Determining best complete subsets of specimens and characters for multivariate morphometric studies in the presence of large amounts of missing data

Biological Journal of the Linnean Society

Volumn 88, Issue 2, 2006, Pages 309-328

  Strauss, Richard E ^a   Atanassov, Momchil N ^a  

^a TEXAS TECH UNIVERSITY   (United States)

Author keywords

Covariance; Discriminant analysis; Eigenanalysis; Expectation maximization; Fossils; Imputation; Matrix condition; Morphometrics; Principal component analysis; Simulation

Indexed keywords

ALGORITHM; DATA ACQUISITION; DOCUMENTARY SOURCE; FOSSIL; VERTEBRATE;

VERTEBRATA;

EID: 33744471130     PISSN: 00244066     EISSN: 10958312     Source Type: Journal    
DOI: 10.1111/j.1095-8312.2006.00671.x     Document Type: Article

References (73)

1. Allison PD. 2001. Missing data. Sage University papers series on quantitative applications in the social sciences, 07-136. Thousand Oaks, CA : Sage Publications.
2. Arbuckle JL. 1996. Full information estimation in the presence of incomplete data. In : Marcouldies GA Schumacker RE, eds. Advanced structural equation modeling techniques. Mahwah, NJ : Lawrence Erlbaum Associates, 243 277.
3. Atanassov MN. 1996. Origin of dog Canis familiaris L. and early dog breeds of Bulgaria [in Bulgarian]. MSc Thesis, Sofia University.
4. Atanassov MN Strauss RE. 1999. Morphometric analysis of Rhamphorhynchus from the Late Jurassic of southern Germany. Journal of Vertebrate Paleontology 19 : 30A 30A.
5. Atanassov MN Strauss RE. 2000. Morphometric analysis of Late Jurassic pterodactyloids from Germany and France. Journal of Vertebrate Paleontology 20 : 27A 27A.
6. Basilevsky A Sabourin D Hum D Anderson A. 1985. Missing data estimators in the general linear model: an evaluation of simulated data as an experimental design. Communications in Statistics Series B (Simulation and Computation) 14 : 371 394.
7. Beale EML Little RJA. 1975. Missing values in multivariate analysis. Journal of the Royal Statistical Society Series B (Statistical Methodology) 37 : 129 145.
8. Bello AL. 1993a. A simulation study of imputation techniques in linear, quadratic and kernel discriminant analyses. Journal of Statistical Computation and Simulation 48 : 167 180.
9. Bello AL. 1993b. Choosing among imputation techniques for incomplete multivariate data: a simulation study. Communications in Statistics Series A (Theory and Method) 22 : 853 877.
10. Bello AL. 1995. Imputation techniques in regression analysis: looking closely at their implementation. Computational Statistics and Data Analysis 20 : 45 57.
11. Bennett SC. 1991. Morphology of the Late Cretaceous pterosaur Pteranodon and systematics of the Pterodactyloidea. PhD Dissertation, University of Kansas.
12. Bennett SC. 1995. A statistical study of Rhamphorhynchus from the Solnhofen Limestone of Germany: year-classes of a single large species. Journal of Paleontology 69 : 569 579.
13. Bennett SC. 1996. Year-classes of pterosaurs from the Solnhofen Limestone of Germany: taxonomic and systematic implications. Journal of Vertebrate Paleontology 16 : 432 444.
14. Brown RL. 1994. Efficacy of the indirect approach for estimating structural equation models with missing data: a comparison of five methods. Structural Equation Modeling 1 : 287 316.
15. Carrano MT Janis CM Sepkoski JJ Jr.. 1999. Hadrosaurs as ungulate parallels: lost lifestyles and deficient data. Acta Palaeontologica Polonica 44 : 237 261.
16. Chen Y McInroy JE. 2002. Estimation of symmetric, positive definite matrices from imperfect measurements. IEEE Transactions on Automatic Control 47 : 1721 1725.
17. Cole DA Maxwell SE Arvey R Salas E. 1994. How the power of MANOVA can both increase and decrease as a function of the intercorrelations among the dependent variables. Psychological Bulletin 115 : 465 474.
18. Dempster AP Laird NM Rubin DB. 1977. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society Series B (Statistical Methodology) 39 : 1 38.
19. Essl A. 1991. Choice of an appropriate bending factor using prior knowledge of the parameters. Journal of Animal Breeding and Genetics 108 : 89 101.
20. Flury BK. 1988. Common principal components and related multivariate models. New York, NY : Wiley.
21. Fomby T. 1998. Messy data: missing observations, outliers, and mixed-frequency data. New York, NY : Elsevier.
22. Frane JW. 1976. Some simple procedures for handling missing data in multivariate analysis. Psychometrika 41 : 409 415.
23. Freeman S Jackson WM. 1990. Univariate metrics are not adequate to measure avian body size. Auk 107 : 69 74.
24. Gauthier O Landry PA Lapointe FJ. 2003. Missing data in craniometrics: a simulation study. Acta Theriologica 48 : 25 34.
25. Gornbein JA Lazaro CG Little RJA. 1992. Incomplete data in repeated measures analysis. Statistical Methods in Medical Research 1 : 275 295.
26. Groß J. 2003. Linear regression. Lecture notes in statistics 175. Berlin : Springer-Verlag.
27. Guerrero JA De Luna E Sánchez-Hernández C. 2003. Morphometrics in the quantification of character state identity for the assessment of primary homology: an analysis of character variation of the genus Artibeus (Chiroptera: Phyllostomidae). Biological Journal of the Linnean Society 80 : 45 55.
28. Gunz P Mitteroecker P Bookstein FL Weber GW. 2002. Approaches to missing data in anthropology. Collegium Antropologicum 26 : 78 79.
29. Hayes JF Hill WG. 1980. A reparameterisation of a genetic selection index to locate its sampling properties. Biometrics 36 : 237 248.
30. Hayes JF Hill WG. 1981. Modification of estimates of parameters in the construction of genetic selection indices ('bending'). Biometrics 37 : 483 493.
31. van der Heijden PGM de Vries H van Hooff JA. 1990. Correspondence analysis of transition matrices, with special attention to missing entries and asymmetry. Animal Behaviour 40 : 49 64.
32. Higham NJ. 1989. Matrix nearness problems and applications. In : Gover MJC Barnett S, eds. Applications of matrix theory. Oxford : Oxford University Press, 1 27.
33. Higham NJ. 2002. Computing the nearest correlation matrix - a problem from finance. IMA Journal of Numerical Analysis 22 : 329 343.
34. Hill WG Thompson R. 1978. Probabilities of non-positive definite between-group or genetic covariance matrices. Biometrics 34 : 429 439.
35. Houck MA Gauthier JA Strauss RE. 1990. Allometric scaling in the earliest fossil bird, Archaeopteryx lithographica. Science 247 : 195 198.
36. Hu H. 1995. Positive definite constrained least-squares estimation of matrices. Linear Algebra and its Applications 229 : 167 174.
37. Jolliffe IT. 1982. A note on the use of principal components in regression. Journal of the Royal Statistical Society Series C (Applied Statistics) 31 : 300 303.
38. Jorjani H Klei L Emanuelson U. 2002. Combining disparate estimates of genetic correlations. Interbull Bulletin 29 : 1 3.
39. Jorjani H Klei L Emanuelson U. 2003. A simple method for weighted bending of genetic (co)variance matrices. Journal of Dairy Science 86 : 677 679.
40. Kaiser HF Dickman K. 1962. Sample and population score matrices and sample correlation matrices from an arbitrary population correlation matrix. Psychometrika 27 : 179 182.
41. Kinziger AP Raesly RL Neely DA. 2000. New species of Cottus (Teleostei: Cottidae) from the middle Atlantic eastern United States. Copeia 2000 : 1007 1018.
42. Knol DL Ten Berge JMF. 1989. Least-squares approximation of an improper correlation matrix by a proper one. Psychometrika 54 : 53 61.
43. Kramer A Konigsberg LW. 1999. Recognizing species diversity among large-bodied hominoids: a simulation test using missing data finite mixture analysis. Journal of Human Evolution 36 : 409 421.
44. Kupiec PH. 1998. Stress testing in a value at risk framework. Journal of Derivatives 1998 3 7 25.
45. Lee WT. 1986. Estimation for structural equation models with missing data. Psychometrika 51 : 93 99.
46. Lien D Rearden D. 1992. A note on estimating regression coefficients with missing data. Econometric Reviews 11 : 119 122.
47. Little RJA. 1992. Regression with missing X's: a review. Journal of the American Statistical Association 87 : 1227 1237.
48. Little RJA Rubin DB. 1987. Statistical Analysis with Missing Data. New York, NY : Wiley.
49. Liu WZ White AP Thompson SG Bramer MA. 1997. Techniques for dealing with missing values in classification. Lecture Notes in Computer Science 1280 : 527 536.
50. Lucas C. 2001. Computing nearest covariance and correlation matrices. MS Thesis, University of Manchester.
51. MacLeod N. 2001. Landmarks, localization, and the use of morphometrics in phylogenetic analysis. In : Edgecombe G Adrain J Lieberman B, eds. Fossils, phylogeny, and form: an analytical approach. New York, NY : Kluwer Academic / Plenum, 197 233.
52. Mathworks. 1997. Matlab reference guide. Natick, MA : Mathworks.
53. Millis SR. 2003. Statistical practices: the seven deadly sins. Child Neuropsychology 9 : 221 233.
54. Proschan MA McMahon RP Shih JH Hunsberger SA Geller NL Knatterud G Wittes J. 2001. Sensitivity analysis using an imputation method for missing binary data in clinical trials. Journal of Statistical Planning and Inference 96 : 155 165.
55. Rae TC. 1998. The logical basis for the use of continuous characters in phylogenetic systematics. Cladistics 14 : 221 228.
56. Rebonato R. 1999. Volatility and correlation. New York, NY : John Wiley and Sons.
57. Roth PL Switzer FS Switzer DM. 1999. Missing data in multiple item scales: a Monte Carlo analysis of missing data techniques. Organizational Research Methods 2 : 211 232.
58. Rubin DB. 1976. Inference with missing data. Biometrika 63 : 581 592.
59. Rubin DB. 1996. Multiple imputation after 18+ years. Journal of the American Statistical Association 91 : 473 489.
60. Schafer JL Olsen MK. 1998. Multiple imputation for multivariate missing-data problems: a data analyst's perspective. Multivariate Behavioral Research 33 : 545 571.
61. Scheiner SM. 1993. MANOVA: multiple response variables and multispecies interactions. In : Scheiner SM Gurevitch J, eds. Design and analysis of ecological experiments. New York, NY : Chapman & Hall, 94 112.
62. Strauss RE. 1989. Associations between genic heterozygosity and morphological variability in freshwater sculpins, genus Cottus (Teleostei: Cottidae). Biochemical Systematics and Ecology 17 : 333 340.
63. Strauss RE. 1991. Correlations between heterozygosity and phenotypic variability in Cottus (Teleostei: Cottidae): character components. Evolution 45 : 1950 1956.
64. Strauss RE Atanassov MN Oliveira JA. 2003. Evaluation of the principal-component and expectation-maximization methods for estimating missing data in morphometric studies. Journal of Vertebrate Paleontology 23 : 284 296.
65. Tabachnick BG Fidell LS. 2006. Using Multivariate Statistics, 5th edn. Boston, MA : Allyn & Bacon.
66. Twedt DJ Gill DS. 1992. Comparison of algorithms for replacing missing data in discriminant analysis. Communications in Statistics Series A (Theory and Method) 21 : 1567 1578.
67. Wellnhofer P. 1970. Die Pterodactyloidea (Pterosauria) der Oberjura-Plattenkalke Süddeutschlands. Bayerische Akademie der Wissenschaften, Abhandlungen 141 : 1 133.
68. Wellnhofer P. 1974. Das fünfte Skelettexemplar von Archaeopteryx. Palaeontographica, Abteilung A (Paläozoologie, Stratigraphie) 147 : 169 216.
69. Wellnhofer P. 1975. Die Rhamphorhynchoidea (Pterosauria) der Oberjura-Plattenkalke Suddeutschlands. Palaeontographica, Abteilung A (Paläozoologie, Stratigraphie) 148 : 1 33.
70. Wellnhofer P. 1988. Ein neues Exemplar von Archaeopteryx. Archaeopteryx 6 : 1 30.
71. Wellnhofer P. 1993. Das siebte Exemplar von Archaeopteryx aus den Solnhofener Schichten. Archaeopteryx 11 : 1 47.
72. Wilks SS. 1932. Moments and distributions of estimates of population parameters for fragmentary samples. Annals of Mathematical Statistics 3 : 165 195.
73. Willig MR Owen RD. 1987. Univariate analyses of morphometric variation do not emulate the results of multivariate analyses. Systematic Zoology 36 : 398 400.