Title: A gentle introduction to quantile regression for ecologists
Abstract: Frontiers in Ecology and the EnvironmentVolume 1, Issue 8 p. 412-420 Review A gentle introduction to quantile regression for ecologists Brian S. Cade, Brian S. Cade Fort Collins Science Center, US Geological Survey, Fort Collins, CO ( E-mail: [email protected]) Graduate Degree Program in Ecology, Colorado State University, Fort Collins, COSearch for more papers by this authorBarry R. Noon, Barry R. Noon Department of Fishery and Wildlife Biology, Colorado State University, Fort Collins, COSearch for more papers by this author Brian S. Cade, Brian S. Cade Fort Collins Science Center, US Geological Survey, Fort Collins, CO ( E-mail: [email protected]) Graduate Degree Program in Ecology, Colorado State University, Fort Collins, COSearch for more papers by this authorBarry R. Noon, Barry R. Noon Department of Fishery and Wildlife Biology, Colorado State University, Fort Collins, COSearch for more papers by this author First published: 01 October 2003 https://doi.org/10.1890/1540-9295(2003)001[0412:AGITQR]2.0.CO;2Citations: 1,297Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogeneous regression models. References Allen, AW, BS Cade, and MW Vandever . 2001. Effects of emergency haying on vegetative characteristics within selected conservation reserve program fields in the northern Great Plains. J Soil Water Conserv 56: 120–25. Web of Science®Google Scholar Brown, RL, and RK Peet . 2003. Diversity and invasibility of southern Appalachian plant communities. Ecology 84: 32–39. 10.1890/0012-9658(2003)084[0032:DAIOSA]2.0.CO;2 Web of Science®Google Scholar Cade, BS . 2003. Quantile regression models of animal habitat relationships (PhD dissertation). Fort Collins, CO: Colorado State University 186 p. Google Scholar Cade, BS, and Q. Guo . 2000. Estimating effects of constraints on plant performance with regression quantiles. Oikos 91: 245–54. 10.1034/j.1600-0706.2000.910205.x Web of Science®Google Scholar Cade, BS, JW Terrell, and RL Schroeder . 1999. Estimating effects of limiting factors with regression quantiles. Ecology 80: 311–23. 10.1890/0012-9658(1999)080[0311:EEOLFW]2.0.CO;2 Web of Science®Google Scholar Cook, JG, and LL Irwin . 1985. Validation and modification of a habitat suitability model for pronghorns. Wildl Soc Bull 13: 440–48. Web of Science®Google Scholar Cunia, T. 1987. Construction of tree biomass tables by linear regression techniques. In: Estimating tree biomass regressions and their error. USDA Forest Service, General Technical Report NE-GTR-117. p 27–36. Google Scholar Dunham, JB, BS Cade, and JW Terrell . 2002. Influences of spatial and temporal variation on fish-habitat relationships defined by regression quantiles. Trans Am Fish Soc 131: 86–98. 10.1577/1548-8659(2002)131<0086:IOSATV>2.0.CO;2 Web of Science®Google Scholar Eastwood, PD, GJ Meaden, and A. Grioche . 2001. Modeling spatial variations in spawning habitat suitability for the sole Solea solea using regression quantiles and GIS procedures. Mar Ecol–Prog Ser 224: 251–66. 10.3354/meps224251 Web of Science®Google Scholar Gerow, K., and C. Bilen . 1999. Confidence intervals for percentiles: an application to estimation of potential maximum biomass of trout in Wyoming streams. North Am J Fish Mana 19: 149–51. 10.1577/1548-8675(1999)019<0149:CIFPAA>2.0.CO;2 Google Scholar Gutenbrunner, C., J. Jurecková, R. Koenker, and S. Portnoy . 1993. Tests of linear hypotheses based on regression rank scores. J Nonparametr Stat 2: 307–31. 10.1080/10485259308832561 Google Scholar Haire, SL, CE Bock, BS Cade, and BC Bennett . 2000. The role of landscape and habitat characteristics in limiting abundance of grassland nesting songbirds in an urban open space. Landscape Urban Plan 48: 65–82. 10.1016/S0169-2046(00)00044-X Web of Science®Google Scholar Hubert, WA, TD Marwitz, and KG Gerow . 1996. Estimation of potential maximum biomass of trout in Wyoming streams to assist management decisions. North Am J Fish Mana 16: 821–29. 10.1577/1548-8675(1996)016<0821:EOPMBO>2.3.CO;2 Google Scholar Huston, MA . 2002. Introductory essay: critical issues for improving predictions. In: Scott JM, et al. (Eds). Predicting species occurrences: issues of accuracy and scale. Covelo, CA: Island Press. p 7–21. Google Scholar Kaiser, MS, PL Speckman, and JR Jones . 1994. Statistical models for limiting nutrient relations in inland waters. J Am Stat Assoc 89: 410–23. 10.1080/01621459.1994.10476763 Web of Science®Google Scholar Knight, CA, and DD Ackerly . 2002. Variation in nuclear DNA content across environmental gradients: a quantile regression analysis. Ecol Lett 5: 66–76. 10.1046/j.1461-0248.2002.00283.x Web of Science®Google Scholar Koenker, R. 1994. Confidence intervals for regression quantiles. In: Mandl P and HusŠková M (Eds). Asymptotic statistics: proceedings of the 5th Prague Symposium. Physica–Verlag: Heidleberg. p 349–59. Google Scholar Koenker, R., and G. Bassett . 1978. Regression quantiles. Econometrica 46: 33–50. 10.2307/1913643 Web of Science®Google Scholar Koenker, R., and V. d’Orey . 1987. Computing regression quantiles. Appl Stat 36: 383–93. 10.2307/2347802 Web of Science®Google Scholar Koenker, R., and O. Geling . 2001. Reappraising medfly longevity: a quantile regression survival analysis. J Am Stat Assoc 96: 458–68. 10.1198/016214501753168172 Web of Science®Google Scholar Koenker, R., and JAF Machado . 1999. Goodness of fit and related inference processes for quantile regression. J Am Stat Assoc 94: 1296–1310. 10.1080/01621459.1999.10473882 Web of Science®Google Scholar Koenker, R., and BJ Park . 1996. An interior point algorithm for nonlinear quantile regression. J Econometrics 71: 265–83. 10.1016/0304-4076(96)84507-6 Web of Science®Google Scholar Koenker, R., and F. Schorfheide . 1994. Quantile spline models for global temperature change. Climatic Change 28: 395–404. 10.1007/BF01104081 CASWeb of Science®Google Scholar Koenker, R., P. Ng, and S. Portnoy . 1994. Quantile smoothing splines. Biometrika 81: 673–80. 10.1093/biomet/81.4.673 Web of Science®Google Scholar McClain, CR, and MA Rex . 2001. The relationship between dissolved oxygen concentration and maximum size in deep-sea turrid gastropods: an application of quantile regression. Mar Biol 139: 681–85. 10.1007/s002270100617 Web of Science®Google Scholar McCullagh, P., and JA Nelder . 1989. Generalized linear models. New York: Chapman and Hall. Google Scholar Mosteller, F., and JW Tukey . 1977. Data analysis and regression. New York: Addison-Wesley. Google Scholar Neter, JM, H. Kutner, CJ Nachtsheim, and W. Wasserman . 1996. Applied linear statistical models. Chicago, IL: Irwin. Google Scholar Portnoy, S. 1991. Asymptotic behavior of the number of regression quantile breakpoints. SIAM J Sci Stat Comp 12: 867–83. 10.1137/0912047 Web of Science®Google Scholar Rosenbaum, PR . 1995. Quantiles in nonrandom samples and observational studies. J Am Stat Assoc 90: 1424–31. Web of Science®Google Scholar Scharf, FS, F. Juanes, and M. Sutherland . 1998. Inferring ecological relationships from the edges of scatter diagrams: comparison of regression techniques. Ecology 79: 448–60. 10.1890/0012-9658(1998)079[0448:IERFTE]2.0.CO;2 Web of Science®Google Scholar Terrell, JW, BS Cade, J. Carpenter, and JM Thompson . 1996. Modeling stream fish habitat limitations from wedged-shaped patterns of variation in standing stock. Trans Am Fish Soc 125: 104–17. 10.1577/1548-8659(1996)125<0104:MSFHLF>2.3.CO;2 Web of Science®Google Scholar Thomson, JD, G. Weiblen, and BA Thomson . 1996. Untangling multiple factors in spatial distributions: lilies, gophers and rocks. Ecology 77: 1698–1715. 10.2307/2265776 Web of Science®Google Scholar Vardeman, S. 1992. What about the other intervals?. Am Stat 46: 193–97. 10.2307/2685212 Web of Science®Google Scholar Welsh, AH, RJ Carroll, and D. Rupert . 1994. Fitting heteroscedastic regression models. J Am Stat Assoc 89: 100–16. 10.1080/01621459.1994.10476450 Web of Science®Google Scholar Yu, K., and MC Jones . 1998. Local linear quantile regression. J Am Stat Assoc 93: 228–37. 10.1080/01621459.1998.10474104 Web of Science®Google Scholar Zhou, KQ, and SL Portnoy . 1996. Direct use of regression quantiles to construct confidence sets in linear models. Ann Stat 24: 287–306. 10.1214/aos/1033066210 Web of Science®Google Scholar Zhou, KQ, and SL Portnoy . 1998. Statistical inference on heteroscedastic models based on regression quantiles. J Nonparametr Stat 9: 239–60. 10.1080/10485259808832745 Web of Science®Google Scholar Citing Literature Volume1, Issue8October 2003Pages 412-420 This article also appears in:Centennial Collection ReferencesRelatedInformation
Publication Year: 2003
Publication Date: 2003-10-01
Language: en
Type: review
Indexed In: ['crossref']
Access and Citation
Cited By Count: 1665
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot