Russel-Research-Method-in-Anthropology

Multivariate Analysis 681
4. Across all three replications, the three factors in tables 21.23 and 21.24 account
for 70%–80% of the variance in the original data matrix. That is, about threefourths
to four-fifths of the variance in the original data is accounted for by just
three underlying variables (the three factors) rather than the full list of original
variables. For women across the Caribbean, the construct of domestic cooperation
is multidimensional and comprised of three subconstructs: sharing of everyday
domestic chores, sharing of responsibilities for children, and affection from
men as defined by being treated as an equal.
Multidimensional Scaling Analysis (MDS)
MDS is another multivariate data-reduction technique. Like factor analysis,
it is used to tease out underlying relations among a set of observations. Also
like factor analysis, MDS requires a matrix of measures of associations—e.g.,
a correlation matrix based on things like r, tau, gamma, etc. But unlike factor
analysis, MDS does not require metric data.
When you measure something like how strongly people feel about something,
the numbers you assign to their feelings don’t have the same meaning
as, say, numbers that express distances in kilometers or kilograms of game
meat killed per month. These latter numbers are called ‘‘metric’’ because they
are grounded in well-understood units of measurement.
Most attitude and cognition data are nonmetric. MDS is particularly useful
for anthropologists, since a lot of the measurements we make are nonmetric.
Also, MDS produces a graphic display of the relation among any set of items,
whether those items are people, or things, or questions about attitudes. (For
more about the theory behind MDS, see Romney et al. [1972].)
How MDS Works
Suppose you measure the association among three variables, A, B, and C,
using Pearson’s r. The association matrix for these three variables is in the
inside box of table 21.25.
Clearly, variables A and C are more closely related to one another than are
A and B, or B and C. You can represent this with a triangle, as in figure 21.3a.
In other words, we can place points A, B, and C on a plane in some position
relative to each other. The distance between A and B is longer than that
between A and C (reflecting the difference between .50 and .80); and the distance
between B and C is longer than that between A and C (reflecting the
difference between .40 and .80). The numbers in this graph are similarities:
The lower the correlation, the longer the distance; the higher the correlation,
the shorter the distance. (We won’t consider negative correlations here.)