Skip to main content
SpringerLink
Log in

Some Models and Their Extensions for Longitudinal Analyses

  • Chapter
  • First Online:
Data Science and SDGs

  • 487 Accesses

Abstract

In this article, I present some of my statistical research in the field of longitudinal data analysis along with applications of these methods to real data sets. The aim is not to cover the whole field; rather, the perspective is based on my own personal preferences. The presented methods are mainly based on growth curve and mixture regression models and their extensions, where the focus is on continuous longitudinal data. In addition, an example of the analysis of extensive register data for categorical longitudinal data is presented. Applica-tions range from forestry and health sciences to social sciences.

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 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
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

References

  • Berkson, J. (1950). Are there two regressions? Journal of the American Statistical Association, 45, 164–180.

    Google Scholar 

  • Green, P., & Silverman, B. (1994). Nonparametric regression and generalized linear models. A roughness penalty approach (58th ed.). Monographs on Statistics and Applied Probability, Boca Raton, FL: Chapman Hall/CRC.

    Google Scholar 

  • Kozak, A. (1988). A variable-exponent taper equation. Canadian Journal of Forest Research, 18, 1363–1368.

    Article  Google Scholar 

  • Kurvinen, A., Jolkkonen, A., Koistinen, P., Lipiäinen, L., Nummi, T. & Virtanen, P. (2018). Työn menetys työuran loppuvaiheessa—Tutkimus 45–60-vuotiaana rakennemuutoksessa työnsä menettäneiden työllisyysurista ja riskistä päätyä työttömäksi tai työvoiman ulkopuolelle, 83, 5–6. (in Finnish with English abstract).

    Google Scholar 

  • Laasasenaho, J. (1982). Taper curve and volume functions for pine, spruce and birch. Communicationes Instituti Forestalis Fenniae, 108. http://urn.fi/URN:ISBN:951-40-0589-9

  • Liski, E. P., & Nummi, T. (1990). Prediction in growth curve models using the EM algorithm. Computational Statistics & Data Analysis, 10(2), 99–108.

    Article  MathSciNet  Google Scholar 

  • Liski, E. P., & Nummi, T. (1995a). Prediction and iinverse estimation in repeated-measures models. Journal of Statistical Planning and Inference, 47, 141–151.

    Article  Google Scholar 

  • Liski, E. P., & Nummi, T. (1995b). Prediction of tree stems to improve efficiency in automatized harvesting of forests. Scandinavian Journal of Statistics, 22(2), 255–269.

    MATH  Google Scholar 

  • Liski, E. P., & Nummi, T. (1996a). Prediction in repeated-measures models with engineering applications. Technometrics, 38(1), 25–36. https://doi.org/10.1080/00401706.1996.10484413

    Article  MathSciNet  MATH  Google Scholar 

  • Liski, E. P., & Nummi, T. (1996b). The marking for bucking under uncertainty in automatic harvesting of forest. International Journal of Production Economics, 46–47, 373–385.

    Article  Google Scholar 

  • Liski E. P., & Nummi T. (1991). Missing data under the GMANOVA model. In Özturk, & van der Meulen (Eds.), Conference Proceedings on the Frontiers of Statistical Scientific Theory—Industrial Applications (Volume II of the Proceedings of ICOSCO-I, The First International Conference on Statistical Computing) (pp. 391–404). Columbus, Ohio: American Science Press Inc.

    Google Scholar 

  • Mesue, N., & Nummi, T. (2013). Testing of growth curves using smoothing spline: A multivariate approach. In V. M. R. Muggeo, V. Capusi, G. Boscaino, & G. Lovison (Eds.), Proceedings of the 28th International Workshop on Statistical Modelling (pp. 281–288). Palermo, Italia: Statistical Modelling Society.

    Google Scholar 

  • Min, Y., & Agresti, A. (2005) Random effect models for repeated measures of zero-inflated count data. Statistical Modelling, 5(1), 1–19.

    Google Scholar 

  • Nagin, D. S. (1999). Analyzing developmental trajectories: A semiparametric, group-based approach. Psychological Methods, 4(2), 139–157. https://doi.org/10.1037/1082-989X.4.2.139

    Article  Google Scholar 

  • Nagin, D. S. (2005). Group-based modeling of development. Harvard University Press.

    Book  Google Scholar 

  • Ngaruye, I., Nzabanita, J., von Rosen, D., & Singull, M. (2017). Small area estimation under a multivariate linear model for repeated measures data. Communications in Statistics—Theory and Methods, 46(21), 10835–10850. https://doi.org/10.1080/03610926.2016.1248784

    Article  MathSciNet  MATH  Google Scholar 

  • Nummi, T. (1997). Estimation in a random effects growth curve model. Journal of Applied Statistics, 24(2), 157–168. https://doi.org/10.1080/02664769723774

    Article  MathSciNet  Google Scholar 

  • Nummi, T. (2000). Analysis of growth curves under measurement errors. Journal of Applied Statistics, 27(2), 235–243. https://doi.org/10.1080/02664760021763

    Article  MathSciNet  MATH  Google Scholar 

  • Nummi, T., & Koskela, L. (2008). Analysis of growth curve data using cubic smoothing splines. Journal of Applied Statistics, 35(6), 681–691. https://doi.org/10.1080/02664760801923964

    Article  MathSciNet  MATH  Google Scholar 

  • Nummi, T., & Möttönen, J. (2000). On the analysis of multivariate growth curves. Metrika, 52, 77–89. https://doi.org/10.1007/s001840000063

    Article  MathSciNet  MATH  Google Scholar 

  • Nummi, T. (1989). APL as a tool for computations in growth studies. In A. Kertesz, L. C. Shaw (Eds.), APL Quote-Quad (Conference Proceedings APL89 - APL as a Tool of Thought, August 7–10, New York City), Volume 19, Number 4 (pp. 293–298).

    Google Scholar 

  • Nummi, T. (1992). On model selection under the GMANOVA model. In P.G. M van der Heyden, W. Jansen, B. Francis, & G. U. H. Seeber (Eds.), Statistical Modelling (pp. 283–292). Amsterdam: Elsevier Science Publishers B.V.

    Google Scholar 

  • Nummi, T., & Mesue, N. (2013). Testing of growth curves with cubic smoothing splines. In R. Dasgupta (Ed.), Advances in Growth Curve Models. Springer Proceedings in Mathematics & Statistics, vol. 46 (pp. 49–59). Springer, New York. https://doi.org/10.1007/978-1-4614-6862-2_3

  • Nummi, T., & Möttönen, J. (2004). Estimation and prediction for low-degree polynomial models under measurement errors with an application to forest harvester. Journal of the Royal Statistical Society: Series C Applied Statistics, 53, 495–505. https://doi.org/10.1111/j.1467-9876.2004.05138.x

  • Nummi, T., Möttönen, J., & Tuomisto, M. T. (2017). Testing of multivariate spline growth model. In D. G. Chen, Z. Jin, G. Li, Y. Li, A. Liu, Y. Zhao (Eds.), New Advances in Statistics and Data Science (pp. 75–85). Springer, Cham: ICSA Book Series in Statistics. https://doi.org/10.1007/978-3-319-69416-0_5.

  • Nummi T., Salonen J., Koskinen, L., & Pan, J. (2018). A semiparametric mixture regression model for longitudinal data. Journal of Statistical Theory and Practice, 12(1), 12–22. https://doi.org/10.1080/15598608.2017.1298062.

  • Potthoff, R. F., & Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems. Biometrika, 51(3–4), 313–326. https://doi.org/10.1093/biomet/51.3-4.313

    Article  MathSciNet  MATH  Google Scholar 

  • Studer, M. (2013) Weighted cluster library manual: Apractical guide to creating typologies of trajectories in the social sciences with R. LIVES (Working Paper No. 24). https://doi.org/10.12682/lives.2296-1658.2013.24

  • Uusitalo, J., Puustelli, A., Kivinen, V. -P., Nummi, T., & Sinha, B. K. (2006). Bayesian estimation of diameter distribution during harvesting. Silva Fennica, 40(4), 663–671.

    Google Scholar 

  • Virtanen, P., Nummi, T., Lintonen, T., Westerlund, H., Hägglöf, B., & Hammarström, A. (2015). Mental health in adolescence as determinant of alcohol consumption trajectories in the Northern Swedish cohort. International Journal of Public Health, 60, 335–342. https://doi.org/10.1007/s00038-015-0651-5

    Article  Google Scholar 

  • von Rosen, D. (1991). The growth curve model: A review. Communications in Statistics—Theory and Methods, 20(9), 2791–2822. https://doi.org/10.1080/03610929108830668

  • Wang, S. G., Liski, E. P., & Nummi, T. (1999). Two-way selection of covariables in multivariate growth curve models. Linear Algebra and Its Applications, 289, 333–342.

    Article  MathSciNet  Google Scholar 

  • Zezula, I., & Klein, D. (2011). Overview of recent results in growth-curve-type multivariate linear models. Mathematica, 50(2), 137–146.

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author thanks an anonymous referee for making some useful comments and suggestions in an earlier draft.

Author information

Authors and Affiliations

  1. Faculty of Information Technology and Communication Sciences, Tampere University, Tampere, Finland

    Tapio Nummi

Authors
  1. Tapio Nummi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tapio Nummi .

Editor information

Editors and Affiliations

  1. Indian Statistical Institute, Kolkata, West Bengal, India

    Bikas Kumar Sinha

  2. Department of Statistics, University of Rajshahi, Rajshahi, Bangladesh

    Md. Nurul Haque Mollah

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nummi, T. (2021). Some Models and Their Extensions for Longitudinal Analyses. In: Sinha, B.K., Mollah, M.N.H. (eds) Data Science and SDGs. Springer, Singapore. https://doi.org/10.1007/978-981-16-1919-9_2

Download citation

Publish with us

Policies and ethics

Search

Navigation