² The phrase “national attribute data” is used to referto qualities of national units as determined by some kind of measurement, such as “Large Percentage of Labor Force Employed in Agriculture.” In this usage I view all measures in this study, other than voting measures, as “national attribute” measures.

³ Vincent, Jack E., The Caucusing Groups of the United Nations: An Examination of Their Attitudes Toward the Organization (Stillwater: Oklahoma State University Press, 1965)Google Scholar.

⁴ Vincent, Jack E., “National Attributes asPredictors of Delegate Attitudes at the United Nations,” American Political Science Review, 62 (1968), 916–931 CrossRefGoogle Scholar.

⁵ Vincent, Jack E., “The Convergence of Voting and Attitude Patterns at the United Nations,” Journal of Politics, 31 (1969), 952–983 CrossRefGoogle Scholar.

⁶ Vincent, Jack E., “An Analysis of Caucusing Group Activity at the United Nations,” Journal of Peace Research,2 (1970), 133–150 CrossRefGoogle Scholar.

⁷ For a full treatment, see the various Dimensionality of Nations Research Reports, in particular, Rummel, R. J., “The DON Project, A Five-Year Research Program,” Research Report No. 9, Dimensionality of Nations Project, University of Hawaii, 1967 Google Scholar; Rummel, R. J., “Field Theory and Indicators of International Behavior,” Research Report No. 29, Dimensionality of Nations Project, University of Hawaii, 1969 Google Scholar; McCormick, David M., “A Field Theory of Dynamic International Processes,” Research Report No. 30, Dimensionality of Nations Project, University of Hawaii, 1969 Google Scholar; Rummel, R. J., “Field and Attribute Theories of National Behavior: Some Mathematical Interrelationships,” Research Report No. 31,Dimensionality of Nations Project, University of Hawaii, 1969 Google Scholar; Park, Tong-Whan, “Asian Conflict in Systematic Perspective: Application of Field Theory (1955 and 1963),” Research Report No. 35, Dimensionality of Nations Project, University of Hawaii, 1969 Google Scholar; Rummel, R. J., “Social Time and International Relations,” Research Report No. 40, Dimensionality of Nations Project, University of Hawaii, 1970 Google Scholar; Rummel, R. J., “U.S. Foreign Relations: Conflict, Cooperation and Attribute Distances,” Research Report No. 41, Dimensionality of Nations Project, University of Hawaii, 1970 Google Scholar; Atta, Richard Van and Rummel, R. J., “Testing Field Theory on the 1963 Behavior Space of Nations,” Research Report No. 43, Dimensionality of Nations Project, University of Hawaii, 1970 Google Scholar; Rummel, R. J., “Field Theory and the 1963 Behavior Space of Nations,” Research Report No. 44, Dimensionality of Nations Project, University of Hawaii, 1970 Google Scholar; Park, Tong-Whan, “Measuring Dynamic Patterns of Development: The Case of Asia, 1949-1968,” Research Report No. 45, Dimensionality of Nations Project, University of Hawaii, 1970 Google Scholar; Rummel, R. J., “Indicators of Cross National and International Patterns,” American Political Science Review, 63 (1969), 127–147 CrossRefGoogle Scholar; Rummel, R. J., “International Pattern and Nation Profile Delineation,” in Bobrow, Davis B. and Schwartz, Judah L., (eds.), Computers and the Policy-Making Community (Englewood Cliffs, N.J.: Prentice-Hall, 1968), 154–202 Google Scholar; and Rummel, R. J.. “Some Attributes and Behavioral Patterns of Nations,” Journal of Peace Research, 2 (1967), 196–206 CrossRefGoogle Scholar.

⁸ Rummel, “Field and Attribute Theories of National Behavior….” op. cit., p. 6.

⁹ Ibid., p. 16.

¹⁰ Ibid., p. 7.

¹¹ Ibid., p. 22.

¹² Rummel, “Field Theory and Indicators of International Behavior,” op. cit., p. 10.

¹³ When Rummel treats UN voting as behavior, he takes the Euclideandistance between the nations on the factor dimensions generated from an analysis of rollcall votes (Ibid., p. 26C). Although this may allow treatment of UN voting data for certain purposes, nevertheless, as pointed out above, voting does not appear tobe dyadic in form in the same sense that exports, threats, etc., are.

¹⁴ Rummel, “Field Theory and Indicators of International Behavior,” op. cit., p. 39.

¹⁵ Vincent, “National Attributes ….” op. cit., p. 930.

¹⁶ In particular, see Alker, Hayward R. Jr., and Russett, Bruce M., World Politics in the General Assembly (New Haven: Yale University Press, 1965)Google Scholar; Russett, Bruce M., “Discovering Voting Groups in the United Nations,” American Political Science Review, 60 (1966), 327–339 CrossRefGoogle Scholar; and Alker, Hayward R. Jr., “Dimensions of Conflict in the General Assembly,” American Political Science Review, 58 (1964), 642–658 CrossRefGoogle Scholar.

¹⁷ The uses and meaning of factor analysis will be made clear in subsequent discussion. In addition, see Harman, Harry H., Modem Factor Analysis (Chicago: University of Chicago Press, 1960)Google Scholar; Kaiser, Henry F., “The Varimax Criterion for Analytic Rotation in Factor Analysis,” Psychometrika, 23 (1958), 187–200 CrossRefGoogle Scholar; Kaiser, Henry F., “Computer Program for Varimax Rotation in Factor Analysis,” Educational and Psychological Measurements, 19 (1959), 413–420 CrossRefGoogle Scholar; Clyde, Dean J., Cramer, Elliott M., Sharin, Richard J., Multivariate Statistical Programs (Coral Gables, Florida: University of Miami, 1966), 15–19 Google Scholar; Russett, Bruce M., International Regions and the International System: A Study in Political Ecology (Chicago: Rand McNally, 1967)Google Scholar; Rummel, Rudolph J., “Dimensions of Conflict Behavior Within and Between Nations,” General Systems, Yearbook for the Advancement of General Systems Theory (Ann Arbor, Michigan, 1963)Google Scholar; Banks, Arthur S. and Gregg, Phillip M., “Grouping Political Systems: Q-Factor Analysis of ACross-Polity Survey,” The American Behavioral Scientist, 9 (1965), 3–6 CrossRefGoogle Scholar; Gregg, Phillip M. and Banks, Arthur S., “Dimensions of Political Systems: Factor Analysis of A Cross Polity Survey,” American Political Science Review, 59 (1965), 602–614 CrossRefGoogle Scholar; Tanter, Raymond, “Dimensions of Conflict Behavior Within and Between Nations, 1958-60,” Journal of Conflict Resolution, 10 (1966), 41–64 CrossRefGoogle Scholar; Rummel, R. J., “Dimensions of Conflict Behavior Within Nations 1946-59,” Journal of Conflict Resolution, 10 (1966), 65–73 CrossRefGoogle Scholar; Vincent, Jack E., Factor Analysis in International Relations: Interpretation, Problem Areas and An Application (Gainesville: University of Florida Press, forthcoming)Google Scholar; Rummel, R. J., Applied Factor Analysis (Evanston: Northwestern University Press, 1970)Google Scholar; Vincent, Jack E., “Factor Analysis as a Research Tool in International Relations: Some Problem Areas, Some Suggestions and An Application,” Proceedings of the 65th Annual Meeting of the American Political Science Association (New York: 1969)Google Scholar; Cattell, Raymond B., “The Measuring and Strategic Use of Factor Analysis,” in Cattell, Raymond B. (ed.) Handbook of Multivariate Experimental Psychology (Chicago: Rand, McNally & Co., 1966), 174–243 Google Scholar; and Cattell, Raymond B., “The Basis of Recognition and Interpretation of Factors,” Educational and Psychological Measurement, 22 (1962), 667–697 CrossRefGoogle Scholar.

¹⁸ Alker and Russett, op. cit., p. 38. Where F is an N × m matrix of factor scores, Z is an N × n matrix of scores on the original variables in standard score form, A is an n × m matrix of factor coefficients (loadings) and N = subjects, n = variables and m = factors.

In the case of Alker and Russett's factor scores, because they chose to set loadings less than ± .25 to 0, there is some discrepancy between such correlations and the loadings. Such procedures generally create stronger correlations of the heaviest loading variables with the factor scores than the loadings themselves would indicate. Also, such “factor scores” are correlated, which is not consistent with the “orthogonal” rotation. As will be seen, this problem is handled by re-factor analyzing Alker and Russett's factor scores (along with Russett's voting group scores) and computing new scores.

For a discussion of factor scores, see Horn, John L. and Miller, Wilbur C., “Evidence on Problems in Estimating Common Factor Scores,” Educational and Psychological Measurements, 26 (1966), 617–622 CrossRefGoogle Scholar; Horn, John L., “An Empirical Comparison of Methods for Estimating Factor Scores,” Educational and Psychological Measurements, 25 (1965), 313–322 CrossRefGoogle Scholar; Glass, Gene V. and Maguire, Thomas O., “Abuses of Factor Scores.” American Educational Research Journal, 3 (1966), 297–304 CrossRefGoogle Scholar; and Jack E. Vincent, “Factor Analysis as a Research Tool …” op. cit.

¹⁹ Alker and Russett, op. cit., pp. 299–307.

²⁰ Russett, “Discovering Voting Groups …” op. cit., pp. 331–334.

²¹ Unlike factor scores computed by the formula F = ZA (A″A)⁻¹ , given above, the subjects' scores, as loadings, tend to be correlated across factors. For this reason, as will be seen, Russett's Q analysis loadings are factor analyzed, along with Alker and Russett's factor scores, and the subjects re-scored using the formula given above.

²² Alker treats eight group membership variables, nine economic variables, six political variables, and three sociological variables in his “Dimensions of Conflict …,” op. cit., pp. 653–654. Alker and Russett treat six economic variables, four political variables, five regional variables, and four social variables in their World Politics in the General Assembly, op. cit., pp. 224–252. These variables, for the most part, snowed varying degrees of association with the voting pattern data only, and no “overall importance analysis,” of the type presented here, has been attempted. This observation is in no way intended to disparage such earlier efforts, but is made to set this analysis off from earlier ones.

²³ It should be apparent by examination of the primary resources that the time the states were scaled on the various variables considered in this study, treated as independent variables, is very close to the time the states were scaled on the voting data.

²⁴ Alker and Russett, op. cit.; Russett, op. cit.

²⁵ Banks, Arthur S. and Textor, Robert B., A Cross Polity Survey (Cambridge: M.I.T. Press, 1963)Google Scholar; Russett, Bruce M., et al., World Handbook of Political and Social Indicators (New Haven: Yale University Press, 1964)Google Scholar.

²⁶ Approximately 10 percent of the data was missing.

²⁷ See Baggaley, Andrew R., Intermediate Correlational Methods (New York: John Wiley and Sons, 1964), pp. 21–23 Google Scholar.

²⁸ See footnote 17.

²⁹ Cattell, “The Basis of Recognition …” op. cit., p. 684.

³⁰ Sometimes the concepts of “unique,” “specific,” and “error” variance are developed. In such a case the variance left over, that is, not explained by the factors, is viewed as unique and subdivided into specific and error factors. The above discussion, then, ignores the problem of error factors and treats all of the unique variance as specific for the purposes of simplification. See Cattell, “The Meaning and Strategic Use …” op. cit., pp. 177, 200–211.

³¹ Thomson, Godfrey H., The Factorial Analysis of Human Ability (Boston: Houghton Mifflin, 1951), pp. 336–337 Google Scholar.

³² Cattell argues, “The components model [putting unities in the principal diagonal] must be rejected for general scientific investigation, because it would be most unlikely that n variables would contain within themselves all the causes for accounting for their own variances. To do this, they would have to lie in a completely self-explanatory subuniverse, self-sufficient as a system entirely isolated from the rest of the universe.” Cattell, “The Meaning and Strategic Use …” op. cit., p. 177.

In the search for factors (viewed as causes) where oblique rotation is used, Cattell maintains that it is necessary to evaluate at least the following matrices: reference vector structure, reference vector pattern, factor pattern, factor structure, factor estimation weights, and reference vector estimation weights. Cattell, “The Basis of Recognition …” op. cit., pp. 673–676. Cattell criticized most factor analysts, who search for causes, for usually dealing with only one of these matrices.

Further, Cattell does not view any of the oblique solutions (oblimax, etc.) as final if the investigator's quest is for simple structure. “All present analytical solutions fail because they are not working with a criterion rightly demanded by the model.” Cattell, “The Meaning and Strategic Use …” op. cit., p. 186. The search for simple structure, as developed by Cattell, is an extremely complicated matter and may prove to be very time consuming. In Cattell's words:

To me, Cattell's case appears reasonable and the burden is on those to use such procedures if they view factor analysis as a search for causes. If we accept Cattell's arguments, the following kinds of practices prevalent in certain factor analytic studies are relatively meaningless: (1) “seeing” similarly in an orthogonal and oblique solution and then concluding that the factors are basically uncorrelated, (2) “seeing” similarly in the factors that emerge across several studies and concluding the same fundamental causes are operative, and (3) rotating to one of the oblique solutions and then concluding that the result is simple structure. Fortunately, those that follow the data reduction school of factor analysis escape the procedural burdens, imposed by Cattell, for the reasons developed above.

³³ See: Hotelling, Harold, “Relations Between Two Sets of Variates,” Biometrika, 28 (1936), 321–377 CrossRefGoogle Scholar; Hotelling, Harold, “The Most Predictable Criterion,” Journal of Educational Psychology, 26 (1935), 139–142 CrossRefGoogle Scholar; Anderson, T. W., An Introduction to Multivariate Statistical Analysis (New York: John Wiley and Sons, 1958), Chapter 12Google Scholar; Bartlett, M. S., “The Statistical Significance of Canonical Correlations,” Biometrika, 32 (1941), 29–38 CrossRefGoogle Scholar; Horst, Paul, Generalized Canonical Correlations and Their Application to Experimental Data (Seattle: University of Washington, 1961, mimeographed)Google Scholar; Horst, Paul, “Relations Among m Sets of Measures,” Psychometrika, 26 (1961), 129–149 CrossRefGoogle Scholar; Kendall, M. G., A Course in Multivariate Analysis (London: Charles Griffin and Co., 1957), Chapter 5Google Scholar; Thomson, G., “The Maximum Correlation of Two Weighted Batteries,” The British Journal of Psychology: Statistical Section, vol. 1, Part 1 (1947), 27–34 Google Scholar; and Clyde, Cramer and Sharin, op. cit., pp. 4–8.

³⁴ When this formula is applied to uncorrelated scores the weights become Pearson r correlations of the variables with the canonical variate scores, a point discussed above.

³⁵ When the variables that are entered into a canonical correlation are not mutually orthogonal, that is, are correlated, the problems of interpreting weights are similar to the problems encountered in interpreting weights when using multiple regression analysis. For example, if there are two very good but correlated predictors, the one with the best relationship will receive the heaviest weight and the one with the second best relationship will receive hardly any weight, or, perhaps, an even opposite sign weighting. Weights in the correlated case, then, are no longer correlations of the variables with the canonical variate scores and, therefore, interpretation becomes difficult It should be apparent that one of the primary uses of factor analysis can be to set up data in a form convenient for analysis and interpretation in a canonical correlation.

³⁶ Another possible mode of analysis is to relate independent factor dimensions to the dependent voting variables, one at a time. Such procedures would generate statements such as, “The higher a state scores on the Development factor, the more likely it will vote Western.” The advantage of this method is the elimination of virtually identical predictors on the independent side, but the disadvantage lies in fairly low predictive power compared to the canonical correlation technique.

Another possibility is to run a multiple regression analysis of independent factors against each of the dependent factors taken individually. These procedures would produce statements such as, “The higher a state is on the Development factor and the Authoritarianism factor, but the lower it is on the U.S. Relations factor, the more likely it is to vote Eastern.” The advantage of this technique is to increase the size of the correlations, and therefore, the accuracy of predictions, by considering numerous independent variables. The disadvantage is in the problem of assessing the overallimportance of the predictors, because the weights assigned to the predictors may vary and probably will vary from dependent variable to dependent variable. As explained above, once both sets of data have been factor analyzed, the most effective way of answering the basic research question is to apply the technique of canonical correlation.

³⁷ In connection with this variable, it should be understood that Alliance was coded as 3 = U.S.S.R. ally, 2 = neutral, and 1 = U.S. ally. Thus, there is a tendency for U.S.S.R. allies to be among the most “Eastern” voting states, neutrals to be more “Eastern” than U.S. allies, and U.S. allies to be the least “Eastern” in their voting patterns. In this connection, the vast majority of variables are not either/or propositions. For example, considering the censorship variable, those with the most censorship tend to be the most “Eastern” voting states. However, the censorship variable expresses four gradations of censorship from complete censorship to cases where censorship is internally and externally absent.

³⁸ The most salient points of the analysis may be summarized as follows: The principal component solution was employed. Unities were placed in the principal diagonal of the correlation matrix and the factor matrix was rotated using Kaiser's varimax criterion. The minimum eigenvalue for which a factor was rotated was 1.0.

The “column sum square” gives the total variance explained in the variables by any particular factor, remembering there are as many units of variance as there are variables, and the “row sum square” gives the variance explained in any one variable by the factors taken collectively. Thus, the first factor explains 17.28 units, of the 77 units of variance, while variable 1 is 86% “explained” by the factors calculated.

³⁹ One should be careful not to confuse the factor names with the really crucial aspects of the analysis. That is, regardless of what name is given to a factor dimension, using the techniques employed here, the factor scores predict all of the variables to the extent of their loadings. Thus, with the exception of a .00 correlation, each variable has some predictive power relative to any particular factor dimension and every factor dimension has some predictive power relative to each variable. Names, then, in descriptive usage are simply convenient labels to describe the heaviest loading variables.

⁴⁰ See footnote 18 for a complete definition of this formula.

⁴¹ The exact probability is even less than this. The .93 correlation produced a Chi-square of 349 with 56 degrees of freedom. The probability in this case is so small as to exceed printout (10 places) capacity on the program used. However, even a third of this Chi-square produces a probability of less than 47 chances out of one million. In this connection the probability statement assesses the likelihood of getting a correlation of a particular magnitude (in this case .93) if we had begun with random numbers in the two sets of variables. This use of the test of significance is distinct from its use in connection with “sampling variability” where the characteristics of a “universe” are estimated from a sample. That is, from one perspective, we are dealing with a universe in this study and the correlations are descriptive. It is of interest, however, to compare the observed correlation with the probability of getting it if we had started with random numbers.

⁴² There are, of course, many ways of weighting the variables in the sets to produce correlations smaller than the maximal correlation. If this is done, the weights are usually assigned under the restriction that each new set of canonical variate scores, generated from a particular set, be orthogonal to all other canonical variate scores generated from that set. Operating under these restrictions, the second largest possible canonical correlation is .86. In this case, Economic Development receives a weight of −.34, Democracy .50, U.S. Relations .42, and Bigness, −.36, with the remaining variables (independent) not weighted at all. On the dependent side, Eastern voting receives a weight of −.43 and Northern voting .88, with very little weight given to the remaining variables. Similarly, operating under the same restraints, still another pattern of weights can be assigned to generate a correlation of .62. In this connection, a number of such canonical correlations can be “statistically significant.” In this study, of course, a decision was made to focus attention upon and interpret the largest correlation, although, in some studies, it may be desirable to interpret several correlations.

⁴³ The judges were 28 upper division students at Florida Atlantic University who had just completed a course focusing on the United Nations.

⁴⁴ The ratio of “positive” to “negative” votes, as evaluated by the judges, is approximately 2 to 1 in the case of the “Eastern” voting dimension (when the votes are “Eastern”) evaluating all votes loading ±.50 or above (59 votes, 39 “positive”) while the “Southern” voting dimension is “pure” with all 10 votes, loading ±.50 or above, being viewed by the judges as evidencing a “positive tendency,” when the votes are “Southern.” If the judges' responses are evaluated by the loadings (±.50 or above), viewing Eastern and Southern votes as “correct answers” and Western and Northern votes as “incorrect answers” and votes on loadings below ±.50 as “irrelevant,” Kuder-Richardson Formula 20 shows a reliability of .78 for the “test” If the judges' most popular categories (positive, negative or neutral) are viewed as providing the “correct answers” and the judges' responses are then evaluated, Kuder-Richardson Formula 20 shows a reliability of .83 for the “test.”

⁴⁵ See: Sawyer, Jack, “Dimensions of Nations: Size, Wealth and Politics,” The American Journal of Sociology, 73 (1967), pp. 145–172 CrossRefGoogle Scholar.

⁴⁶ Because both sets of variables (attribute and voting) are internally uncorrelated, the simple correlations of the attribute measures with any voting measure are equal to beta weights in a multiple correlation (of such variables with the voting measure) and the sum of the simple correlations squared equal R² . See Vincent, Factor Analysis in International Relations … op. cit. Strictly speaking the “fit” ought to be evaluated in such terms because, although the attribute theory formula allows weights and linear combinations on the “attribute side,” it does not make such an allowance on the “behavior side,” and, of course, weights and linear combinations do occur on both sides, in the application of the canonical model. The section dealing with the simple correlation of the factor scores, then, if this limitation is imposed, can be viewed as evidence for the above statement.