Robust tests for one or more allometric lines

Journal of Theoretical Biology

Volumn 333, Issue , 2013, Pages 38-46

  Taskinen, S ^a,b   Warton, D I ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Common slope tests; Huber's M estimator; Major axis; Robust statistics; Standardised major axis

Indexed keywords

ALLOMETRY; PRINCIPAL COMPONENT ANALYSIS; STATISTICAL ANALYSIS;

ALLOMETRY; ARTICLE; LINEAR REGRESSION ANALYSIS; MATHEMATICAL VARIABLE; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; SIMULATION;

COMMON SLOPE TESTS; HUBER'S M-ESTIMATOR; MAJOR AXIS; ROBUST STATISTICS; STANDARDISED MAJOR AXIS;

MODELS, THEORETICAL;

EID: 84878704320     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2013.05.010     Document Type: Article

References (33)

1. Anderson T.W. An Introduction to Multivariate Statistical Analysis 2003, Wiley, New York. third ed.
2. Boente G., Orellana L. A robust approach to common principal components. Statistics in Genetics and in the Environmental Sciences 2001, 117-147. Birkhauser. L. Fernholz, S. Morgenthaler, W. Stahel (Eds.).
3. Boente G., Pires A.M., Rodrigues I.M. Influence functions and outlier detection under the common principal components model: a robust approach. Biometrika 2002, 89:861-875.
4. Boente G., Pires A.M., Rodrigues I.M. Robust tests for the common principal components model. J. Stat. Plann. Inference 2009, 139:1332-1347.
5. Chamoli U., Wroe S. Allometry in the distribution of material properties and geometry of the felid skull: why larger species may need to change and how they may achieve it. J. Theor. Biol. 2011, 283(1):217-226.
6. Chappell R. Fitting bent lines to data, with applications to allometry. J. Theor. Biol. 1989, 138(2):235-256.
7. Cheng C.-L., Van Ness J.W. Generalized m-estimators for errors-in-variables regression. Ann. Stat. 1992, 20:385-397.
8. Creasy M.A. Confidence limits for the gradient in the linear functional relationship. J. R. Stat. Soc. B 1957, 18:65-69.
9. Croux C., Haesbroeck G. Principal component analysis based on robust estimators of the covariance or correlation matrix: influence functions and efficiencies. Biometrika 2000, 87:603-618.
10. Devlin S.J., Gnandesikan R., Kettenring J.R. Robust estimation of dispersion matrices and principal components. J. Am. Stat. Assoc. 1981, 76:354-362.
11. Ebert T.A., Russell M.P. Allometry and model ii non-linear regression. J. Theor. Biol. 1994, 168(4):367-372.
12. Fekri M., Ruiz-Gazen A. Robust weighted orthogonal regression in the errors-in-variables model. J. Multivariate Anal. 2004, 88:89-108.
13. Flury B.N. Common principal components in k groups. J. Am. Stat. Assoc. 1984, 79:892-898.
14. Hallin M., Paindaveine D., Verdebout T. Testing for common principal components under heterokurticity. J. Nonparametric Stat. 2010, 22:879-895.
15. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.J. Robust Statistics: The Approach Based on Influence Functions 1986, Wiley, New York.
16. Huber P.J. Robust Statistics 1981, Wiley, New York.
17. Maronna R.A. Robust m-estimators of multivariate location and scatter. Ann. Stat. 1976, 4:51-67.
18. McArdle B.H. Lines, models, and errors: regression in the field. Limnol. Oceanogr. 2003, 48:1363-1366.
19. Niklas K.J. Plant Allometry: The Scaling of Form and Process 1994, University of Chicago Press, Chicago.
20. Pitman E.T.G. A note on normal correlation. Biometrika 1939, 31:9-12.
21. Price C.A., Ogle K., White E.P., Weitz J.S. Evaluating scaling models in biology using hierarchical Bayesian approaches. Ecol. Lett. 2009, 12(7):641-651.
22. Price C.A., Wing S., Weitz J.S. Scaling and structure of dicotyledonous leaf venation networks. Ecol. Lett. 2012, 15(February (2)):87-95.
23. Reiss M.J. The Allometry of Growth and Reproduction 1989, Cambridge University Press, Cambridge.
24. Robinson A.P., Hamann J.D. Forest Analytics with R 2011, Springer Science+Business Media.
25. Smith R.J. Use and misuse of the reduced major axis for line-fitting. Am. J. Phys. Anthropol. 2009, 140:476-486.
26. Taskinen S., Warton D.I. Robust estimation and inference for bivariate line-fitting in allometry. Biometrical J. 2011, 53:652-672.
27. Warton D., Duursma R., Falster D., Taskinen S. smatr 3-an r package for estimation and inference about allometric lines. Methods Ecol. Evol. 2012, 2:257-259.
28. Warton D.I. Robustness to failure of assumptions of tests for a common slope amongst several allometric lines-a simulation study. Biometrical J. 2007, 49(2):286-299.
29. Warton D.I., Weber N.C. Common slope tests for errors-in-variables models. Biometrical J. 2002, 44(2):161-174.
30. Warton D.I., Wright I.J., Falster D.S., Westoby M. Bivariate line-fitting methods for allometry. Biol. Rev. 2006, 81(2):259-291.
31. Wright I.J., Reich P.B., Westoby M., Ackerly D.D., Baruch Z., Bongers F., Cavender-Bares J., Chapin T., Cornelissen J.H.C., Diemer M., Flexas J., Garnier E., Groom P.K., Gulias J., Hikosaka K., Lamont B.B., Lee T., Lee W., Lusk C., Midgley J.J., Navas M.L., Niinemets U., Oleksyn J., Osada N., Poorter H., Poot P., Prior L., Pyankov V.I., Roumet C., Thomas S.C., Tjoelker M.G., Veneklaas E.J., Villar R. The worldwide leaf economics spectrum. Nature 2004, 428:821-827.
32. Wright I.J., Westoby M. Leaves at low versus high rainfall: coordination of structure, lifespan and physiology. New Phytol. 2002, 155:403-416.
33. Zamar R. Robust estimation in the errors-in-variables model. Biometrika 1989, 76:149-160.