Skip to main content
SpringerLink
Log in

Continuous Time Modeling of Panel Data by means of SEM

  • Chapter
  • First Online:
Longitudinal Research with Latent Variables

Abstract

After a brief history of continuous time modeling and its implementation in panel analysis by means of structural equation modeling (SEM), the problems of discrete time modeling are discussed in detail. This is done by means of the popular cross-lagged panel design. Next, the exact discrete model (EDM) is introduced, which accounts for the exact nonlinear relationship between the underlying continuous time model and the resulting discrete time model for data analysis. In addition, a linear approximation of the EDM is discussed: the approximate discrete model (ADM). It is recommended to apply the ADM-SEM procedure by means of a SEM program such as LISREL in the model building phase and the EDM-SEM procedure by means of Mx in the final model estimation phase. Both procedures are illustrated in detail by two empirical examples: Externalizing and Internalizing Problem Behavior in children; Individualism, Nationalism and Ethnocentrism in the Flemish electorate.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

  • Arnold, L. (1974). Stochastic differential equations. New York: Wiley.

    MATH  Google Scholar 

  • Arminger, G. (1986). Linear stochastic differential equations for panel data with unobserved variables. In N. B. Tuma (Ed.), Sociological methodology (pp. 187-212). Washington: Jossey-Bass.

    Google Scholar 

  • Bartlett, M. S. (1946). On the theoretical specification and sampling properties of autocorrelated time-series. Journal of the Royal Statistical Society (Supplement), 7, 27-41.

    Article  MathSciNet  Google Scholar 

  • Blalock, H. M., Jr. (1969). Theory construction: From verbal to mathematical formulations. Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

  • Bergstrom, A. R. (1966). Nonrecursive models as discrete approximations to systems of stochastic differential equations. Econometrica, 34, 173-182.

    Article  MATH  MathSciNet  Google Scholar 

  • Bergstrom, A. R. (1984). Continuous time stochastic models and issues of aggregation over time. In Z. Griliches & M. D. Intriligator (Eds.), Handbook of econometrics: Vol. 2 (pp. 1145-1212). Amsterdam: North-Holland.

    Google Scholar 

  • Bergstrom, A. R. (1988). The history of continuous-time econometric models. Econometric Theory, 4, 365-383.

    MathSciNet  Google Scholar 

  • Boker, S., Neale, M., & Rausch, J. (2004). Latent differential equation modeling with multivariate multi-occasion indicators. In K. van Montfort, J. Oud, & A. Satorra (Eds.), Recent developments on structural equations models: Theory and applications (pp. 151-174). Dordrecht, The Netherlands: Kluwer Academic Publishers.

    Google Scholar 

  • Browne, M. W. & R. Cudeck (1993). Alternative ways of assessing model fit. In K. A. Bollen & J. Scott Long (Eds.), Testing structural equation models (pp. 136-162). Newbury Park: Sage.

    Google Scholar 

  • Bui, K. V. T., Ellickson, P. L., & Bell, R. M. (2000). Cross-lagged relationships among adolescent problem drug use, delinquent behavior, and emotional distress. Journal of Drug Issues, 30, 283-303.

    Google Scholar 

  • Burke, J. D., Loeber, R., Lahey, B. B., & Rathouz, P. J. (2005). Developmental transitions among affective and behavioral disorders in adolescent boys. Journal of Child Psychology and Psychiatry, 46, 1200-1210.

    Article  Google Scholar 

  • Capaldi, D. M. (1992). Co-occurrence of conduct problems and depressive symptoms in early adolescent boys: II. A 2-year follow-up at grade 8. Development and Psychopathology, 4, 125-144.

    Article  Google Scholar 

  • Carlson, G. A., & Cantwell, D. P. (1980). Unmasking masked depression in children and adolescents. American Journal of Psychiatry, 137, 445-449.

    Google Scholar 

  • Coleman, J. S. (1968). The mathematical study of change. In H.M. Blalock, Jr. & A. Blalock (Eds.), Methodology in social research (pp. 428-478). New York: McGraw-Hill.

    Google Scholar 

  • De Bruyn, E. E. J., Scholte, R. H. J., & Vermulst, A. A. (2005). Psychometric analyses of the Nijmegen problem behavior list (NPBL): A research instrument for assessing problem behavior in community samples using self- and other reports of adolescents and parents. Nijmegen, The Netherlands: Institute of Family and Child Studies, Radboud University Nijmegen

    Google Scholar 

  • Delsing, M. J. M. H., Oud, J. H. L., van Aken, M. A. G., De Bruyn, E. E. J., & Scholte, R. J. H. (2005). Family loyalty and adolescent problem behavior: The validity of the family group effect. Journal of Research on Adolescence, 15, 127-150.

    Article  Google Scholar 

  • Gold, M., Mattlin, M., & Osgood, D. W. (1989). Background characteristics and response to treatment of two types of institutionalized delinquent boys. Criminal Justice and Behaviour, 16, 5-33.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Haselager, G. J. T., & van Aken, M. A. G. (1999). Codebook of the research project Family and Personality: Vol. 1. First measurement wave. Nijmegen, The Netherlands: University of Nijmegen, Faculty of Social Science.

    Google Scholar 

  • Homans, G. C. (1950). The human group. New York: Harcourt, Brace & World.

    Google Scholar 

  • Jöreskog, K. G. (1977). Structural equation models in the social sciences: Specification, estimation and testing. In Krishnaiah, P. R. (Ed.), Applications of statistics (pp. 265-287). Amsterdam: North-Holland.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1976). LISREL III: Estimation of linear structural equation systems by maximum likelihood methods: A FORTRAN IV program. Chicago: National Educational Resources.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1996). LISREL 8: User’s reference guide. Chicago: Scientific Software International.

    Google Scholar 

  • Kuo, H.-H. (2006). Introduction to stochastic integration. New York: Springer.

    MATH  Google Scholar 

  • Neale, M.C. (2000). Individual fit, heterogeneity, and missing data in multigroup structural equation modeling. In T.D. Little, K.U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data (pp. 219-240). Mahwah NJ: Lawrence Erlbaum.

    Google Scholar 

  • Neale, M. C., Boker, S. M., Xie, G., & Maes, H. H. (2006). Mx: Statistical Modeling (7th ed.). Richmond, VA: Department of Psychiatry.

    Google Scholar 

  • Neiderhiser, J. M., Reiss, D., Hetherington, E. M., & Plomin, R. (1999). Relationships between parenting and adolescent adjustment over time: Genetic and environmental contributions. Developmental Psychology, 35, 680-692.

    Article  Google Scholar 

  • Oud, J. H. L. (1978). Systeem-methodologie in sociaal-wetenschappelijk onderzoek [Systems methodology in social science research]. Doctoral dissertation. Nijmegen: Alfa.

    Google Scholar 

  • Oud, J. H. L. (2007a). Comparison of four procedures to estimate the damped linear differential oscillator for panel data. In K. van Montfort, J. Oud, & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences (pp. 19-39). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Oud, J. H. L. (2007b). Continuous time modeling of reciprocal effects in the cross-lagged panel design. In S.M. Boker & M.J. Wenger (Eds.), Data analytic techniques for dynamical systems in the social and behavioral sciences. Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Oud, J. H. L., & Jansen, R. A. R. G. (1996). Nonstationary longitudinal LISREL model estimation from incomplete panel data using EM and the Kalman smoother. In U. Engel & J. Reinecke (Eds.), Analysis of change: Advanced techniques in panel data analysis (pp. 135-159). Berlin: Walter de Gruyter.

    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  MathSciNet  Google Scholar 

  • Oud, J. H. L., Jansen, R. A. R. G., van Leeuwe, J.F.J., Aarnoutse, C. A. J., & Voeten, M. J. M. (1999). Monitoring pupil development by means of the Kalman filter and smoother based upon SEM state space modeling. Learning and Individual Differences, 10, 121-136.

    Article  Google Scholar 

  • Oud, J. H. L., van Leeuwe, J. F. J, & Jansen, R. A. R. G., (1993). Kalman filtering in discrete and continuous time based on longitudinal LISREL models. In J. H. L. Oud & A. W. van Blokland-Vogelesang (Eds.), Advances in longitudinal and multivariate analysis in the behavioral sciences (pp.3-26). Nijmegen: ITS.

    Google Scholar 

  • Oud, J. H. L., & Singer, H. (2008). Continuous time modeling of panel data: SEM versus filter techniques. Statistica Neerlandica, 62, 4-28.

    Article  MATH  MathSciNet  Google Scholar 

  • Overbeek, G. J., Vollebergh, W. A. M., Meeus, W. H. J., Luijpers, E. T. H., & Engels, R. C. M. E. (2001). Course, co-occurence and longitudinal associations between emotional disturbance and delinquency from adolescence to young adulthood: A six-year three-wave study. Journal of Youth and Adolescence, 30, 401-426.

    Article  Google Scholar 

  • Phillips, P. C. B. (1993). The ET Interview: A. R. Bergstrom. In P. C. B. Phillips (Ed.), Models, methods, and applications of econometrics (pp. 12-31). Cambridge, MA: Blackwell.

    Google Scholar 

  • Rueter, M. A., & Conger, R. D. (1998). Reciprocal influences between parenting and adolescent problem-solving behavior. Developmental Psychology, 34, 1470-1482.

    Article  Google Scholar 

  • Simon, H. A. (1952). A formal theory of interaction in small groups. American Sociological Review, 17, 202-211.

    Article  Google Scholar 

  • Singer, H. (1990). Parameterschätzung in zeitkontinuierlichen dynamischen Systemen [Parameter estimation in continuous time dynamic systems]. Konstanz: Hartung-Gorre.

    Google Scholar 

  • Singer, H. (1991). LSDE - A program package for the simulation, graphical display, optimal filtering and maximum likelihood estimation of linear stochastic differential equations: User’s guide. Meersburg: Author.

    Google Scholar 

  • Singer, H. (1993). Continuous-time dynamical systems with sampled data, errors of measurement and unobserved components. Journal of Time Series Analysis, 14, 527-545.

    Article  MATH  MathSciNet  Google Scholar 

  • Singer, H. (1995). Analytical score function for irregularly sampled continuous time stochastic processes with control variables and missing values. Econometric Theory, 11, 721–735.

    Article  MathSciNet  Google Scholar 

  • Singer, H. (1998). Continuous panel models with time dependent parameters. Journal of Mathematical Sociology, 23, 77-98.

    MATH  Google Scholar 

  • Toharudin, T., Oud, J. H. L., & Billiet, J. B. (2008). Assessing the relationships between Nationalism, Ethnocentrism, and Individualism in Flanders using Bergstrom’s approximate discrete model. Statistica Neerlandica, 62, 83-103.

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Vuchinich, S., Bank, L., & Patterson, G. R. (1992). Parenting, peers, and the stability of antisocial behavior in preadolescent boys. Developmental Psychology, 38, 510-521.

    Article  Google Scholar 

  • Wothke, W. (2000). Longitudinal and multigroup modeling with missing data. In T.D. Little, K.U. Schnabel, & J. Baumert (Eds.), Modeling longitudinal and multilevel data (pp. 219-240). Mahwah NJ: Lawrence Erlbaum.

    Google Scholar 

  • Zadeh, L. A., & Desoer, C. A. (1963). Linear system theory: The state space approach. New York: McGraw-Hill.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Behavioural Science Institute, Radboud University Nijmegen, Nijmegen, The Netherlands

    Johan H. L. Oud

  2. Praktikon, Radboud University Nijmegen, Nijmegen, The Netherlands

    Marc J. M. H. Delsing

Authors
  1. Johan H. L. Oud
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marc J. M. H. Delsing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Johan H. L. Oud .

Editor information

Editors and Affiliations

  1. Dept. Econometrics & Operations, Research, Vrije Universiteit Amsterdam, De Boelelaan 1105, Amsterdam, 1081 HV, Netherlands

    Kees van Montfort

  2. Behavioural Science Institute, Radboud University Nijmegen, Montessorilaan 3, Nijmegen, 6525 HR, Netherlands

    Johan H.L. Oud

  3. , Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, Barcelona, 08005, Spain

    Albert Satorra

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Oud, J.H.L., Delsing, M.J.M.H. (2010). Continuous Time Modeling of Panel Data by means of SEM. In: van Montfort, K., Oud, J., Satorra, A. (eds) Longitudinal Research with Latent Variables. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11760-2_7

Download citation

Publish with us

Policies and ethics

Search

Navigation