A function for estimating the locations of missing landmarks

1 | ```
estimate.missing(A, method = c("TPS", "Reg"))
``` |

`A` |
An array (p x k x n) containing landmark coordinates for a set of specimens |

`method` |
Method for estimating missing landmark locations |

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).

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. To do this, see functions `complete.cases`

(use: mydata[complete.cases(mydata),])
or `na.omit`

(use: newdata <- na.omit(mydata)) to make a dataset of only the complete specimens.
These functions require the dataset to be a matrix in the form of a 2d array (see `two.d.array`

).

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). These data need to be Procrustes Superimposed prior to analysis (seesee `gpagen`

).

Dean Adams

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.

1 2 3 4 5 6 7 8 | ```
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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