Skip to main content
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

Ekológia (Bratislava)
Volume 35 (2016): Issue 2 (June 2016)
By: ,   and    
Open Access
|May 2016
References

References

  1. Anderson, M.J. & Wilis T.J. (2003). Canonical analysis of principal coordinates: a useful method of constrained ordination for ecology., 84, 511–525. DOI: 10.1890/0012-9658(2003)084[0511:CAOPCA]2.0.CO;2.
    Search in Google Scholar
  2. APHA, (1992).. American Washington: Public Health Association.
    Search in Google Scholar
  3. Bandalos, D.L. & Boehm-Kaufman M.R. (2009). Four common misconceptions in exploratory factor analysis. In C.E. Lance & R.J. Vandenberg (Eds.),(pp. 61–87). New York: Routledge Publisher.
    Search in Google Scholar
  4. Barrett, P.T. & Kline P. (1981). The observation to variable ratio in factor analysis., 23−33.
    Search in Google Scholar
  5. Bray, J.R. & Curtis J.T. (1957). An ordination of the upland forest communities of Southern Wisconsin.., 27, 325–349. DOI: 10.2307/1942268.
    Open DOISearch in Google Scholar
  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.),p. 99−136). Washington: American Psycholgical Association.
    Search in Google Scholar
  7. Burd, B.J.A., Nemec, A. & Brinkhurst R.O. (1990). The development and application of analytical methods in benthic marine faunal studies.., 26, 169−247. DOI: 10.1016/S0065-2881(08)60201-1.
    Open DOISearch in Google Scholar
  8. Cadima, J. & Jolliffe I.T. (1995). Loadings and correlations in the interpretation of principal components., 22, 203−214. DOI: 10.1080/757584614.
    Open DOISearch in Google Scholar
  9. Cattell, R.B. (1966). The Scree test for the number of factors., 1, 245–276. DOI: 10.1207/s15327906mbr0102_10.
    Open DOISearch in Google Scholar
  10. Cattell, R.B. (1978).. New York: Plenum Press.
    Open DOISearch in Google Scholar
  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.),. Heidelberg: Physica Verlag.
    Search in Google Scholar
  12. Chatfield, C. & Collins A.J. (1980).. London, New York: Chapman & Hall.
    Open DOISearch in Google Scholar
  13. Comrey, A.L. & Lee H.B. (1992).. London: Taylor and Francis.
    Search in Google Scholar
  14. de Winter, J.C.F., Dodou, D. & Wieringa P.A. (2009). Exploratory factor analysis with small sample sizes.44, 147−181. DOI: 10.1080/00273170902794206.
    Open DOISearch in Google Scholar
  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.., 20, 754−766. DOI: 10.1111/j.1654-1103.2009.01073.x.
    Open DOISearch in Google Scholar
  16. Diaconis, P. & Efron B. (1983). Computer-intensive methods in statistics., 248, 116−130. doi:10.1038/scientificamerican0583-116
    Open DOISearch in Google Scholar
  17. Dochtermann, N.A. & Jenkins S.H. (2011). Multivariate methods and small sample sizes., 117, 95−101. DOI: 10.1111/j.1439-0310.2010.01846.x.
    Open DOISearch in Google Scholar
  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., 58, 551−561. DOI: 10.2307/1939004
    Open DOISearch in Google Scholar
  19. Forcino, F.L. (2012). Multivariate assessment of the required sample size for community paleoecological research.315−316, 134−141. DOI: 10.1016/j.palaeo.2011.11.019.
    Open DOISearch in Google Scholar
  20. Gamito, S. & Raffaelli D. (1992). The sensitivity of several ordination methods to sample replication in benthic surveys.., 164, 221−232. DOI: 10.1016/0022-0981(92)90176-B.
    Open DOISearch in Google Scholar
  21. Gauch, H.G. & Whittaker R.H. (1972). Comparison of ordination techniques., 53, 868–875. DOI: 10.2307/1934302.
    Open DOISearch in Google Scholar
  22. Gauch, H.G., Whittaker R.H. & Wentworth T.R. (1977). A comparative study of reciprocal averaging and other ordination techniques.., 65, 157–174. DOI: 10.2307/2259071.
    Open DOISearch in Google Scholar
  23. Gauch, H.G., Whittaker R.H. & Singer S.B. (1981). A comparative study of nonmetric ordinations.., 69, 135–152. DOI: 10.2307/2259821
    Open DOISearch in Google Scholar
  24. Gehlhausen, S.M., Schwartz, M.W. & Augspurger C.K. (2000). Vegetation and microclimatic edge effects in two mixed mesophytic forest fragments.., 147, 21−35. DOI: 10.1023/A:1009846507652.
    Open DOISearch in Google Scholar
  25. Goff, F.G. & Mitchell R. (1975). A comparison of species ordination results from plot and stand data., 31, 15−22. DOI: 10.1007/BF00127871.
    Open DOISearch in Google Scholar
  26. Goodall, D.W. (1953). Objective methods for the classification of vegetation. III. An essay in the use of factor analysis.., 1, 39−63. DOI: 10.1071/BT9530039.
    Open DOISearch in Google Scholar
  27. Gorsuch, R.L. (1983).. Hillsdale NJ: Lawrence Erlbaum Associates.
    Search in Google Scholar
  28. Hatcher, L. (1994).. Cary: SAS Institute.
    Search in Google Scholar
  29. Hill, M.O. (1973). Reciprocal averaging: an eigenvector method of ordination.., 61, 237−249. DOI: 10.2307/2258931.
    Open DOISearch in Google Scholar
  30. Hill, M.O. & Gauch H.G. (1980). Detrended correspondence analysis: an improved technique., 42, 47−58. DOI: 10.1007/BF00048870.
    Open DOISearch in Google Scholar
  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.., 58, 267−281. DOI: 10.1016/S0034-4257(96)00068-5.
    Open DOISearch in Google Scholar
  32. Hirst, C.N. & Jackson D.A. (2007). Reconstructing community relationships: the impact of sampling error, ordination approach and gradient length.., 13, 361–371. DOI: 10.1111/j.1472-4642.2007.00307.x.
    Open DOISearch in Google Scholar
  33. Hutcheson, G. & Sofroniou N. (1999).. London: Sage Publication.
    Open DOISearch in Google Scholar
  34. Jackson, D.A. (1993). Stopping rules in principal components analysis: A comparison of heuristical and statistical approaches., 74, 2204−2214. DOI: 10.2307/1939574.
    Open DOISearch in Google Scholar
  35. Jackson, J.A. (1991).. New York: Wiley Inter Science.
    Open DOISearch in Google Scholar
  36. James, F.C. & McCulloch C.E. (1990). Multivariate analysis in ecology and systematics: panacea or Pandoras box.., 21, 129−166. DOI: 10.1146/annurev.es.21.110190.001021.
    Open DOISearch in Google Scholar
  37. Joliffe, I. (2002).. New York: Springer-Verlag.
    Search in Google Scholar
  38. Kendall, M. (1980).. London: Charles Griffin.
    Search in Google Scholar
  39. Kline, P. (1979).. London: Academic Press.
    Search in Google Scholar
  40. Knox, R.G. & Peet R.K. (1989). Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis., 80, 153−165. DOI: 10.1007/BF00048039.
    Open DOISearch in Google Scholar
  41. Lawley, D.N. & Maxwell A.E. (1971).. New York: Macmillan.
    Search in Google Scholar
  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.),5:(pp. 167−200). Dordrecht: Springer. DOI: 10.1007/978-94-007-2745-8_7.
    Open DOISearch in Google Scholar
  43. MacCallum, R.C., Widaman, K.F., Zhang, S. & Hong S. (1999). Sample size in factor analysis., 4, 84−99. DOI: 10.1037/1082-989X.4.1.84.
    Open DOISearch in Google Scholar
  44. MacCallum, R.C., Widaman, K.F., Preacher, K.J. & Hong S. (2001). Sample size in factor analysis: The role of model error., 36, 611–637. DOI: 10.1207/S15327906MBR3604_06.
    Open DOISearch in Google Scholar
  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.., 19, 200−213. DOI: 10.1111/j.1365-2400.2011.00817.x.
    Open DOISearch in Google Scholar
  46. Manly, B.F.J. (1998).. London: Chapman & Hall.
    Search in Google Scholar
  47. Minchin, P.R. (1987). An evaluation of the relative robustness of techniques for ecological ordination., 69, 89−107. DOI: 10.1007/BF00038690.
    Open DOISearch in Google Scholar
  48. Mundfrom, D.J., Shaw, D.G. & Ke T.L. (2005). Minimum sample size recommendations for conducting factor analyses.5, 159−168. DOI: 10.1207/s15327574ijt0502_4.
    Open DOISearch in Google Scholar
  49. Okland, R.H., Eilersten, O. & Okland T. (1990). On the relationship between sample size and beta diversity in boreal coniferous forests., 87, 187−190. DOI: 10.1007/BF00042954.
    Open DOISearch in Google Scholar
  50. Orloci, L. (1966). Geometric models in ecology 1. The theory and application of some ordination methods.., 54, 193−215. DOI: 10.2307/2257667.
    Open DOISearch in Google Scholar
  51. Orloci, L. (1978).. The Hague: Junk.
    Search in Google Scholar
  52. Osborne, J.W. & Costello A.B. (2004). Sample size and subject to item ratio in principal components analysis., 9, 15−23.
    Search in Google Scholar
  53. Otypkova, Z. & Chytry M. (2006). Effects of plot size on the ordination of vegetation samples.., 17, 465−472. DOI: 10.1111/j.1654-1103.2006.tb02467.x.
    Open DOISearch in Google Scholar
  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., 84, 2347–2363.
    Open DOISearch in Google Scholar
  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., 49, 974−997. DOI: 10.1016/j.csda.2004.06.015.
    Open DOISearch in Google Scholar
  56. Pillar, V. de P. (1999). The bootstrapped ordination re-examined.., 10, 895−902. DOI: 10.2307/3237314.
    Open DOISearch in Google Scholar
  57. Preacher, K.J. & MacCallum R.C. (2002). Exploratory factor analysis in behavioral genetics research: Factor recovery with small sample sizes.32, 153−161. DOI: 10.1023/A:1015210025234.
    Open DOISearch in Google Scholar
  58. Rao, C.R. (1964). The use and interrelation of principal component analysis in applied research.(), 26, 329−358.
    Search in Google Scholar
  59. Richman, M.B. (1988). A cautionary note concerning a commonly applied eigen analysis procedure., 40, 50−58. DOI: 10.1111/j.1600-0889.1988.tb00212.x.
    Open DOISearch in Google Scholar
  60. Shaukat, S.S. (1985).. PhD. thesis, University of Western Ontario, London, Canada.
    Search in Google Scholar
  61. Shaukat, S.S. & Uddin M. (1989a). A comparison of principal component and factor analysis as an ordination model with reference to desert ecosystem., 4, 15−28.
    Search in Google Scholar
  62. Shaukat, S.S. & Uddin M. (1989b). An application of canonical and principal component analysis to the study of desert environment., 13, 17−45.
    Search in Google Scholar
  63. Shaukat, S.S. & Siddiqui I.A. (2005). Essentials of Mathematical Ecology: Computer Programs in BASIC, FORTRAN and C++. Karachi: Farquan Publishers.
    Search in Google Scholar
  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.., 2, 617−627.
    Search in Google Scholar
  65. Stauffer, D. F., Garton E.O. & Steinhorst R.K. (1985). A comparison of principal component from real and random data., 66, 1693−1698. DOI: 10.2307/2937364.
    Open DOISearch in Google Scholar
  66. Swan, J.M.A. & Dix R.L. (1966). The phytosociological structure of upland forest at Candle Lake, Saskatchewan.., 54, 13−40. DOI: 10.2307/2257657.
    Open DOISearch in Google Scholar
  67. Ter Braak, C.J.F. (1986). Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis.67, 1167−1179. DOI: 10.2307/1938672.
    Open DOISearch in Google Scholar
  68. Velicer, W.F. & Fava J.L. (1998). The effects of variable and subject sampling on factor pattern recovery., 3, 231−251. DOI: 10.1037/1082-989X.3.2.231.
    Open DOISearch in Google Scholar
  69. Walker, S.C. & Jackson D.A. (2011). Random-effects ordination: describing and predicting multivariate correlations and co-occurrences.., 81, 635–663.
    Open DOISearch in Google Scholar
  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.., 75, 363−376. DOI: 10.2307/2260424.
    Open DOISearch in Google Scholar
  71. Wikum, D.A. & Wali M.K. (1974). Analysis of a North Dakota gallery forest: Vegetation in relation to topographic and soil gradients.., 44, 441–464. DOI: 10.2307/1942449.
    Open DOISearch in Google Scholar
DOI: https://doi.org/10.1515/eko-2016-0014 | Journal eISSN: 1337-947X | Journal ISSN: 1335-342X
Journal RSS Feed
Language: English
Page range: 173 - 190
Published on: May 28, 2016
Published by: Slovak Academy of Sciences, Institute of Landscape Ecology
In partnership with: Paradigm Publishing Services
Keywords:
eigenstructure,
environmental data,
ordination,
PCA
Related subjects:
Chemistry,
Chemistry, other,
Geosciences,
Geography,
Life sciences,
Ecology,
Life sciences, other

© 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.

Volume 35 (2016): Issue 2 (June 2016)
Previous article
Next article