A function for estimating the locations of missing landmarks
estimate.missing(A, method = c("TPS", "Reg"))Function returns an array (p x k x n) of the same dimensions as input A, including coordinates for the target specimens
(the original landmarks plus the estimated coordinates for the missing landmarks).
If the input is a geomorphShapes object, this is returned with the original and estimated coordinates in $landmarks
In both cases, these data need to be Procrustes Superimposed prior to analysis, including sliding of semilandmarks (see gpagen).
An array (p x k x n) containing landmark coordinates for a set of specimens or a geomorphShapes object
Method for estimating missing landmark locations
Dean Adams
The function estimates the locations of missing landmarks for incomplete specimens in a set of landmark configurations, where missing landmarks in the incomplete specimens are designated by NA in place of the x,y,z coordinates. Two distinct approaches are implemented.
The first approach (method = "TPS") uses the thin-plate spline to interpolate landmarks on a reference specimen to estimate the locations of missing landmarks on a target specimen. Here, a reference specimen is obtained from the set of specimens for which all landmarks are present, Next, each incomplete specimen is aligned to the reference using the set of landmarks common to both. Finally, the thin-plate spline is used to estimate the locations of the missing landmarks in the target specimen (Gunz et al. 2009).
The second approach (method = "Reg") is multivariate regression. Here each landmark with missing values is regressed on all other landmarks for the set of complete specimens, and the missing landmark values are then predicted by this linear regression model. Because the number of variables can exceed the number of specimens, the regression is implemented on scores along the first set of PLS axes for the complete and incomplete blocks of landmarks (see Gunz et al. 2009). Note, however, that a minimum of k*m+k specimens are required to estimate m missing landmarks (of k-dimension) in any one specimen using the regression method. More generally, if the number of missing landmarks approaches the number of reference specimens used to estimate them, estimation will become increasingly imprecise with the regression method. Additionally, the location of missing landmarks (contiguous versus disparate in location) can also influence the precision of estimation. The user should be aware that the function will produce results but the results from the regression method might be influenced by the number of specimens, the number of total landmarks, and the number and location of missing landmarks in any one specimen. It might be wise to compare multiple methods for specific cases, if uncertain about the precision of estimation.
One can also exploit bilateral symmetry to estimate the locations of missing landmarks. Several possibilities exist for implementing this approach (see Gunz et al. 2009). Example R code for one implementation is found in Claude (2008).
NOTE: Because all geometric morphometric analyses and plotting functions implemented in geomorph require a full complement of landmark coordinates, the alternative to estimating the missing landmark coordinates is to proceed with subsequent analyses EXCLUDING specimens with missing values.
Claude, J. 2008. Morphometrics with R. Springer, New York.
Bookstein, F. L., K. Schafer, H. Prossinger, H. Seidler, M. Fieder, G. Stringer, G. W. Weber, J.-L. Arsuaga, D. E. Slice, F. J. Rohlf, W. Recheis, A. J. Mariam, and L. F. Marcus. 1999. Comparing frontal cranial profiles in archaic and modern Homo by morphometric analysis. Anat. Rec. (New Anat.) 257:217-224.
Gunz, P., P. Mitteroecker, S. Neubauer, G. W. Weber, and F. L. Bookstein. 2009. Principles for the virtual reconstruction of hominin crania. J. Hum. Evol. 57:48-62.
if (FALSE) {
data(plethodon)
plethland <- plethodon$land
plethland[3,,2] <- plethland[8,,2] <- NA #create missing landmarks
plethland[3,,5] <- plethland[8,,5] <- plethland[9,,5] <- NA
plethland[3,,10] <- NA
estimate.missing(plethland, method = "TPS")
estimate.missing(plethland, method = "Reg")
}
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