Skip to main content
SpringerLink
Log in

Methods for Dynamic Change Hypotheses

  • Chapter
Recent Developments on Structural Equation Models

Part of the book series: Mathematical Modelling: Theory and Applications ((MMTA,volume 19))

Abstract

In this rcscarch wc describe longitudinal structural equaiion modeis useful for testing dynamic hypothesis. The Statistical modeis described here come from recent research on latent variable siruclural equaiion modeling (SEM) for longiiudinal data. The initial set of analyses arc hased on considerations about measurement modeis with changing scales over timc following modcls used by McArdle & Woodcock (1997). A second set of analyses are based directly on the latent growth curvc model of Meredith & Tisak (1990). A third set of analyses are based on latent difference score modcls of McArdle & Nesselroade (1994) and McArdle (2001). In a fourth and final set of analyses we present some new bivariate dynamic model across different variables at different ages from McArdle & Hamagami (2001). These SEM analyses permit a dynamk Interpretation of the developmental influences of onc variable upon another over timc and can bc used with many form of repeated mcasures longiiudinal data. This rcscarch paper emphasi/cs practica! aspects of testing dynamic hypolheses with SEM, but implications for turther experimcntal and developmental rcscarch arc also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Arminger, G. (1986). Linear stochastic differential equation modeis for panel data with unobserved variables. In N. Tuma (Ed.), Sociological Methodology 1986(pp. 187–212). San Francisco: Jossey-Bass.

    Google Scholar 

  • Arbuckle, J.L. & Wothke, W. (1999). AMOS 4.0 User’s Guide. Chicago: Small waters.

    Google Scholar 

  • Baltes, P.B. & Nesselroade, J.R. (1979). History and rationale of longitudinal research. In Nesselroade, J.R. & Baltes, P.B. (Eds.) (1979). Longitudinal research in the study of behavior and development. New York: Academic Press.

    Google Scholar 

  • Bayley, N. (1956). Individual patterns of development. Child Development, 27(1), 45–74.

    PubMed  Google Scholar 

  • Bradway, K. P. & Thompson, C. W. (1962). Intelligence at adulthood: A 25 year follow-up. Journal of Educational Psychology, 53(1), 1–14.

    Article  Google Scholar 

  • Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation modeis (pp. 132–162). Beverly Hills, CA: Sage.

    Google Scholar 

  • Browne, M. & du Toit, S. H.C. (1991). Models for learning data. In L. Collins & J.L. Hörn, (Eds.), Best Methods for the Analysis of Change. Washington, D.C.: APA Press, (pp. 47–68).

    Google Scholar 

  • Boker, S.M. (2001). Differential structural equation modeis. In L. Collins & A. Sayer (Eds.). New Methods for the Analysis of Change. Washington, DC: APA Press.

    Google Scholar 

  • Boker, S.M. & McArdle, J.J. (1995). A Statistical vector field analysis of longitudinal aging data. Experimental Aging Research, 21, 77–93.

    Article  PubMed  Google Scholar 

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

    Google Scholar 

  • Burr, J., & Nesselroade, J. R. (1990). Change measurement. In A. von Eye (Ed.), Statistical methods in longitudinal research. Vol. 1: Principles and structuring change(pp.3–34). New York: Academic Press.

    Google Scholar 

  • Cattell, R.B. (1971, 1987). Intelligence: Its structure, growth and action. Amsterdam: Elsevier.

    Google Scholar 

  • Cattell, R.B. (1941). Some theoretical issues in adult intelligence testing. Psychological Bulletin, 38, 592.

    Google Scholar 

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

    Article  PubMed  Google Scholar 

  • Coleman, J. (1968). The mathematical study of change. In H. M. Blalock & A.B. Blalock (Eds.), Methodology in social research(pp. 428–475). New York: McGraw-Hill.

    Google Scholar 

  • Cook, T.D. & Campbell, D.T. (1979). Quasi-experimentation design and analysis issues for field settings. Skokie, DL: Rand-McNally.

    Google Scholar 

  • Cudeck, R. & du Toit, S. H. C. (2003). Nonlinear multilevel modeis forrepeated measures data. In Duan, N. & Reise, S. P. (Eds.), Multilevel modeling: Methodological advances, issues and applications (pp. 1–24).Mahwah, NJ: Erlbaum

    Google Scholar 

  • Duncan, S.C. & Duncan, T.E. (1995). Modeling the processes of development via latent variable growth curve methodology. Structural Equation Modeling: A Multidisciplinary Journal, 2, 187–213.

    Article  Google Scholar 

  • Embretson, S. E. (1996). The new rules of measurement. Psychological Assessment, 4, 341–349.

    Article  Google Scholar 

  • Fischer, G.H. & I. Molenaar (Eds.) (1995). Rasch modeis - foundations, recent developments, andapplications. NY: Springer (pp.157–180).

    Google Scholar 

  • Goldstein, H. (1995). Multilevel Statistical modeis, Second Edition. New York: Oxford Press.

    Google Scholar 

  • Gollob, H. F., & Reichardt, C. S. (1987). Taking account of time lags in causal modeis. Child Development, 58, 80–92.

    Article  PubMed  Google Scholar 

  • Guilford, J.P. (1967). The nature of human intelligence. New York: McGraw-Hill.

    Google Scholar 

  • Guilford, J.P. (1980). Fluid and crystallized intelligence: Two fanciful concepts. Psychological Bulletin, 88, 408–412.

    Article  Google Scholar 

  • Hagenaars, J.A. & McCutcheon, A.L. (Eds., 2002). Applied latent class analysis. Cambridge: Cambridge University Press.

    Google Scholar 

  • Hamagami, F. (1998). A developmental-based item factor analysis. In McArdle, J.J. & Woodcock, R.W. (Eds.). Human Abilities in Theory and Practice(231–246). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Hamagami, F. & McArdle, J.J. (2000). Advanced studies of individual differences linear dynamic modeis for longitudinal data analysis. In G. Marcoulides & R. Schumacker (Eds.), Advanced structural equation modeling: Issues and techniques (pp. 203–246). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Harris, C.W. (Ed.). Problems in measuring change. Madison, WI: University of Wisconsin Press.

    Google Scholar 

  • Heathcote, A., Brown, S. & Mewhort, D. J.K. (2002). The Power Law repealed: The case for an exponential law of practice. Psychonomic Bulletin & Review (in press).

    Google Scholar 

  • Hedecker, D. & Gibbons, R. (1997). Application of random-effects pattern-mixture modeis for missing data in longitudinal studies. Psychological Methods, 2, 64–78.

    Article  Google Scholar 

  • Hörn, J.L. (1972). The State, trait, and change dimensions of intelligence. British Journal of Educational Psychology(2) 159–185

    Article  Google Scholar 

  • Hörn, J.L. (1988). Thinking about human abilities. In J. R. Nesselroade (Ed.), Handbook of Multivariate Psychology(pp. 645–685). New York: Academic Press.

    Chapter  Google Scholar 

  • Hörn, J.L. & Cattell, R.B. (1982). Whimsy and misunderstandings of Gf-Gc theory. Psychological Bulletin, 91, 623–633.

    Article  Google Scholar 

  • Hörn, J.L. & McArdle, J.J. (1980). Perspectives on Mathematical and Statistical Model Building (MASMOB) in Research on Aging. In L. Poon (Ed.), Aging in the 1980’s: Psychological Issues. Washington, D. C: American Psychological Association, 503–541.

    Chapter  Google Scholar 

  • Hörn, J.L. & McArdle, J.J. (1992). A practical guide to measurement invariance in research on aging. Experimental Aging Research, 18(3), 117–144.

    Article  PubMed  Google Scholar 

  • Jöreskog, K.G. (1970). Estimation and testing of simplex model. British Journal of Mathematical and Statistical Psychology, 23, 121–145.

    Article  Google Scholar 

  • Jöreskog, K. G. (1977). Analysis of longitudinal data. In D.V. Aigner & A.S. Goldberger (Eds). Latent variables in socioeconomic modeis. Amsterdam: North Holland Pub. Co. (Ch.16).

    Google Scholar 

  • Jöreskog, K.G., & Sörbom, D. (1979). Advances in factor analysis and structural equation modeis. In J. Magdson (Ed.), Cambridge, MA: Abt Books.

    Google Scholar 

  • Jöreskog, K.G., & Sörbom, D. (1999). LISREL 8.30: LISREL 8: Structural equation modeling with the S1MPLIS command language. Hillsdale, NJ: Scientific Software International.

    Google Scholar 

  • Kangas, J. & Bradway, K. P. (1971). Intelligence at middle age: A thirty-eight year follow-up. Developmental Psychology, 5(2), 333–337.

    Article  Google Scholar 

  • Litteil, R.C., Miliken, G.A., Stoup, W.W., & Wolfinger, R.D. (1996). SAS System for mixed modeis. Cary, N.C.: SAS institute.

    Google Scholar 

  • Little, R.T.A (1995). Modeling the dropout mechanism in repeated-measures studies. Journal of the American Statistical Association, 90, 1112–1121.

    Article  Google Scholar 

  • Little, R.T.A. & Rubin, D.B. (1987). Statistical analysis with missing data. New York: Wiley.

    Google Scholar 

  • MacCallum, R.C. & Ashby, F.G. (1986). Relationship between linear Systems theory and covariance structure modeling. Journal of Mathematical Psychology, 30, 1–27.

    Article  Google Scholar 

  • McArdle, J.J. (1986). Latent variable growth within behavior genetic modeis. Behavior Genetics, 16(1), 163–200.

    Article  PubMed  Google Scholar 

  • McArdle, J.J. (1988). Dynamic but structural equation modeling of repeated measures data. In J.R. Nesselroade & R.B. Cattell (Eds.), The Handbook of Multivariate Experimental Psychology, Volume2. New York, Plenum Press, 561–614.

    Chapter  Google Scholar 

  • McArdle, J.J. (1994). Structural factor analysis experiments with incomplete data. Multivariate Behavioral Research, 29(4), 409–454.

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • McArdle, JJ. & Bell, R.Q. (2000). Recent trends in modeling longitudinal data by latent growth curve methods. In Little, T.D., Schnabel, K.U. & Baumert, J. (Eds.). Modeling longitudinal and multiple-group data: practical issues, applied approaches, and scientific examples(69–108).Mahwah, NJ: Erlbaum.

    Google Scholar 

  • McArdle, JJ. & Boker, S. M. (1990). RAMpath: A Computer Program for Automatic Path Diagrams. Hillsdale, NJ: Lawrence Erlbaum Publishers.

    Google Scholar 

  • McArdle, JJ. & Cattell, R.B. (1994). Structural equation modeis of factorial invariance in parallel proportional profiles and oblique confactor Problems. Multivariate Behavioral Research, 29(1), 63–113.

    Article  Google Scholar 

  • McArdle, JJ. & Epstein, D.B. (1987). Latent growth curves within developmental structural equation modeis. Child Development, 58(1), 110–133.

    Article  PubMed  Google Scholar 

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

    Article  PubMed  Google Scholar 

  • McArdle, JJ. & Hamagami, E. (1992). Modeling incomplete longitudinal and cross-sectional data using latent growth structural modeis. Experimental Aging Research, 18(3), 145–166.

    Article  PubMed  Google Scholar 

  • McArdle, JJ. & Hamagami, F. (1996). Multilevel modeis from a multiple group structural equation perspective. In G. Marcoulides & R. Schumacker (Eds.), Advanced Structural Equation Modeling Techniques(89–124). Hillsdale, N.J.: Erlbaum.

    Google Scholar 

  • McArdle, JJ. & Hamagami, F. (2001). Linear dynamic analyses of incomplete longitudinal data. In L. Collins & A. Sayer (Eds.). New Methods for the Analysis of Change (137–176). Washington, DC: APA-Press.

    Google Scholar 

  • McArdle, J.J., Hamagami, F., Meredith, W., & Bradway, K.P. (2001). Modeling the dynamic hypotheses of Gf-Gc theory using longitudinal life-span data. Learning and Individual Dijferences, 12(2000), 53–79.

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • McArdle, J.J., Prescott, CA., Hamagami, F. & Hörn, J.L. (1998) A contemporary method for developmental-genetic analyses of age changes in intellectual abilities. Developmental Neuropsychology, 74(1), 69–114.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • McArdle, JJ. & Woodcock, R.W. (Eds.). Human Abilities in Theory and Practice. Mahwah, NJ: Erlbaum, p. 157–195.

    Google Scholar 

  • McDonald, R.P. (1999). Test theory: A unified treatment. Mahwah, NJ: Erlbaum.

    Google Scholar 

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

    Article  Google Scholar 

  • Metha, P.D. & West, S.G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5(1), 23–43.

    Article  Google Scholar 

  • Molenaar, P. C. M. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50, 181–202.

    Article  Google Scholar 

  • Muthen, B.O. & Curran, P. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological Methods, 2,371–402.

    Article  Google Scholar 

  • Muthen, L.K. & Muthen, B.O. (1998). Mplus, the comprehensive modeling program for applied researchers user’s guide. Los Angeles, CA: Muthen & Muthen.

    Google Scholar 

  • Nagin, D. (1999). Analyzing developmental trajectories: Semi-parametric. Group-based approach. Psychological Methods. 4, 139–177.

    Article  Google Scholar 

  • Neale, M.C., Boker, S.M., Xie, G. & Maes, H.H. (1999). Mx Statistical Modeling(5 Ed.) Unpublished program manual, Virginia Institute of Psychiatric and Behavioral Genetics, Medical College of Virginia, Virginia Commonwealth University, Richmond, VA.

    Google Scholar 

  • Nesselroade, J.R. & Boker, S.M. (1994). Assessing constancy and change. In T.F. Heatherton & J.L. Weinberger (Eds.), Can personality change?American Psychological Association: Washington, D.C.

    Google Scholar 

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

    Article  Google Scholar 

  • Piaget, J. (1977). The development of thought: Equilibration of cognitive structures. New York: Viking Press.

    Google Scholar 

  • Pinherio, J.C. & Bates, D.M. (2000). Mixed-effects modeis in S and S-PLUS. New York: Springer.

    Book  Google Scholar 

  • Rogosa, D. (1978). Causal modeis in longitudinal research: Rationale, formulation, and Interpretation. In J.R. Nesselroade & P.B. Baltes (Eds.), Longitudinal research in the study of behavior and development. New York: Academic Press.

    Google Scholar 

  • Rao, CR. (1958). Some Statistical methods for the comparison of growth curves. Biometrics, 14,1–17.

    Article  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model. Annal of Statistics, 6,461–464.

    Article  Google Scholar 

  • Singer, J.D. (1998). Using SAS PROC MDCED to fit multilevel modeis, hierarchical modeis, and individual growth modeis. Journal of Educational and Behavioral Statistics, 24(4), 323–355.

    Google Scholar 

  • Sliwinski, M. & Buschke, H. (1999). Cross-sectional and longitudinal relationships among age, Cognition, and processing speed. Psychology and Aging14(1), 18–33.

    Article  PubMed  Google Scholar 

  • Snijders, T.A.B., & Bosker, R. (1994). Modeled variance in two-level modeis. Sociological Methods & Research, 22, 342–363.

    Article  Google Scholar 

  • Sörbom, D. (1975). Detection of correlated errors in longitudinal data. British Journal of Mathematical and Statistical Psychology, 28, 138–151.

    Article  Google Scholar 

  • Sörbom, D. (1978). An alternative to the methodology for analysis of covariance. Psychometrika, 43, 381–396.

    Article  Google Scholar 

  • Tisak, J. & Tisak, M.S. (1996). Longitudinal modeis of reliability and validity: A latent curve approach. Applied Psychological Measurement, 20(3), 275–288.

    Article  Google Scholar 

  • Tuma, N. & Hannan, M. (1984). Social dynamics. New York: Academic Press.

    Google Scholar 

  • Tucker, L.R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19–23.

    Article  Google Scholar 

  • Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1–10.

    Article  Google Scholar 

  • Verbeke, G. & Molenberghs, G. (2000). Linear mixed modeis for longitudinal data. New York: Springer.

    Google Scholar 

  • Wiley, D.E. & Wiley, J.A. (1970). The identification of measurement errors in panel data. American Sociological Review, 35, 112–117.

    Article  Google Scholar 

  • Willett, J.B. & Sayer, A.G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363–381.

    Article  Google Scholar 

  • Wohwill, J. F. (1973). The study of behavioral development. New York: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Virginia, Charlottesville, Virginia, USA

    John McArdle & Fumiaki Hamagami

Authors
  1. John McArdle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fumiaki Hamagami
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Free University Amsterdam, Amsterdam, The Netherlands

    Kees van Montfort

  2. University of Nijmegen, Nijmegen, The Netherlands

    Johan Oud

  3. Universitat Pompeu Fabra, Barcelona, Spain

    Albert Satorra

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

McArdle, J., Hamagami, F. (2004). Methods for Dynamic Change Hypotheses. In: van Montfort, K., Oud, J., Satorra, A. (eds) Recent Developments on Structural Equation Models. Mathematical Modelling: Theory and Applications, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1958-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-1958-6_15

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6549-0

  • Online ISBN: 978-1-4020-1958-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation