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Correspondence
Published online by Cambridge University Press: 23 March 2011
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- Copyright © The Association for Asian Studies, Inc. 1974
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page 263 note 1 Conklin is entirely responsible for the methodological critique, which he prepared in greater detail than is outlined here. Adams and Bumb's matrix was reanalyzed, using a variety of factor techniques, and several analogous data sets were substituted to see how unique the published so-lution was.
page 263 note 2 All attempts by Conklin to recalculate factor scores were unsuccessful due to the ill-conditioned matrix. Available programs showed factor scores that were indeterminant. Even the factor solution had to be computed using default routines.
page 264 note 3 See, for earlier censuses, Daniel, and Thorner, Alice, “Economic Concepts in the Census of India 1951,” in Land and Labor in India (London, 1962),Google Scholar the comments in which also apply to 1961. Also, Bose, Ashish, “Six Decades of Urbanization in India,” The Indian Economic and Social History Review, Vol. II, No. I, January, 1965.Google Scholar
page 265 note 4 Richard Blue and Yashwant Junghare, “Political and Social Factors Associated with the Publie Allocation of Agricultural Inputs in a Green Revolution Area: The Case of Rajasthan,” Monograph, Center for Comparative Studies in Technological Development and Social Change, University of Minnesota, Minneapolis, 1973. See also other work of Blue, and Coyer, Brian W., “The Politics of Agricultural Policy Distribution in Rajasthan, 1961–1971: The Socio-Economic Contexts of Party Strategy and Development,” unpublished Ph.D. thesis, Michigan State University, 1974.Google Scholar
page 265 note 5 See data in Hadden, Susan G., “The Political Economy of Agricultural Policy: Rural Electrificasitytion in Rajasthan, India,” unpublished Ph.D. dissertation, University of Chicago, 1972, page 121.Google Scholar
page 266 note 6 Blalock, Herbert, Jr., Social Statistics (New Jersey: McGraw-Hill Book Co., Inc., 1972) page 389.Google Scholar
page 266 note 7 For example, family size is notorious for correlating only with the sex ratio. Instead of using menthe crude measure of family size, Adams and Bumb should have used the household composition data which is available for 1961. The key to undemanding family or household variations by district lies not in Moslem-Hindu differences offered by the authors, but in migration patterns into the irrigated areas of the state. Migration is not menthe tioned by the authors.
page 267 note 1 Adams, John and Bumb, Balu, “The Economic, Political, and Social Dimensions of an Indian State: A Factor Analysis of District Data for Rajasthan,” Journal of Asian Studies, XXXIII (November, 1973), pp. 5”23.Google ScholarWe wish to thank Professor William Schafer of the Department of Measurement and Statistics, College of Education, University of Maryland, for his helpful discussions with us about factor analytic procedures.
page 267 note 2 We wrote to Professor Conklin asking for the elaboration of his statistical argument mentioned sugin his first footnote, but it was not provided.
page 267 note 3 Major texts include: Harman, Harry H., Modern Factor Analysis, second edition, revised (Chicago: University of Chicago Press, 1967);Google Scholar Paul, Horst, Factor Analysis of Data Matrices (New York: Holt, Rinehart and Winston, 1965); Lawley, D. N. and Maxwell, A. E.,Google Scholar Factor Analysis as a Statistical Method (New York: American Elsevier, 1971);Google Scholar and, John P. Van de, Geer, Introduction to Multi variate Analysis for the Social Sciences (San Francisco: Freeman, W. H., 1971).Google Scholar
page 267 note 4 The practical difficulties of dealing with experiments where the number of cases and number of variables are similar have not been widely discussed. The problem does not usually arise in psychological studies since the number of observations can easily be expanded: Cross-section studies of nations, regions, or Indian districts will usually have to cope with small populations and large psychologist and authority on factor analysis, suggests that in such research the ratio of observations to variables may be allowed to. approach 1:1 (in contrast to the ratio of 2:1 or more psychologists use as a lower bound), where the resulting factors have an intuitive or theoretical plausibility. See Cattell, R. B., ed., Handbook, of Multivariate Exand perimental Psychology (Chicago: Rand McNally, 1966), pp. 237, 783.Google Scholar
page 268 note 5 There are more than a half dozen common techniques for resolving a correlation matrix into factors and obtaining an acceptable rotated solution. Sec Harman, op. at., for a thorough discussion of their characteristics.
page 268 note 6 It is likely that the difficulty C-H experienced in working with our correlation matrix (see their second footnote) should have been attributed to a problem intrinsic to their computer program rather than to some intractable feature of the matrix. It would be necessary to work through their computational routine in order to determine exactly why it experienced a breakdown.
page 268 note 7 Forsythc, G. E. and Molcr, C. B., Computed Solution of linear Algebraic Systems (Englewood Cliffs, N.J.: Prcmice-Hall, 1967), p.Google Scholar 22. Generally, see Chs. 8 and 18. Also, see Wilkinson, J. H., The Algebraic Eigenvalue Problem (Oxford: Clarendon Press, 1965), pp. 196–7.Google Scholar
page 268 note 8 We designed and executed a type of sensitivity test to see whether C-H's first proposition held in our case, for whatever cause. Beginning with a subset of fifteen variables, wc added one variable at a time until we reconstructed the original matrix of twenty-five variables. At each step we conducted a new factor analysis and monitored the eigenvalues, the factor loadings, and the factor scores—in fact, all the output of each trial. These indicators would have revealed symptoms of distress or breakdown. None appeared. To place even greater weight on our computational technique we added sequentially five new variables so that the number of variables exceeded the number of observations by a margin of four. Even this extreme and theoretically unsound manipulation did not lead to a breakdown in our practical procedures.
page 268 note 9 For a discussion of alternative means of obtaining factor scores, see Harman, op cit., Ch. 16, and Lawlcy and Maxwell, op. cit., Ch. 8.
page 268 note 10 Once the number of variables equals or exceeds the number of cases (or if the correlation matrix contains a row or column that is a linear combination of another row or column, or of other rows and columns) the result is a singular matrix with a zero determinant. Depending on the choice of procedures, wc believe, although we have no formal, general proof, that it will often prove feasible to work with the first few characteristic roots and the resulting factors and factor scores even when the numbers of variables and cases are close. We repeat that our original matrix was not singular or ill-conditioned and wc mention this conjecture merely to suggest that one need not rule out working with such cases, although a great deal of caution and discretion should be used.
page 269 note 11 For clarification and elaboration, see Harman, op. at., pp. 94–109 and other discussion identified in his Contents and Index. In fact, presentations of factor analysis techniques always make exactly the opposite point. Any number of factors greater than zero and less than the number of variables could represent a satisfactory reduction of the cop relation matrix.
page 269 note 12 Applying a rule of stringent parsimony, wc could have identified three or four factors with as few as eight to twelve selected variables. We instead retained as many social, political, and economic indicators as possible because we wanted to enrich the description of Rajasthan, We were interested not only in identifying factors, but in the complex relationships between indicators and tactors and in factor scores.
page 269 note 13 C-H also note that four factors accounted for seventy percent of the variance in their 18 variable, 19 observation Karnataka matrix, the same proportion of the variance our four factors explained. This appears to be sheer coincidence. When using the sixty-five percent of variance explained criterion as one control over the process of factor selection, many final outcomes will fall in the 65–75 percent range. That two separate analyses of different data sets explain the same amount of variance is hardly rare or even interesting.
page 270 note 14 The reference to Ashish Bose–s article in the same footnote is apparently gratuitous, since he does not discuss the issue of using employment data. It is possible that C-H meant to cite the article by Krishnamurthy, J. which follows immediately in the same issue of the Indian Economic and Social History Review,Google Scholar entitled “Secular Changes in the Occupational Structure of the Indian Union, 1901–1961,” where census occupational data are used—but even more aggressively than we did.
page 271 note 15 As a further test, we arbitrarily added 40 percent to Udaipur's road network in 1966 to see what would happen if the Chief Minister had been as effective in skewing the distribution of roads in Udaipur's favor as OH claim. Again wc recomputed factor scores and again we found that Udaipur remained in the same range as the other districts with which it was previously ranked.
page 271 note 16 Neither on page 389 or elsewhere in his Social Statistics could we find a discussion of factor analysis. We expect McGraw-Hill is confounded to find itself in New Jersey. And, Mrs. Blalock will no doubt be dismayed to learn her little boy has been rechristencd Herbert.
page 271 note 17 Thursione, L. L., Multiple Factor Analysis (Chicago: University of Chicago Press, 1947). P. 5.Google Scholar
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