Janda and Gillies: "How well does 'region' explain political party characteristics?" --> back to first page
Discriminant analysis of parties into regions

The preceding analysis demonstrated the pervasive influence of region on party characteristics, taken one at a time. The question arises, does region have an even stronger influence on configurations of party characteristics? For example, are we likely to find that parties in Western Europe tend to be both more institutionalized and less Marxist than parties in Africa? In general terms, can we improve regional explanations of party politics by analyzing party characteristics simultaneously? If so, how can we conduct such an analysis? The familiar technique of multiple regression will not serve here due to the polychotomous nature of 'region' as a variable in the analysis. A better technique for our purposes is discriminant analysis.

As described by Klecka (1980: 7), discriminant analysis 'allows the researcher to study the differences between two or more groups of objects with respect to several variables simultaneously'. The variables are combined in a 'canonical discriminant function' that maximizes the differences of the group means on that function. Additional canonical discriminant functions can be derived to maximize remaining group differences under the condition that values on subsequent functions are uncorrelated with values on the preceding ones. In practice, the discriminating power of additional functions drops rapidiy after the initial one.

The explanatory power of a discriminant function can be judged by the canonical correlation coefficient, which measures the relationship between the grouping and the discriminant function. When squared, the canonical correlation can be interpreted as the proportion of variance in the discriminant function explained by the groups (Klecka, 1980: 37).5 It is thus analogous to the eta-squared statistic reported in our analysis of variance, except that now we are predicting to a linear combination of party characteristics (the discriminant function) rather than to a single characteristic. Discriminant functions can also be used to classify cases in the group to which they 'properly' belong. The success of the analysis can be judged by determining the percentage of correct classifications.

In our application, we are concerned with finding a parsimonious set of variables that yields a high rate of success in classifying parties into regions on the basis of their characteristics as combined in one or more discriminant functions. In practice, the technique of discriminant analysis involves an iterative search for good discriminating variables and, in some instances, for optimum groupings of cases. If there are meaningful differences among the groups on the variables, however, the analyses usually converge on functions and classifications that are quite similar. Our analysis began with the 10 groups of nations involved in the analyses of variance and with all 11 variables except the parties' liberal orientation, which sacrificed too many cases due to missing data. Initial analyses soon eliminated two additional variablesÐgovernmental status and coherence of party behavior--that showed the least variation by region. Two other variables--degree of organization and Marxist orientation--seemed to be interchangeable in the analysis, producing similar results when one or the other was included. For simplicity's sake, we focus on the set of seven variables that included the parties' Marxist orientation. There were valid data for 138 parties on all seven variables in this analysis.

These variables yielded two meaningful discriminant functions with canonical correlations of 0.82 and 0.66 when all 10 regions were involved in the analysis. When these two functions were used to classify the parties into regions, the correct classification--a rather demanding test--was made for 40 per cent of the parties. Many of the errors came from misclassifying Western and African parties in adjacent regions. Seeking to improve on success, the number of regions was reduced to seven by combining Anglo-America, West Central, and Northern Europe into the 'Western Community' and by combining West and East Africa into 'Subsaharan Africa'. The canonical correlations remained almost unchanged but success in classification climbed to 58 per cent.

In general, the success of classification rose as the number of regions declined after merging regions into larger geographical areas. In part, this is artifactual with the method, but not for the reasons that Clark and Avery (1976) describe as a consequence of data aggregation in correlational analysis. In discriminant analysis, the probability of correct classification without knowledge of predictive factors is a function of the number of categories and the distribution of cases among those categories. The proportion of cases in the model category determines the expected success in classification given no knowledge about predictive factors. However, the success in prediction climbed more steadily than expected simply from a smaller numbei~ of regions. When the regions had dropped to three--the Western Community, Eastern Europe, and the developing areas-- 88 per cent of the cases were correctly classified, although the two canonical correlations had dropped to 0.76 and 0.59. The three regions produced by our analysis are close to the familiar 'three worlds' of development: the Western Community, the Communist Party-states of Eastern Europe and elsewhere, and the Third World of developing nations.6 We can perfect the fit by reassigning two Communist Party-states--North Korea and Cuba--to the Eastern World for our final discriminant analysis. This results in the same Western Community (with 54 parties), increases the Eastern World to nine parties with valid data on all seven variables, and drops the Third World of non-Western and non-Communist nations to 76 parties.

The effort to explain the analysis is limited by concentrating on the discriminant functions that produced the final classification of parties into one of these three 'worlds'. Klecka notes that the discriminant function coefficients themselves often constitute poor guides to the 'meaning' of the function (1980: 34). He proposes instead looking at the product-moment correlations between the individual variables and the discriminant functions. He refers to these correlations as 'total structure coefficients'. They tell 'how closely a variable and a function are related' (1980: 31). These structure coefficients are reported in Table 2.

The two functions in Table 2 can be labelled with reference to the variables that correlate highly with them. Thus we call the first function an 'anti-competitive' function, for it correlates inversely with the two alternative party strategies. This function, which explains the most variance in the parties grouped into the 'three worlds', thus spreads the parties along the first dimension of classification. The second function reflects the influence of 'institutionalized' party structure--including also membership involvement and diversity of support. It spreads the parties along the second dimension of classification.

 TABLE 2. Structure coefficients for the discriminant functions: correlations between the variables and the functionsa 1st Function: 2nd Function: Discriminating variables anti-competitive institutionalized Open competition -.82 .37 Restricting competition .79 -.08 Marxist orientation .50 .22 Centralization of power .38 .01 Institutionalization -.57 .74 Involvement of members .19 .48 Diversity of support -.23 .40 a Values are the simple correlations between the variables and the composite variable computed by the discriminant function, whose values are not given to conserve space.

The parties' scores on the seven variables were multiplied by the discriminant function coefficients to give every party a score on both functions. The differences between the three groups of parties can be seen by examining the group averages on each function:

 Anti-competitive Institutionalized Western World -1.36 0.56 Eastern World 3.71 2.75 Third World 0.61 -0.64

The inter-group distances on the discriminant functions can be readily seen by plotting the group means along the two dimensions. The computer program used in the analysis7 plotted these group means, called group 'centroids', in a two-dimensional 'territorial map' that identified the boundaries separating parties in one group from those in another. This map is reproduced in Figure 1. We see that the means for parties in the Western World are diametrically different from those for parties in the Third World. The Western parties are very low on the anti-competitive function and relatively high on the institutionalized function. Third World parties tend to be just the reverse. Parties in the Eastern World, on the other hand, are extremely high on both functions. As shown on the territorial map, parties in the Eastern World are clustered in the upper-right portion, the Western parties are grouped on the left-hand side, and Third World parties are spread somewhat more loosely in the central lower segment.

FIGURE 1. Territorial map of boundaries separating parties into three world groupings
based on the discriminant functions, with misclassified parties identified.
All-groups scatterplot:
black dots indicates group centroids.

Of 138 political parties plotted on the territorial map according to their scores on both functions, 124 (90 per cent) were correctly classified in 'their' world. The classification results are summarized in Table 3. All of the seven ruling Communist Parties are correctly classified into the Eastern World, and two parties in Third World countries (the Democratic Party of Guinea and the Paraguayan Colorado Party) are more like the ruling Communist Parties than the other parties in the Third World. On the other hand, three parties in Western countries (the Greek EPEK, the Greek EDA, and the Portuguese National Union) were more like Third World parties than the other Western parties. Finally, nine of the 76 Third World parties (two each in India, Ecuador, and Uruguay, plus the Malayan MCA, the Lebanese National Bloc, and the Turkish Republican Party) stood closer to the Western parties than to other Third World parties.

 TABLE 3. Per cent success in classifying parties into three worlds using seven variables in a discriminant analysis Predicted group membership Actual group membership Western Eastern Third Western world 94.4 0 5.6 (number of parties in parentheses) (51) (3) Eastern world 0 100 0 (7) Third world 11.7 2.6 85.7 (9) (2) (66) 124 of 138 parties correctly classified (90 per cent)

Lest one should think that the distinctiveness of the Eastern parties in this analysis was due to their strong Marxist orientation, it should be noted that they were also classified together when the analysis was conducted with the degree of organization variable instead of the Marxism variable. (That analysis, however, correctly classified only 88 per cent of the cases, rather than the 90 per cent using Marxist orientation.) One might also wonder whether the broad 'three world' grouping of parties performs better in the analysis of variance than the 10 regional groupings that were used. The answer is no. The finer grouping of parties into regions consistently explains as much variance, and usually substantially more, than grouping the parties into the 'three worlds'. This phenomenon is consistent with a 'hierarchy of regions' in geographic theory (Cox, 1969: 76), which allows that large areas, relatively distinctive on some traits, may contain smaller areas that are in turn distinctive from one another. The broader grouping is superior for capturing the configuration of party characteristics, but the impact of region on individual characteristics is greater when the regions are more homogeneous.

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