Impact of multicollinearity on small sample hydrologic regression models

Water Resources Research

Volumn 49, Issue 6, 2013, Pages 3756-3769

  Kroll, Charles N ^a   Song, Peter ^a,b  

^a STATE UNIVERSITY OF NEW YORK   (United States)

^b Anchor QEA LLC   (United States)

Author keywords

low flows; multicollinearity; regression models; streamflow prediction

Indexed keywords

LEAST SQUARES APPROXIMATIONS; MONTE CARLO METHODS; PARAMETER ESTIMATION; STREAM FLOW;

CORRELATION COEFFICIENT; LEAVE-ONE-OUT CROSS VALIDATIONS; LOW FLOW; MULTICOLLINEARITY; PARTIAL LEAST SQUARES REGRESSION; PRINCIPAL COMPONENT REGRESSION; REGRESSION MODEL; STREAMFLOW PREDICTION;

REGRESSION ANALYSIS;

CORRELATION; DATA ACQUISITION; HYDROLOGICAL MODELING; INFLATION; MONTE CARLO ANALYSIS; REGRESSION ANALYSIS; STREAMFLOW;

UNITED STATES;

EID: 84879217261     PISSN: 00431397     EISSN: 19447973     Source Type: Journal    
DOI: 10.1002/wrcr.20315     Document Type: Article

References (50)

1. Arditi, R., (1989), Avoiding fallacious significance tests in stepwise regression: A Monte Carlo method applied to a meteorological theory for the Canadian lynx cycle, Int. J. Biometeorol., 33 (1), 24-26. (Pubitemid 20181513)
2. Chatterjee, S., and, B. Price, (1990), Regression Diagnostics, Wiley, New York.
3. Draper, N. R., and, H. Smith, (1981), Applied Regression Analysis, Wiley, New York.
4. Driver, N. E., and, B. M. Troutman, (1989), Regression models for estimating urban storm-runoff quality and quantity in the United States, J. Hydrol., 109 (3-4), 221-236.
5. Falcone, J. A., D. M. Carlisle, D. M. Wolock, and, M. R. Meador, (2010), GAGES: A stream gage database for evaluating natural and altered flow conditions in the conterminous United States, Ecology, 91 (2), 621-621.
6. Frank, I. E., and, J. H. Friedman, (1993), A statistical view of some chemometrics regression tools, Technometrics, 35 (2), 109-135.
7. Gallo, E. L., P. D. Brooks, K. A. Lohse, and, J. E. T. McLain, (2012), Temporal patterns and controls on runoff magnitude and solution chemistry of urban catchments in the semiarid southwestern United States, Hydrol. Processes, 27 (7), 995-1010, doi: 10.1002/hyp.9199.
8. Gardner, K. K., and, R. M. Vogel, (2005), Predicting groundwater nitrate concentration from land use in Nantucket, Massachusetts, Groundwater, 43 (3), 343-352. (Pubitemid 40707580)
9. Geladi, P., and, B. R. Kowalski, (1986), Partial least-squares regression: A tutorial, Anal. Chim. Acta, 185, 1-17.
10. Graham, M. H., (2003), Confronting multicollinearity in ecological multiple regression, Ecology, 84 (11), 2809-2815. (Pubitemid 38261430)
11. Greene, W., (1990), Econometric Analysis, Macmillan, New York.
12. Grewal, R., J. A. Cote, and, H. Baumgartner, (2004), Multicollinearity and measurement error in structural equation models: implications for theory testing, Marketing Sci., 23 (4), 519-529.
13. Haan, C. T., and, D. M. Allen, (1972), Comparison of multiple regression and principal component regression for predicting water yields in Kentucky, Water Resour. Res., 8 (6), 1593-1596.
14. Hardison, C. H., (1971), Prediction error of regression estimates of streamflow characteristics at ungauged sites, U.S. Geol. Surv. Prof. Pap. 750-C, C228-C236.
15. Helland, I. S., and, T. Almoy, (1994), Comparison of prediction methods when only a few components are relevant, J. Am. Stat. Assoc., 89 (426), 583-591.
16. Hoerl, A. E., and, R. W. Kennard, (2000), Ridge regression: Biased estimation for nonorthogonal problems, Technometrics, 42 (1, special 40th Anniversary Issue), 80-86.
17. Johnston, J., (1972), Econometric Methods, McGraw-Hill, New York.
18. Jolliffe, I. T., (1986), Principal Component Analysis, Wiley, New York.
19. Kelsey, H., D. E. Porter, G. Scott, M. Neet, and, N. White, (2004), Using geographic information systems and regression analysis to evaluate relationships between land use and fecal coliform bacterial pollution, J. Exp. Mar. Biol. Ecol., 298 (2), 197-209. (Pubitemid 38192771)
20. Kiers, H., and, A. Smilde, (2007), A comparison of various methods for multivariate regression with highly collinear variables, Stat. Methods Appl., 16 (2), 193-228.
21. Kreuger, J., and, L. Tornqvist, (1998), Multiple regression analysis of pesticide occurrence in streamflow related to pesticide properties and quantities applied, Chemosphere, 37 (2), 189-207. (Pubitemid 28254274)
22. Kroll, C., J. Luz, B. Allen, and, R. M. Vogel, (2004), Developing a watershed characteristics database to improve low streamflow prediction, J. Hydrol. Eng., 9 (2), 116-125. (Pubitemid 38382019)
23. Kroll, C. N., and, J. R. Stedinger, (1998), Regional hydrologic analysis: Ordinary and generalized least squares revisited, Water Resour. Res., 34 (1), 121-128. (Pubitemid 28031194)
24. Kroll, C. N., and, J. R. Stedinger, (1999), Development of regional regression relationships with censored data, Water Resour. Res., 35 (3), 775-784. (Pubitemid 29111807)
25. Laaha, G., and, G. Bloschl, (2007), A national low flow estimation procedure for Austria, Hydrol. Sci. J., 52 (4), 625-644. (Pubitemid 47241719)
26. Mansfield, E. R., and, B. P. Helms, (1982), Detecting multicollinearity, Am. Stat., 36 (3), 158-160.
27. Mason, C. H., and, W. D. Perreault Jr,. (1991), Collinearity, power, and interpretation of multiple regression analysis, J. Market. Res., 28 (3), 268-280.
28. McElroy, F. W., (1967), A necessary and sufficient condition that ordinary least-squares estimators be best linear unbiased, J. Am. Stat. Assoc., 62 (320), 1302-1304.
29. Mela, C. F., and, P. K. Kopalle, (2002), The impact of collinearity on regression analysis: The asymmetric effect of negative and positive correlations, Appl. Econ., 34 (6), 667-677. (Pubitemid 34409542)
30. O'brien, R., (2007), A caution regarding rules of thumb for variance inflation factors, Qual. Quant., 41 (5), 673-690.
31. Pope, P. T., and, J. T. Webster, (1972), The use of an F-statistic in stepwise regression procedures, Technometrics, 14 (2), 327-340.
32. Rawlings, J. O., S. G. Pantula, and, D. A. Dickey, (1988), Applied Regression Analysis: A Research Tool, 2nd ed., Springer, New York.
33. Reis, K.G. III, J. G. Guthrie, A. H. Rea, P. A. Steeves, and, D. W. Stewart, (2008), StreamStats: A water resources web application, U.S. Geol. Surv. Fact Sheet 2008-3067, 6 pp.
34. Rencher, A. C., and, F. C. Pun, (1980), Inflation of R2 in Best Subset Regression, Technometrics, 22 (1), 49-53.
35. Riggs, H. C., (1972), Low Streamflow Investigations, Techniques of Water-Resources Investigations of the United States Geological Survey, Book 4, chap. B1.
36. Roman, D., R. M. Vogel, and, G. E. Schwarz, (2012), Regional regression models of watershed suspended-sediment discharge for the eastern United States, J. Hydrol., 472-473, 53-62.
37. Smakhtin, V. U., (2001), Low flow hydrology: A review. J. Hydrol., 240 (3-4), 147-186. (Pubitemid 32108798)
38. Stedinger, J. R., and, G. D. Tasker, (1985), Regional hydrologic analysis: 1. Ordinary, weighted, and generalized least squares compared, Water Resour. Res., 21 (9), 1421-1432. (Pubitemid 17270095)
39. Stedinger, J. R., R. M. Vogel, and, E. Foufoula-Georgiou, (1992), Frequency analysis of extreme events, in Handbook of Hydrology, edited by, D. R. Maidment, chap. 18, pp. 18.19-18.21, McGraw-Hill, New York.
40. Sun, R. J., and, J. B. Weeks, (1991), Bibliography of regional aquifer-systems analysis program of the U.S. Geological Survey, 1978-91, U.S. Geol. Surv. Water-Resour. Invest. Rep. 91-4122, 92 pp.
41. Syvitski, J. P. M., and, J. D. Milliman, (2007), Geology, geography, and humans battle for dominance over the delivery of fluvial sediment to the coastal ocean, J. Geol., 115 (1), 1-19. (Pubitemid 46139280)
42. Tasker, G. D., (1980), Hydrologic regression with weighted least squares, Water Resour. Res., 16 (6), 1107-1113.
43. Tasker, G.D., and, N. E. Driver, (1988), Nationalwide regression models for predicting urban runoff water quality at unmonitored sites, J. Am. Water Resour. Assoc., 24 (5), 1091-1101. (Pubitemid 19049489)
44. Thomas, B., and, R. M. Vogel, (2012), The impact of stormwater recharge practices on Boston groundwater levels, J. Hydrol. Eng., 17 (8), 923-932.
45. Tootle, G. A., A. K. Singh, T. C. Piechota, and, I. Farnham, (2007), Long lead-time forecasting of U.S. streamflow using partial least squares regression, J. Hydrol. Eng., 12 (5), 442-451. (Pubitemid 47307894)
46. U.S. Geological Survey (2010), National streamflow statistics program (NSS), January. [Available at http://water.usgs.gov/osw/programs/nss/index.html. ].
47. Vogel, R. M., and, C. N. Kroll, (1992), Regional geohydrologic-geomorphic relationships for the estimation of low-flow statistics, Water Resour. Res., 28 (9), 2451-2458. (Pubitemid 23376340)
48. Vogel, R. M., I. Wilson, and, C. Daly, (1999), Regional regression models of annual streamflow for the United States, J. Irrig. Drain. Eng., 125 (3), 148-157. (Pubitemid 29401058)
49. Wallis, J. R., (1965), Multivariate statistical methods in hydrology-A comparison using data of known functional relationship, Water Resour. Res., 1 (4), 447-461.
50. Wold, S., M. Sjöström, and, L. Eriksson, (2001), PLS-regression: A basic tool of chemometrics, Chemom. Intell. Lab. Syst., 58 (2), 109-130. (Pubitemid 33033283)