Missing data in craniometrics: a simulation study

Abstract

J. 2003. Missing data in craniometrics: a simulation study. Acta Theriologica 48: 25-34.Craniometric measurements represent a useful tool for studying the differentiation of mammal populations. However, the fragility of skulls often leads to incomplete data matrices. Damaged specimens or incomplete sets of measurements are usually discarded prior to statistical analysis. We assessed the performance of two strategies that avoid elimination of observations: (1) pairwise deletion of missing cells, and (2) estimation of missing data using available measurements. The effect of these distinct approaches on the computation of inter-individual distances and population differentiation analyses were evaluated using craniometric measurements obtained from insular populations of deer mice Peromyscus maniculatus (Wagner, 1845). In our simulations, Euclidean distances were greatly altered by pairwise deletion, whereas Gower's distance coefficient corrected for missing data provided accurate results. Among the different estimation methods compared in this paper, the regression-based approximations weighted by coefficients of determination (r 2 ) outperformed the competing approaches. We further show that incomplete sets of craniometric measurements can be used to compute distance matrices, provided that an appropriate coefficient is selected. However, the application of estimation procedures provides a flexible approach that allows researchers to analyse incomplete data sets.Département de sciences biologiques, Université de Montréal C. P. 6128, Succ. centre--ville Montréal,

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

“…Every missing value that is estimated typically allows the introduction of many more ‘good’ values into the analysis (and thus increases the degrees of freedom for the actual values introduced, but not for those estimated from the existing data). Although imputation methods are well established in psychometrics and other scientific disciplines and in the clinical medical literature, their use in morphometric studies is uncommon and has remained largely untested (Gunz et al ., 2002; Gauthier et al ., 2003; Strauss et al ., 2003). The stepwise methods that we have described here provide an initial, conservative approach to the estimation of missing data, based again on the principle of providing the most stable statistical results while attempting to minimize both the loss of actual data and the number of missing values estimated.…”

“…The second, much more common solution to the problem of incomplete data is to omit the specimens or characters having missing values (marginalization), which can seriously reduce the sample size available for analysis (Gauthier, Landry, & Lapointe, 2003). Although omitting missing data reduces statistical power and can potentially lead to bias of results (Millis, 2003), it may be necessary if the proportion of missing data is large.…”

Overview of Current Research on Wolves in Russia

“…Morphological approach, and craniometric measurements in particular, represent an effective tool for studying the polymorphism and differentiation of mammal populations (Palmeirim, 1998;Gauthier et al, 2003). In Russia, the morphological research traditions are strong; therefore, the morphological variability of the gray wolf has always been the subject of a wide range of studies.…”

Assessing 3d Photogrammetry Techniques in Craniometrics

“…Craniometric measurements represent an effective tool for studying the difference in morphology of mammal populations (Gauthier et al 2003). New morphometric methodological approaches are effective in capturing reliable information about the shape of an organism and result in powerful statistical procedures for testing differences in shape (Rohlf and Marcus 1993).…”