Have a personal or library account? Click to login
Impact of sample size on principal component analysis ordination of an environmental data set: effects on eigenstructure Cover

Impact of sample size on principal component analysis ordination of an environmental data set: effects on eigenstructure

Open Access
|May 2016

References

  1. Anderson, M.J. & Wilis T.J. (2003). Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology. Ecology, 84, 511–525. DOI: 10.1890/0012-9658(2003)084[0511:CAOPCA]2.0.CO;2.
  2. APHA, (1992). Standard methods for the examination of water and waste water. American Washington: Public Health Association.
  3. Bandalos, D.L. & Boehm-Kaufman M.R. (2009). Four common misconceptions in exploratory factor analysis. In C.E. Lance & R.J. Vandenberg (Eds.), Statistical and methodological myths and urban legends (pp. 61–87). New York: Routledge Publisher.
  4. Barrett, P.T. & Kline P. (1981). The observation to variable ratio in factor analysis. Personality Study and Group Behaviour, 1, 23−33.
  5. Bray, J.R. & Curtis J.T. (1957). An ordination of the upland forest communities of Southern Wisconsin. Ecol. Monogr., 27, 325–349. DOI: 10.2307/1942268.10.2307/1942268
  6. Bryant, F.B. & Yarnold P.R. (1995). Principal components analysis and exploratory and confirmatory factor analysis. In L.G. Grimm & R.R. Yarnold (Eds.), Reading and understanding multivariate statistics (pp. 99−136). Washington: American Psycholgical Association.
  7. Burd, B.J.A., Nemec, A. & Brinkhurst R.O. (1990). The development and application of analytical methods in benthic marine faunal studies. Adv. Mar. Biol., 26, 169−247. DOI: 10.1016/S0065-2881(08)60201-1.10.1016/S0065-2881(08)60201-1
  8. Cadima, J. & Jolliffe I.T. (1995). Loadings and correlations in the interpretation of principal components. Journal of Applied Statistics, 22, 203−214. DOI: 10.1080/757584614.10.1080/757584614
  9. Cattell, R.B. (1966). The Scree test for the number of factors. Multivariate Behavioral Research, 1, 245–276. DOI: 10.1207/s15327906mbr0102_10.10.1207/s15327906mbr0102_1026828106
  10. Cattell, R.B. (1978). The scientific use of factor analysis in behavioral and life sciences. New York: Plenum Press.10.1007/978-1-4684-2262-7
  11. Chateau, F. & Lebart L. (1996). Assessing sample variability in the visualization techniques related to principal component analysis: Bootstrap and alternative simulation methods. In A. Prats (Ed.), Proceedings of COMPSTAT 2006. Heidelberg: Physica Verlag.
  12. Chatfield, C. & Collins A.J. (1980). Introduction to multivariate analysis. London, New York: Chapman & Hall.10.1007/978-1-4899-3184-9
  13. Comrey, A.L. & Lee H.B. (1992). A first course in factor analysis. London: Taylor and Francis.
  14. de Winter, J.C.F., Dodou, D. & Wieringa P.A. (2009). Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research, 44, 147−181. DOI: 10.1080/00273170902794206.10.1080/0027317090279420626754265
  15. Dengler, J., Lobel, S. & Dolnik C. (2009). Species constancy depends on plot size a problem for vegetation classification and how it can be solved. J. Veg. Sci., 20, 754−766. DOI: 10.1111/j.1654-1103.2009.01073.x.10.1111/j.1654-1103.2009.01073.x
  16. Diaconis, P. & Efron B. (1983). Computer-intensive methods in statistics. Sci. Am., 248, 116−130. doi:10.1038/scientificamerican0583-11610.1038/scientificamerican0583-116
  17. Dochtermann, N.A. & Jenkins S.H. (2011). Multivariate methods and small sample sizes. Ethology, 117, 95−101. DOI: 10.1111/j.1439-0310.2010.01846.x.10.1111/j.1439-0310.2010.01846.x
  18. Fasham, M.J.R. (1977). The comparison of nonmetric multidimensional scaling, principal component analysis and reciprocal averaging for the ordination of simulated coenocline and coenoplanes. Ecology, 58, 551−561. DOI: 10.2307/193900410.2307/1939004
  19. Forcino, F.L. (2012). Multivariate assessment of the required sample size for community paleoecological research. Palaeogeo. Palaeoclimatol. Palaeoecol., 315−316, 134−141. DOI: 10.1016/j.palaeo.2011.11.019.10.1016/j.palaeo.2011.11.019
  20. Gamito, S. & Raffaelli D. (1992). The sensitivity of several ordination methods to sample replication in benthic surveys. J. Exp. Mar. Biol. Ecol., 164, 221−232. DOI: 10.1016/0022-0981(92)90176-B.10.1016/0022-0981(92)90176-B
  21. Gauch, H.G. & Whittaker R.H. (1972). Comparison of ordination techniques. Ecology, 53, 868–875. DOI: 10.2307/1934302.10.2307/1934302
  22. Gauch, H.G., Whittaker R.H. & Wentworth T.R. (1977). A comparative study of reciprocal averaging and other ordination techniques. J. Ecol., 65, 157–174. DOI: 10.2307/2259071.10.2307/2259071
  23. Gauch, H.G., Whittaker R.H. & Singer S.B. (1981). A comparative study of nonmetric ordinations. J. Ecol., 69, 135–152. DOI: 10.2307/225982110.2307/2259821
  24. Gehlhausen, S.M., Schwartz, M.W. & Augspurger C.K. (2000). Vegetation and microclimatic edge effects in two mixed mesophytic forest fragments. Plant Ecol., 147, 21−35. DOI: 10.1023/A:1009846507652.10.1023/A:1009846507652
  25. Goff, F.G. & Mitchell R. (1975). A comparison of species ordination results from plot and stand data. Vegetatio, 31, 15−22. DOI: 10.1007/BF00127871.10.1007/BF00127871
  26. Goodall, D.W. (1953). Objective methods for the classification of vegetation. III. An essay in the use of factor analysis. Aust. J. Bot., 1, 39−63. DOI: 10.1071/BT9530039.10.1071/BT9530039
  27. Gorsuch, R.L. (1983). Factor analysis. Hillsdale NJ: Lawrence Erlbaum Associates.
  28. Hatcher, L. (1994). A step-by-step approach to using the SAS system for factor analysis and structural equation modeling. Cary: SAS Institute.
  29. Hill, M.O. (1973). Reciprocal averaging: an eigenvector method of ordination. J. Ecol., 61, 237−249. DOI: 10.2307/2258931.10.2307/2258931
  30. Hill, M.O. & Gauch H.G. (1980). Detrended correspondence analysis: an improved technique. Vegetatio, 42, 47−58. DOI: 10.1007/BF00048870.10.1007/BF00048870
  31. Hirosawa, Y., Marsh, S.E. & Kliman D.H. (1996). Application of standardized principal component analysis to land-cover characterization using multi temporal AVHRR data. Remote Sens. Environ., 58, 267−281. DOI: 10.1016/S0034-4257(96)00068-5.10.1016/S0034-4257(96)00068-5
  32. Hirst, C.N. & Jackson D.A. (2007). Reconstructing community relationships: the impact of sampling error, ordination approach and gradient length. Divers. Distrib., 13, 361–371. DOI: 10.1111/j.1472-4642.2007.00307.x.10.1111/j.1472-4642.2007.00307.x
  33. Hutcheson, G. & Sofroniou N. (1999). The multivariate social scientist: Introductory statistics using generalized linear models. London: Sage Publication.10.4135/9780857028075
  34. Jackson, D.A. (1993). Stopping rules in principal components analysis: A comparison of heuristical and statistical approaches. Ecology, 74, 2204−2214. DOI: 10.2307/1939574.10.2307/1939574
  35. Jackson, J.A. (1991). A user’s guide to principal component analysis. New York: Wiley Inter Science.10.1002/0471725331
  36. James, F.C. & McCulloch C.E. (1990). Multivariate analysis in ecology and systematics: panacea or Pandoras box. Annu. Rev. Ecol. Evol. Syst., 21, 129−166. DOI: 10.1146/annurev.es.21.110190.001021.10.1146/annurev.es.21.110190.001021
  37. Joliffe, I. (2002). Principal component analysis. New York: Springer-Verlag.
  38. Kendall, M. (1980). Multivariate analysis. London: Charles Griffin.
  39. Kline, P. (1979). Psychometrics and psychology. London: Academic Press.
  40. Knox, R.G. & Peet R.K. (1989). Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis. Vegetatio, 80, 153−165. DOI: 10.1007/BF00048039.10.1007/BF00048039
  41. Lawley, D.N. & Maxwell A.E. (1971). Factor analysis as a statistical method. New York: Macmillan.
  42. Legendre, P. & Birks H.J.B. (2012). Clustering and partitioning. In H.J.B. Birks, A.F. Lotter, S. Juggins & J.P. Smol (Eds.), Tracking environmental change using lake sediments Vol. 5: Data handling and numerical techniques (pp. 167−200). Dordrecht: Springer. DOI: 10.1007/978-94-007-2745-8_7.10.1007/978-94-007-2745-8_7
  43. MacCallum, R.C., Widaman, K.F., Zhang, S. & Hong S. (1999). Sample size in factor analysis. Psychological Methods, 4, 84−99. DOI: 10.1037/1082-989X.4.1.84.10.1037/1082-989X.4.1.84
  44. MacCallum, R.C., Widaman, K.F., Preacher, K.J. & Hong S. (2001). Sample size in factor analysis: The role of model error. Multivariate Behavioral Research, 36, 611–637. DOI: 10.1207/S15327906MBR3604_06.10.1207/S15327906MBR3604_0626822184
  45. Manjarres-Martinez, L.M., Gutiérrez-Estrada, J.C., Hernando, J.J.A. & Soriguer M.C. (2012). The performance of three ordination methods applied to demersal fish data sets: stability and interpretability. Fish. Manag. Ecol., 19, 200−213. DOI: 10.1111/j.1365-2400.2011.00817.x.10.1111/j.1365-2400.2011.00817.x
  46. Manly, B.F.J. (1998). Randomization, bootstrap and Monte Carlo methods in biology. London: Chapman & Hall.
  47. Minchin, P.R. (1987). An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio, 69, 89−107. DOI: 10.1007/BF00038690.10.1007/BF00038690
  48. Mundfrom, D.J., Shaw, D.G. & Ke T.L. (2005). Minimum sample size recommendations for conducting factor analyses. International Journal of Testing, 5, 159−168. DOI: 10.1207/s15327574ijt0502_4.10.1207/s15327574ijt0502_4
  49. Okland, R.H., Eilersten, O. & Okland T. (1990). On the relationship between sample size and beta diversity in boreal coniferous forests. Vegetatio, 87, 187−190. DOI: 10.1007/BF00042954.10.1007/BF00042954
  50. Orloci, L. (1966). Geometric models in ecology 1. The theory and application of some ordination methods. J. Ecol., 54, 193−215. DOI: 10.2307/2257667.10.2307/2257667
  51. Orloci, L. (1978). Multivariate analysis in vegetation research. The Hague: Junk.
  52. Osborne, J.W. & Costello A.B. (2004). Sample size and subject to item ratio in principal components analysis. Practical Assessment Research & Evaluation, 9, 15−23.
  53. Otypkova, Z. & Chytry M. (2006). Effects of plot size on the ordination of vegetation samples. J. Veg. Sci., 17, 465−472. DOI: 10.1111/j.1654-1103.2006.tb02467.x.10.1111/j.1654-1103.2006.tb02467.x
  54. Peres-Neto, P.R., Jackson, D.A. & Somers K.M. (2003). Giving meaningful interpretation to ordination axes: assessing loading significance in principal component analysis. Ecology, 84, 2347–2363. http://www.jstor.org/stable/345014010.1890/00-0634
  55. Peres-Neto, P.R., Jackson, D.A. & Somers K.M. (2005). How many principal components? Stopping rules for determining the number of non-trivial axes revisited. Computational Statistics and Data Analysis, 49, 974−997. DOI: 10.1016/j.csda.2004.06.015.10.1016/j.csda.2004.06.015
  56. Pillar, V. de P. (1999). The bootstrapped ordination re-examined. J. Veg. Sci., 10, 895−902. DOI: 10.2307/3237314.10.2307/3237314
  57. Preacher, K.J. & MacCallum R.C. (2002). Exploratory factor analysis in behavioral genetics research: Factor recovery with small sample sizes. Behav. Genet., 32, 153−161. DOI: 10.1023/A:1015210025234.10.1023/A:1015210025234
  58. Rao, C.R. (1964). The use and interrelation of principal component analysis in applied research. Sankhya (Ser. A), 26, 329−358. http://www.jstor.org/stable/25049339
  59. Richman, M.B. (1988). A cautionary note concerning a commonly applied eigen analysis procedure. Tellus B, 40, 50−58. DOI: 10.1111/j.1600-0889.1988.tb00212.x.10.1111/j.1600-0889.1988.tb00212.x
  60. Shaukat, S.S. (1985). Approaches to the analysis of ruderal weed vegetation. PhD. thesis, University of Western Ontario, London, Canada.
  61. Shaukat, S.S. & Uddin M. (1989a). A comparison of principal component and factor analysis as an ordination model with reference to desert ecosystem. Coenoses, 4, 15−28. http://www.jstor.org/stable/43461254
  62. Shaukat, S.S. & Uddin M. (1989b). An application of canonical and principal component analysis to the study of desert environment. Abstracta Botanica (Budapest), 13, 17−45. http://www.jstor.org/stable/43519176
  63. Shaukat, S.S. & Siddiqui I.A. (2005). Essentials of Mathematical Ecology: Computer Programs in BASIC, FORTRAN and C++. Karachi: Farquan Publishers.
  64. Shaukat, S.S., Sheikh I.H. & Siddiqui I.A. (2005). An application of correspondence analysis, Detrended correspondence analysis and Canonical correspondence analysis to the vegetation and environment of calcareous hills around Karachi. Int. J. Biol. Biotechnol., 2, 617−627.
  65. Stauffer, D. F., Garton E.O. & Steinhorst R.K. (1985). A comparison of principal component from real and random data. Ecology, 66, 1693−1698. DOI: 10.2307/2937364.10.2307/2937364
  66. Swan, J.M.A. & Dix R.L. (1966). The phytosociological structure of upland forest at Candle Lake, Saskatchewan. J. Ecol., 54, 13−40. DOI: 10.2307/2257657.10.2307/2257657
  67. Ter Braak, C.J.F. (1986). Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology, 67, 1167−1179. DOI: 10.2307/1938672.10.2307/1938672
  68. Velicer, W.F. & Fava J.L. (1998). The effects of variable and subject sampling on factor pattern recovery. Psychological Methods, 3, 231−251. DOI: 10.1037/1082-989X.3.2.231.10.1037/1082-989X.3.2.231
  69. Walker, S.C. & Jackson D.A. (2011). Random-effects ordination: describing and predicting multivariate correlations and co-occurrences. Ecol. Monogr., 81, 635–663. http://www.jstor.org/stable/2320847810.1890/11-0886.1
  70. Whittaker, R.J. (1987). An application of detrended correspondence analysis and nonmetric multidimensional scaling to the identification and analysis of environmental factor complexes and vegetation structures. J. Ecol., 75, 363−376. DOI: 10.2307/2260424.10.2307/2260424
  71. Wikum, D.A. & Wali M.K. (1974). Analysis of a North Dakota gallery forest: Vegetation in relation to topographic and soil gradients. Ecol. Monogr., 44, 441–464. DOI: 10.2307/1942449.10.2307/1942449
DOI: https://doi.org/10.1515/eko-2016-0014 | Journal eISSN: 1337-947X | Journal ISSN: 1335-342X
Language: English
Page range: 173 - 190
Published on: May 28, 2016
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2016 S. Shahid Shaukat, Toqeer Ahmed Rao, Moazzam A. Khan, published by Slovak Academy of Sciences, Institute of Landscape Ecology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.