baumert, J. (eds.) Modeling Longitudinal and Multiple-Group Data: Practical Issues, Applied Approaches, and Scientific Examples, pp. 109–127. Erlbaum, Mahwah (2001)

    Google Scholar 

  • Verbeke, G., Molenberghs, G.: Linear Mixed Models for Longitudinal Data. Springer, New York (2000)

    MATH  Google Scholar 

  • Walls, T.A., Schafer, J.L.: Models of Intensive Longitudinal Data. Oxford University Press, London (2006)

    Google Scholar 

  • Wang, L., McArdle, J.J.: A simulation study comparison of Bayesian estimation with conventional methods for estimating unknown change points. Struct. Equ. Model. 15(1), 52–74 (2008)

    Article  MathSciNet  Google Scholar 

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Correspondence to John J. McArdle.

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Presented at: The ZiF Scientific Meeting, Bielefeld, April 2010.

Prepared for Inclusion in: Haupt, H. (2011).

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McArdle, J.J. Longitudinal dynamic analyses of cognition in the health and retirement study panel. AStA Adv Stat Anal 95, 453–480 (2011). https://doi.org/10.1007/s10182-011-0168-z

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