Statistical Models for Landmark Coordinate Data - An Invariant Approach to Statistical Analysis of Shapes - page 111

Table 3.5 Efficiency Comparisons Between the Method of Moments and the
Method of Maximum Likelihood.
Scenarios Parameters EDMA MLE Unobserved

MLE

( M 1 ,

K ,1 , I 2 ) Mean distances* 1.0 1.0 1.0

Variances* 23.2 19.5 16.3

Covariances* 45.6 37.7 28.4

( M 1 ,

K ,2 , I 2 )

Mean distances 1.5 1.5 1.5

Variances 21.4 18.7 14.6

Covariances 36.4 31.0 24.7

( M 2 ,

K ,1 , I 2 ) Mean distances 2.2 2.2 2.2

Variances 24.2 19.4 14.9

Covariances 48.4 41.3 30.1

* Because of the non-convergence of the maximum likelihood routine, these are based
on only 98 out of 100 simulations.

Table 3.6 The Mean Form Coordinates (centered) and the Covariance
Matrices Used in the Simulation Study.

In estimating the inter-landmark distances or the variance-covariance
parameters, none of the methods exhibited any bias, therefore Table
3.5 concentrates on the relative root mean square error, which primar-
ily reflects variability. Since performance of the methods was similar
within the mean parameters, within the variance parameters and
within the covariance parameters, the results are averaged across the
(three in each case) parameters. We can see that, for estimating the
mean form, both EDMA and the MLE do as well as the unobservable
MLE. For estimating the variance parameters EDMA and the MLE
perform worse than the unobservable MLE, and EDMA performs
slightly worse than the MLE. For the covariance parameters, there is
some loss of efficiency in using EDMA compared to the MLE, but not a
dramatic amount.