Flexible quantile regression modelsapplication to the study of the purple sea urchin

  1. Martínez Silva, Isabel
  2. Roca Pardiñas, Javier
  3. Lustres Pérez, Vicente
  4. Lorenzo-Arribas, Altea
  5. Cadarso Suárez, Carmen María
Journal:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Year of publication: 2013

Volume: 37

Issue: 1

Pages: 81-94

Type: Article

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Abstract

In many applications, it is often of interest to assess the po ssible relationships between covariates and quantiles of a response variable through a regression mo del. In some instances, the effects of continuous covariates on the outcome are highly nonlinear. Consequently, appropriate modelling has to take such flexible smooth effects into account. In this work, various flexible quantile regression techniques were reviewed and compared by simula tion. Finally, all the techniques were used to construct the overall zone specific reference cu rves of morphologic measures of sea urchin Paracentrotus lividus (Lamarck, 1816) located in NW Spain.

Bibliographic References

  • Benedetti-Cecchi, L. and Cinelli, F. (1995). Habitat heterogeneity, sea urchin grazing and the distribution of algae in litoral rock pools on the west coast of italy (western mediterranean). Marine Ecology Progress Series, 126, 203–212.
  • Breiman, L. (1998). Arcing classifiers (with discussion). Annals of Statistics, 26, 801–849.
  • Breiman, L. (1999). Prediction games and arcing algorithms. Neural Computation, 11, 1493–1517.
  • Brian, S., Cade, B. and Noon, R. (2003). A gentle introduction to quantile regression for ecologists. Frontiers in Ecology and the Environment, 1, 412–420.
  • Buehlmann, P. and Hothorn, T. (2007). Boosting algorithms: regularization, prediction and model fitting. Statistical Science, 22, 477–505.
  • Cole, T. J. (1988). Using the lms method to measure skewness in the nchs and dutch national height standards. Annals of Human Biology, 16, 407–419.
  • de Boor, C. (1978). A Practical Guide to Splines. Springer.
  • Fenske, N., Kneib, T. and Hothorn, T. (2009). Identifying risk factors for severe childhood malnutrition by boosting additive quantile regression. Technical report, Department of Statistics University of Munich.
  • Fenske, N., Kneib, T. and Hothorn, T. (2011). Childhood malnutrition by boosting additive quantile regression. Journal of the American Statistical Association, 106, 494–510.
  • Fernández Pulpeiro, E., César Aldariz, J., Lustres-Pérez, V. and Ojea Bouzo, C. (1999). Ordenación integral del espacio marı́timo-terrestre de Galicia. Fauna asociada a sustratos rocosos. Informe final, 1996-1999. Technical report, Consellerı́a de Pesca, Marisqueo e Acuicultura-Xunta de Galicia.
  • Freund, Y. and Schapire, R. (1997). A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 55, 119–139.
  • Friedman, J. (2001). Greedy function approximation: a gradient boosting machine. Annals of Statistics, 29, 1189–1232.
  • Friedman, J., Hastie, T. and Tibshirani, R. (2000). Additive logistic regression: a statistical view of boosting (with discussion). Annals of Statistics, 28, 379–407.
  • González Barcala, F. J., Cadarso-Suárez, C., Valdés Cuadrado, L., Leis Trabazo, R., Cabanas, R. and Tojo Sierra, R. (2008). Lung function reference values in children and adolescents aged 6 to 18 years in Galicia. Arch Bronconeumology, 44, 295–302.
  • Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman and Hall, London.
  • Kitching, J. and Ebling, F. (1961). The ecology os lough ine. xi. the control of algae by paracentrotus lividus (echinoidea). Journal of Animal Ecology, 30, 373–383.
  • Klein, B. and Korsholm, L., editor (2001). The GAMLSS Project: a Flexible Approach to Statistical Modelling.
  • Koenker, R. W. and D’Orey, V. (1994). Computing regression quantiles. Applied Statistics, 43, 410–414.
  • Koenker, R. and Hallock, K. F. (2001). Quantile regression. Journal of Economic Perspectives, 15, 143– 156.
  • Koenker, R. W. and Bassett, G. W. (1978). Regression quantiles. Econometrica, 46, 33–50.
  • Lustres-Pérez, V. (2006). El erizo de mar: Paracentrotus lividus (Lamarck, 1816) en las costas de Galicia. PhD thesis. Universidad de Santiago de Compostela.
  • R Development Core Team (2011). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0.
  • Rigby, R. A. and Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape, (with discussion). Applied Statistics, 54, 507–554.
  • Ruitton, S., Francour, P. and Boudouresque, C. (2000). Relationships between algae, benthic herbivorous invertebrates and fishes in rocky sublittoral communities of a temperature sea (mediterranean). Estuarine, coastal and Shelf Science, 50, 217–230.
  • Wahba, G. (1990). Spline Models for Observational Data. SIAM, Philadelphia.
  • Yee, T. W. and Wild, C. J. (1996). Vector generalized additive models. Journal of Royal Statistical SocietySeries B, 58(3), 481–493.
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