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Circular piecewise regression with applications to cell‐cycle data

Author

Listed:
  • Cristina Rueda
  • Miguel A. Fernández
  • Sandra Barragán
  • Kanti V. Mardia
  • Shyamal D. Peddada

Abstract

Applications of circular regression models appear in many different fields such as evolutionary psychology, motor behavior, biology, and, in particular, in the analysis of gene expressions in oscillatory systems. Specifically, for the gene expression problem, a researcher may be interested in modeling the relationship among the phases of cell‐cycle genes in two species with differing periods. This challenging problem reduces to the problem of constructing a piecewise circular regression model and, with this objective in mind, we propose a flexible circular regression model which allows different parameter values depending on sectors along the circle. We give a detailed interpretation of the parameters in the model and provide maximum likelihood estimators. We also provide a model selection procedure based on the concept of generalized degrees of freedom. The model is then applied to the analysis of two different cell‐cycle data sets and through these examples we highlight the power of our new methodology.

Suggested Citation

  • Cristina Rueda & Miguel A. Fernández & Sandra Barragán & Kanti V. Mardia & Shyamal D. Peddada, 2016. "Circular piecewise regression with applications to cell‐cycle data," Biometrics, The International Biometric Society, vol. 72(4), pages 1266-1274, December.
    • Handle: RePEc:bla:biomet:v:72:y:2016:i:4:p:1266-1274
    DOI: 10.1111/biom.12512
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    References listed on IDEAS

    as
    1. Rueda, Cristina & Fernández, Miguel A. & Peddada, Shyamal Das, 2009. "Estimation of Parameters Subject to Order Restrictions on a Circle With Application to Estimation of Phase Angles of Cell Cycle Genes," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 338-347.
    2. Marco Di Marzio & Agnese Panzera & Charles C. Taylor, 2013. "Non-parametric Regression for Circular Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(2), pages 238-255, June.
    3. Rueda, Cristina, 2013. "Degrees of freedom and model selection in semiparametric additive monotone regression," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 88-99.
    4. Kato, Shogo & Jones, M. C., 2010. "A Family of Distributions on the Circle With Links to, and Applications Arising From, Möbius Transformation," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 249-262.
    5. Zhang, Bo & Shen, Xiaotong & Mumford, Sunni L., 2012. "Generalized degrees of freedom and adaptive model selection in linear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 574-586.
    6. Hankin, Robin K. S., 2015. "Circular Statistics in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(b05).
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    Cited by:

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