IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0008915.html
   My bibliography  Save this article

Parameter Identifiability and Redundancy: Theoretical Considerations

Author

Listed:
  • Mark P Little
  • Wolfgang F Heidenreich
  • Guangquan Li

Abstract

Background: Models for complex biological systems may involve a large number of parameters. It may well be that some of these parameters cannot be derived from observed data via regression techniques. Such parameters are said to be unidentifiable, the remaining parameters being identifiable. Closely related to this idea is that of redundancy, that a set of parameters can be expressed in terms of some smaller set. Before data is analysed it is critical to determine which model parameters are identifiable or redundant to avoid ill-defined and poorly convergent regression. Methodology/Principal Findings: In this paper we outline general considerations on parameter identifiability, and introduce the notion of weak local identifiability and gradient weak local identifiability. These are based on local properties of the likelihood, in particular the rank of the Hessian matrix. We relate these to the notions of parameter identifiability and redundancy previously introduced by Rothenberg (Econometrica 39 (1971) 577–591) and Catchpole and Morgan (Biometrika 84 (1997) 187–196). Within the widely used exponential family, parameter irredundancy, local identifiability, gradient weak local identifiability and weak local identifiability are shown to be largely equivalent. We consider applications to a recently developed class of cancer models of Little and Wright (Math Biosciences 183 (2003) 111–134) and Little et al. (J Theoret Biol 254 (2008) 229–238) that generalize a large number of other recently used quasi-biological cancer models. Conclusions/Significance: We have shown that the previously developed concepts of parameter local identifiability and redundancy are closely related to the apparently weaker properties of weak local identifiability and gradient weak local identifiability—within the widely used exponential family these concepts largely coincide.

Suggested Citation

  • Mark P Little & Wolfgang F Heidenreich & Guangquan Li, 2010. "Parameter Identifiability and Redundancy: Theoretical Considerations," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-6, January.
  • Handle: RePEc:plo:pone00:0008915
    DOI: 10.1371/journal.pone.0008915
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0008915
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0008915&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0008915?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. E. A. Catchpole & B. J. T. Morgan & A. Viallefont, 2002. "Solving problems in parameter redundancy using computer algebra," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(1-4), pages 625-636.
    2. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barraquand, Frédéric & Gimenez, Olivier, 2021. "Fitting stochastic predator–prey models using both population density and kill rate data," Theoretical Population Biology, Elsevier, vol. 138(C), pages 1-27.
    2. Philip J. Schmidt & Monica B. Emelko & Mary E. Thompson, 2020. "Recognizing Structural Nonidentifiability: When Experiments Do Not Provide Information About Important Parameters and Misleading Models Can Still Have Great Fit," Risk Analysis, John Wiley & Sons, vol. 40(2), pages 352-369, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2019. "On the estimation of treatment effects with endogenous misreporting," Journal of Econometrics, Elsevier, vol. 208(2), pages 487-506.
    2. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    3. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    4. Neusser, Klaus, 2016. "A topological view on the identification of structural vector autoregressions," Economics Letters, Elsevier, vol. 144(C), pages 107-111.
    5. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    6. Chrysanthos Dellarocas & Charles A. Wood, 2008. "The Sound of Silence in Online Feedback: Estimating Trading Risks in the Presence of Reporting Bias," Management Science, INFORMS, vol. 54(3), pages 460-476, March.
    7. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    8. Naimoli, Antonio & Storti, Giuseppe, 2019. "Heterogeneous component multiplicative error models for forecasting trading volumes," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1332-1355.
    9. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
    10. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers CWP63/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    11. Zirogiannis, Nikolaos & Tripodis, Yorghos, 2013. "A Generalized Dynamic Factor Model for Panel Data: Estimation with a Two-Cycle Conditional Expectation-Maximization Algorithm," Working Paper Series 142752, University of Massachusetts, Amherst, Department of Resource Economics.
    12. Gary Koop & M. Hashem Pesaran & Ron P. Smith, 2013. "On Identification of Bayesian DSGE Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 300-314, July.
    13. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    14. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 49-87.
    15. Juan Carlos Parra-Alvarez & Olaf Posch & Mu-Chun Wang, 2017. "Estimation of Heterogeneous Agent Models: A Likelihood Approach," CESifo Working Paper Series 6717, CESifo.
    16. Luis Alvarez & Cristine Pinto & Vladimir Ponczek, 2022. "Homophily in preferences or meetings? Identifying and estimating an iterative network formation model," Papers 2201.06694, arXiv.org, revised Mar 2024.
    17. Matthew Read, 2023. "Estimating the Effects of Monetary Policy in Australia Using Sign‐restricted Structural Vector Autoregressions," The Economic Record, The Economic Society of Australia, vol. 99(326), pages 329-358, September.
    18. Tito Belchior Silva Moreira & Benjamin Miranda Tabak & Mario Jorge Mendonça & Adolfo Sachsida, 2016. "An Evaluation of the Non-Neutrality of Money," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-20, March.
    19. repec:hal:spmain:info:hdl:2441/293qice3lj861rvos9ns14n0h0 is not listed on IDEAS
    20. Hsiao, Cheng & Fujiki, Hiroshi, 1998. "Nonstationary Time-Series Modeling versus Structural Equation Modeling: With an Application to Japanese Money Demand," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 16(1), pages 57-79, May.
    21. Irina Zviadadze, 2017. "Term Structure of Consumption Risk Premia in the Cross Section of Currency Returns," Journal of Finance, American Finance Association, vol. 72(4), pages 1529-1566, August.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0008915. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.