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Columbia’s CCP: A Case Study

decided to analyze the results at the individual level, primarily because of some highly visible individuals who played central roles in the conceptualiza- tion and implementation of CCP programs. Still, we are able to connect indi- viduals to organizations, and tend to view them as representatives of the or- ganizations with which they are affiliated. We are likely to use organizations as the unit of analysis for a planned longitudinal analysis because of the at- trition problem in network and panel data.

To determine the appropriate number of dimensions for the data, a series of analyses were performed and a “stress” statistic was calculated for each solu- tion. In MDS, stress is the most widely used goodness-of-fit measure for di- mensionality, with smaller values indicating that the solution is a better fit to the data (Kruskal & Wish, 1978).5 By plotting the stress values for solu- tions with up to four dimensions, it became apparent that the “elbow” point (i.e. where any additional increase in the number of dimensions fails to yield sizeable reductions in stress) occurs at two dimensions. This pattern was evident at all five sites, and hence, we elected to use a two-dimensional solu- tion across the board. Beyond relative stress levels there is the issue of abso- lute stress values. Stress values ranged from 18 to 20 percent, with one ex- ception (25%). These values are considered acceptable in the literature, al- though figures above 20 percent suggest a weak fit (see Kruskal, 1964; Scott, 1991).

The data were analyzed, presented, and interpreted separately for each CCP

site.

Stress

Statistics reported include stress values calculated

Formula

1

and

the

squared

correlation

(R²).

The

from Kruskal’s value indicates

the proportion of variance of the by their corresponding distances.

disparity

matrix

data

that

is

accounted

for

After calculating the solution and mapping a multidimensional configuration, the final step is interpretation. This involves assigning meaning to the di- mensions and providing some explanation for the observed arrangement of points in space. In other words, what do the clusters of points mean and how should they be interpreted? As Scott notes (1991, p. 166), “...this process of interpretation is a creative and imaginative act on the part of the researcher. It is not something that can be produced by a computer alone.”

5Technically, stress is defined as “the square root of a normalized ‘residual sum of squares.’” Dimensionality is defined as “the number of coordinate axes, that is, the number of coordinate values used to locate a point in the space.” (Kruskal &Wish, 1978, p. 48-49).

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