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Left-Right Dimensions of Canadian Federal Party Identification: A Discriminant Analysis*

Published online by Cambridge University Press:  10 November 2009

John F. Zipp
Affiliation:
Duke University

Abstract

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Type
Articles
Copyright
Copyright © Canadian Political Science Association (l'Association canadienne de science politique) and/et la Société québécoise de science politique 1978

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References

1 Downs, Anthony, An Economic Theory of Democracy (New York: Harper, 1957).Google Scholar

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3 Ibid., 13. This ordering of the parties will be referred to as the “standard” left-right dimension throughout this paper.

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7 Another peculiarity of the Canadian system is that, while the minor parties are drawn to the centre, there also has been a centrifugal push to keep themselves distinct from the centre. This force has been supplied by the Liberal party which has managed simultaneously to take positions of the three other parties, thus co-opting support. Certainly this has to be regarded as one of the keys to the Liberals’ success in retaining control of the government.

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20 In Table I, column three, row seven, the “omitted” category is “Other” religion, which is comprised of Jews, Mormons and lower status Protestants. Because this is a rather amorphous grouping, it was decided to use it as the omitted category. Note: All religion coefficients represent deviations from it.

21 For example, see Smith, , et al., “Patterns of Early Political Socialization,” and Hyman, Herbert H., Political Socialization (Glencoe: Free Press, 1959).Google Scholar

22 The fourth set is only for the mass sample.

23 Although there are minor difficulties, favouring special status for Quebec is used as a liberal response.

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29 Ogmundson, “On the Measurement of Party Class Positions.”

30 Smith, Joel and Kornberg, Allan, “Self-Concepts of American and Canadian Party Officials: Their Development and Consequences,” Social Forces 49 (1970), 210–26CrossRefGoogle Scholar. Kornberg, and Smith, , “Self-Concepts of American and Canadian Party Officials,” Polity 3(1970), 7099.CrossRefGoogle Scholar

31 As an anonymous reviewer noted, there is an alternative perspective based on the voting literature which suggests that since party identification may be the only important political cue for the majority of the electorate, it may serve as the basis upon which other political attitudes are organized. This line of reasoning leads one to argue that party identification may be as or more salient for the mass electorate than for the party officials. While I agree in general that this is a plausible interpretation, in this instance because my variables may measure perceptions of the performance of the party in power at a given level, I expect that the very closeness of party officials to their party may allow their party identification to influence their opinions more than the opinions of the mass electorate.

32 Because discriminant analysis stems from the experimental design literature, the dependent variables often represent control and experimental groups. Hence, it assumed that the dependent variables are measured without error and that they are a priori given. These, of course, are the usual assumptions made of independent variables in other statistical techniques; for example, path analysis. As such, there may be some confusion as I will refer to party identification as affecting attitudes.

33 They maximize the F ratio of the mean square between groups/mean square within groups. For good discussions of discriminant analysis, see Tatsuoka, Maurice M., Discriminant Analysis (Champaign: Institute for Personality and Ability Testing, 1970)Google Scholar; Finn, Jeremy D., A General Model for Multivariate Analysis (New York: Holt, Rinehart and Winston, 1975)Google Scholar; or Huberty, Carl J., “Discriminant Analysis,” Review of Educational Research 45 (1975), 543–98. The first is the least mathematical, while the last two require some mathematical facility.CrossRefGoogle Scholar

34 Darlington, R. B., Weinberg, S. L., AND Walberg, H. L., “Canonical Variate Analysis and Related Techniques,” Review of Educational Research 43 (1973), 433–54CrossRefGoogle Scholar. Mulaik, S. S., The Foundations of Factor Analysis (New York: McGraw-Hill. 1972).Google Scholar

35 Huberty, “Discriminant Analysis.”

36 Eisenbeis, R. A. and Avery, R. B., Discriminant Analysis and Classification Procedures (Lexington, MA: Heath, 1972).Google Scholar

37 The fact that standardized coefficients may be misleading for dichotomous variables can be illustrated. Suppose that one is using an ordinal variable, decomposed into three “dummy” variables: XI, X2, and X3. The means for these variables are simply the proportion in that category and the standard deviations are the square root of (pxq), where p equals the mean of X and q equals one minus p. Given the following data:

suppose that the unstandardized coefficients, dl, d2, and d3, are equal; i.e., d 1 = d2 = d3 = d. Even though the unstandardized coefficients are equal, the standardized coefficients, dl*, d2*. and d3*. would not be equal:

and only because there are a different number of respondents in each of the three categories. Thus, while dl has the same effect as d2, the use of standardized coefficients would make it appear that dl was larger than d2.

38 An assumption of linear discriminant analysis is the homogeneity of within-groups covariances matrices, an assumption that is rarely met in practice. When this assumption is violated, quadratic, as opposed to linear, discriminant analysis should be undertaken. However, various authors, for example Eisenbeis and Avery, suggest that the performance of the discriminatory rule (linear or quadratic) varies from case to case. In some situations one clearly is better, while in others both perform adequately. In my situation, the within-groups covariances matrices were not homogeneous in six of the seven discriminations. As a result, 1 performed quadratic discriminant analysis and obtained results extremely similar to those obtained from the linear analysis. For reasons of parsimony, I have utilized the linear analysis throughout this paper.

39 This is calculated as the ratio of the eigenvalue associated with a given function over the sum of all eigenvalues.

40 Strictly speaking, it is the function which accounts for 98 per cent of the discriminatory power of the independent variables, but, as noted earlier, since these functions are unmeasured constructs, I have no way of interpreting them except through the independent variables which weight heavily on them. Thus, I shall characterize functions by the independent variables most strongly related to them. Another point bears mentioning: 98 per cent of the discriminating ability of the independent variables is not equivalent to an R2 of .98 in the regression sense. The appropriate statistic in this regard is the canonical correlation and the reader is referred to them. I shall concentrate on my measure since I am primarily interested in the relative explanatory powers of the different functions.

41 The fact that univariate analyses may be misleading can be seen in the mass sample. The univariate F ratios of all three independent variables are significant (data not given), however, due to their intercorrelations in a multivariate analysis, only one of them (early life family situation) is a significant discriminator of the four parties.

42 Centroids are weighted estimates of the group means on the discriminant functions. They may be calculated by forming linear composites of the within-group means on the individual independent variables multiplied by their respective unstandardized coefficients, and then summed along with the constant. They are to be interpreted relative to each other on a dimension defined by the independent variables (the discriminant function).

43 From Table 3 one can see that there are three additional variables which are statistically significant. However, I am interpreting both significance and magnitude, a procedure that I shall follow throughout this paper.

44 Terry and Schultz, “Canadian Electoral Behaviour.”

45 Schwartz, Mildred A., Politics and Territory (Montreal: McGill-Queen's University Press, 1974); Alford, Party and Society; Terry and Schultz, “Canadian Electoral Behaviour.”CrossRefGoogle Scholar

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47 Perhaps, as an anonymous reviewer suggested, this is the real left-right dimension. As I shall discuss in the following pages, my findings indicate that there are two left-right dimensions: the major-minor party one which Ogmundson terms the economic left-right and the standard left-right. Ogmundson's social or religious leftright (“On the Kieasurement of Party Class Positions”).

49 Hamilton, Richard F., Class and Politics in the United States (New York: Wiley, 1972).Google Scholar

50 Ogmundson, “Mass-Elite Linkages and Class Issues in Canada,” Canadian Review of Sociology and Anthropology 13(1976), 1–12.

51 These party officials certainly are political elites as 34 per cent of them have been candidates for public office.