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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Facet theory | 6/8 | https://en.wikipedia.org/wiki/Facet_theory | reference | science, encyclopedia | 2026-05-05T09:54:10.375224+00:00 | kb-cron |
Given this POSAC solution, an attempt is made to interpret the two coordinates, X1 and X2, as two fundamental scales of the investigated phenomenon of evening TV watching by the investigated population. This is done by, first, interpreting the intervals (equivalence classes) within each coordinate, and then trying to conceptualize the derived meanings of the ordered intervals, in terms of a meaningful notion that may be attributed to the coordinate. In the present simplified example, this is easy: Inspecting the map, we attempt to identify the feature that distinguishes all profiles with given score in X1. Thus, we find that profiles with X1=4, and only they, represent TV watching in the fourth hour. Profiles with X1 = 3 all have 1 in the third watching hour but 0 at the fourth hour, i.e., the third hour is the latest watching hour. X1 = 2 is assigned to, and only to, profiles whose latest watching hour is the second hour. And, finally, X1 = 1 is for the profile 1000 which represents the fact that the first hour is the only – and therefore the latest – watching hour (ignoring the profile 0000 of those who didn't watch TV at the specified hours, and could be assigned (0,0) in this coordinate-space). Hence, it may be concluded that intervals of coordinate X1 represent j=the latest hour—among the four hours observed—in which TV was watched, (j = 1, ..., 4). Similarly, it is found that intervals of coordinate X2 represent 5 − k for k (k = 1, ..., 4) is the earliest hour of TV watching. Indeed, for profiles of the observed set, which represent a single sequence of continuous TV watching, specification of the earliest and latest watching hours, provide full description of the watching hours. Example 3 illustrates key features of Multiple Scaling by POSAC that render this procedure a theory-based multivariate measurement:
The two scores assigned by Multiple Scaling to every observed profile—and hence to every person in the observed sample—replace the more numerous scores (four, in the present example) of the observed variables, while retaining all observed order relations, including incomparability. The new scores assess observed persons on the two coordinate-scales, taken to constitute Nature's fundamental variables. The two coordinate-scales have intrinsic meanings that probe into a deeper significance than the observed variables considered severally. In the present example, the earliest and the latest hour indeed exhaust the essential aspects of the pattern of TV watching, given the particular set of observed profiles. The concepts derived for the fundamental, unobserved coordinate-scales retain the CMR—the essential meaning common to all observed variables. In the present example, the CMR is more (vs. less) TV watching. For, considering the observed variables, each of them records high (1) vs. low (0) TV watching in a given hour. And the derived coordinate-scales, too, record high (4) vs. low (1) TV watching, since ceteris paribus, the later is the latest watching hour, the more TV one watches (X1); and the earlier is the earliest watching hour, the more TV one watches ( X2). These features are present also in applications that are less obvious, to produce scales with novel meanings.
=== Example 4. Measuring distributive justice attitudes === In the systemic theory of distributive justice (DJ), alternative allocations of a given amount of an educational resource (100 supplementary teaching hours) between gifted and disadvantaged pupils, may be classified by one of four types, the preference for each reflecting one's DJ attitude: Equality, where the gifted and the disadvantaged pupils get the same amount of the supplementary resource; Fairness, where the disadvantaged pupils get more of the resource than the gifted, in proportion to their weakness relative to the gifted; Utility, where the gifted get more of the resource than the disadvantaged pupils (so as to promote future contribution to the general good); Corrective Action, where the disadvantaged pupils get more of the resource than the gifted over and above the proportion of their weakness relative to the gifted pupils, (so as to compensate them for past accumulated disadvantage); Following the Faceted SSA validation of the four DJ modes of Equality, Fairness, Utility, and Corrective Action, profiles based on eight dichotomized DJ attitudes variables observed on a sample of 191 respondents, were created. 35 of the 256 combinatorially possible profile were observed and analyzed by POSAC to obtain the measurement space shown in Figure 4. For each of the variables an optimal partition- line was computed that separates a high from a low score in that variable. (Logically, partition-lines must look like non-increasing step functions.) Then, for each of the four attitude types, the characteristic partition-line was identified as follows:
Fairness—a straight vertical line; Utility—a straight horizontal line; Equality—an L-shaped line; Corrective action—an inverted-L-shaped line The content significance of the intervals induced by these partition-lines on the X coordinate and on the Y coordinate of the POSAC space, are now identified and thereby define the contents of the X and Y Coordinate Scales of DJ attitudes. The X-coordinate Scale, interpreted as Enhanced Fairness Attitude Scale:
Interval 1. Low Fairness & Low Equality DJ Attitude Interval 2. Low Fairness & High Equality DJ Attitude Interval 3. High Fairness & Low Corrective Action DJ Attitude Interval 4. High Fairness & High Corrective Action DJ Attitude That is, Enhanced Fairness Attitude, even if low, (interval 1 and 2) is somewhat present when Equality is favored (interval 2). And if Enhanced Fairness Attitude is high (intervals 3 and 4), it reaches the extreme level (interval 4) when Corrective Action is favored. The Y-coordinate Scale, interpreted as Enhanced Utility Attitude Scale: