The Study of Growth - An Invariant Approach to Statistical Analysis of Shapes - page 222

3
2 136
2 129

GM A (, A ) .

.

21

What this GM tells us is that the distance between landmarks 1
and 2 is three times larger in form A at time 2 than it was at time 1.
The distance between landmarks 1 and 3 and between landmarks 2
and 3 is just over two times larger at time 2 than at time 1.

5.6 Estimation of growth using EDMA

The example above uses information from a single form at two differ-
ent points in time. In certain settings (e.g., clinical), growth of an
individual may be of interest, but researchers rarely operate under the
assumption that analysis of a single individual is a valid representa-
tion of growth for all individuals. Common sense and previous research
tells us that growth of a single individual cannot be assumed to repre-
sent growth for a population. It is at this point that the difference
between longitudinal and cross-sectional data becomes apparent.
Sudden spurts and long periods of stasis mark growth of the individu-
al. Even though some of these episodes are held generally in common
within members of a species (e.g., the adolescent growth spurt in
humans), the exact timing and character of these episodes varies from
individual to individual. Consequently, any statistical analysis of
growth, whether the data are cross-sectional, longitudinal, or mixed
longitudinal, will obscure individual patterns and may smooth the
growth pattern for the sample. A measure of the variance will provide
some indication of individual differences but will not reconstruct indi-
vidual patterns of growth. If a generalized pattern of growth is the
desired outcome of the analysis, the procedure described below is
appropriate. If variability in individual growth patterns is the focus of
research, it may be more useful to study the growth of individuals sep-
arately and then compare the individual patterns. Such comparisons
can be accomplished using Growth Difference Matrix Analysis (see fol-
lowing sections).
Since the true mean forms for any population are never available
(see Chapter 3 ), we need to collect data from many individuals and
analyze representative growth patterns using mean forms estimated