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An ANOVA test for parameter estimability using data cloning with application to statistical inference for dynamic systems

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  • Campbell, David
  • Lele, Subhash

Abstract

Models for complex systems are often built with more parameters than can be uniquely identified by the available data. Because of the variety of causes, identifying a lack of parameter identifiability typically requires the mathematical manipulation of models, Monte Carlo simulations, and examination of the Fisher Information Matrix. A simple test for parameter estimability is introduced, using Data Cloning, a Markov Chain Monte Carlo based algorithm. Together, Data cloning and the ANOVA based test determine if the model parameters are estimable and if so, determine their maximum likelihood estimates and provide the asymptotic standard errors. When not all model parameters are estimable, the Data Cloning results and the ANOVA test can be used to determine estimable parameter combinations or infer identifiability problems in the model structure. The method is illustrated using three different real data systems that are known to be difficult to analyze.

Suggested Citation

  • Campbell, David & Lele, Subhash, 2014. "An ANOVA test for parameter estimability using data cloning with application to statistical inference for dynamic systems," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 257-267.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:257-267
    DOI: 10.1016/j.csda.2013.09.013
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    References listed on IDEAS

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    1. Adrian E. Raftery & Le Bao, 2010. "Estimating and Projecting Trends in HIV/AIDS Generalized Epidemics Using Incremental Mixture Importance Sampling," Biometrics, The International Biometric Society, vol. 66(4), pages 1162-1173, December.
    2. Sulieman, H. & Kucuk, I. & McLellan, P.J., 2009. "Parametric sensitivity: A case study comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2640-2652, May.
    3. Lele, Subhash R. & Nadeem, Khurram & Schmuland, Byron, 2010. "Estimability and Likelihood Inference for Generalized Linear Mixed Models Using Data Cloning," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1617-1625.
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    Cited by:

    1. Diana J. Cole, 2019. "Parameter redundancy and identifiability in hidden Markov models," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 105-118, August.

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