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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

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