Modeling social interaction: Marital miscegenation in colonial Spanish America

NOTES

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• Nevertheless , B. Rimland . 1971 . “The Differentiation of Childhood Psychoses: An Analysis of Checklists of 2,218 Psychotic Children,” . Journal of Autism and Childhood Schizophrenia , 1 : 161 – 74 . The lower bound of Kappa is variable and determined by the marginals. This has not been discussed in the psychometric literature, perhaps because diagnosticians tend to agree much more than they disagree, in a study of 456 autistic children found more relative disagreement than agreement in seven of eight most commonly diagnosed behavior disorders. The minimum Kappa computed for these data is – .19, suggesting only modest disagreement. However, adjusting the index as a proportion of its arithmetical lower limit produces a picture of shockingly large disagreements. The figures go beyond – .50 in all instances except one. In social history where marital exogamy, social mobility, or status disinheritance (i.e., greater concentrations of counts in the off-diagonal cells) is of central concern, a variable lower bound is undesirable. An unfortunate effect of the statistical features of Kappa is to rivet attention on the main diagonal while valuable off-diagonal information is ignored. Strauss' conclusion (p. 203) that “K values can be usefully compared for societies with different numbers of groups” seems to overlook the very contingent nature of the measure. Many years ago, L. A. Goodman and G. H. Kruskal (“Measures of Association for Cross-Classification,” Journal of American Statistical Association 49 [1954]: 738) noted that the need for norming a measure diminishes as its interpretability and meaningfulness increases
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• Goodman . “How to Ransack,” 27 – 34 .
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• Bishop , Fienberg and Holland . Discrete Multivariate Analysis 180 Ibid., p. 30–34
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• Goodman , L. A. “Some Multiplicative Models for the Analysis of Cross-Classified Data,” . Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability . Edited by: Le Cam , L. vol. 1 , pp. 649 – 96 . Berkeley
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• Cook and Borah . Essays , vol. 2 257 A lack of space prevents reanalysis of their data here
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• Bishop , Fienberg and Holland . Discrete Multivariate Analysis 49 – 55 . For a discussion of geometrical presentation of log-linear models
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• Goodman , Leo A. 1979 . “Simple Models for the Analysis of Association in Cross–Classifications Having Ordered Categories,” . Journal of American Statistical Association , 74 : 537 – 52 . Otis Dudley Duncan, “How Destination Depends upon Origin in the Occupational Mobility Table,” American Journal of Sociology 84 (1979): 793–803; Leo A. Goodman, “Multiplicative Models for the Analysis of Occupational Mobility Tables and Other Kinds of CrossClassification Tables,” American Journal of Sociology 84 1979. 804-19
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• Bishop , Fienberg and Holland . Discrete Multivariate Analysis 281 – 309 . Goodman, “Simple Models,” pp. 544, 550, notes that the quasi-symmetry model is equivalent to the Symmetrie association model
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• Goodman . “Some Multiplicative Models,”. ” . In Discrete Multivariate Analysis 656 – 63 . 320 – 22 . Bishop, Fienberg, and Holland. .
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• Featherman , David and Hauser , Robert . 1978 . Opportunity and Change 147 – 59 . New York Goodman, “Some Multiplicative Models,” p. 656
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• Featherman and Hauser . Opportunity and Change 151
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• Dixon , W. J. , ed. 1977 . BMDP-77 Biomedical Computer Programs P-Series 278 ff Los Angeles The observed counts for all data analyzed here have been adjusted with a pseudo-Bayesian smoothing algorithm programmed according to suggestions by Bishop, Fienberg, and Holland (Discrete Multivariate Analysis, pp. 401–33) using expressions 12–1-2,12–7-3,18 and 20. Model fitting programs are not at present generally available. SPSS log-linear procedures are of a single type (independence) and are not as elegant as other SPSS sub-packages. BMD models are limited to independence and quasi-independence but are much more flexible, Goodman's ECTA program was unavailable. Instead, a specially designed program was developed to generate maximum likelihood estimates (by iterative proportional fitting), goodness of fit statistics, and interaction parameters. The program permits specification of any user-determined design matrix and configuration of blanked-out cells as well as selecting models to be fit and detail of statistical output
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• Goodman . “Some Multiplicative Models,” 675 679 “Simple Models,” p. 540; Bishop, Fienberg, and Holland, Discrete Multivariate Analysis, p. 209
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• Ibid., p. 168. The model fitting strategy involved four stages as data came to my attention: (1) exploratory: Leon, 1782; (2) confirmatory: Leon, Antequera, Chilean parishes; (3) confirmatory and adjustment: Parral; and (4) confirmatory: remaining northern parishes
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• Bishop , Fienberg and Holland . Discrete Multivariate Analysis 324
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• Brading and Wu . “Population Growth,” 8 – 9 . Differences by sex may in effect be real and even substantively significant, but they are also statistically small. According to the law of small numbers, “events with low frequency in a large population can be fitted by a Poisson distribution even when the probability of an event varies somewhat among the strata of a population” (Bishop, Fienberg and Holland, Discrete Multivariate Analysis, p. 327). In other words, tiny differences may be real; their substantive significance may or may not be small
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• Just as we should not be surprised to find two bivariate displays with similar marginals and different joint interaction structures, tables with different marginal structures can have similar patterns of interaction
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• Chance . Race and Class note on pp. 128–29; Morner (Race Mixture, p. 20) characterizes the conventional ordering. Goodman (“Simple Models,” pp. 547–48) describes the process of selecting a statistically optimal ordering and the collapsing of categories
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• Sharlin , Allan . 1979 . “From the Study of Social Mobility to the Study of Society,” . American Journal of Sociology , 85 : 351 – 56 . in his study of nineteenth-century Frankfurt shopkeepers persuasively argues their ambiguous social status. Model fitting of father-son intergenerational occupational mobility confirms his impressions. Sharlin's emphasis on the multidimensionality of the social structure and the ambiguity of shopkeepers' status is revealed in the QS interaction ratios (G2 = 21.6, df = 19, P> .30). Most shopkeepers' sons did not succeed to their fathers' occupation (0.9 ×) but scattered amongst merchants (1.0 ×), Professionals (0.8 ×), the trades (1.1 ×), and non-guild occupations (1.3 ×). Artisans rank below shopkeepers because of their comparatively lower interaction with merchants and Professionals (0.5 ×). Both shopkeepers and clerks seem to have been a transitional group between the upper and working classes. Sharlin's doubly standardized percentages indicate general order of magnitude but are sometimes misleading on the relative degree of social in heritance and magnitude of social mobility between particular groups. For shopkeepers' sons, his figures suggest that the greatest tendency is toward status inheritance (26 percent) followed by a movement into non-guild and artisanal occupations (21 percent), commerce (19 percent), and the professions (14 percent). QS effects parameters indicate slight status disinheritance and a very narrow spread of interactions (0.8–1.3 ×). The indicators are weakly correlated (r = .38). Sharlin's preferred ordering—merchants, Professionals, artisans, shopkeepers, and non-guild workers—is not supported by the best fitting log-linear models of occupational mobility. The optimal ordering is shopkeepers above artisans (Model = CA', ⊖ = 1.2, G2 = 3.4, df = 6, P> .70; versus G2 = 25.4, P< .001 for his preferred ordering)
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• Swann . “Spatial Dimensions,” 152 – 53 . 160 165 – 66 . Robinson, “Population Patterns,” pp. 89–90; Chance and Taylor, “Estate and Class,” p. 479. Cook and Borah (Essays, vol. 2, pp. 248–49) are an exception. By accepting the QS model, I chose to attribute the differences by gender to random variations and differing group sizes
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• McAlister , Lyle N. 1963 . “Social Structure and Social Change in New Spain,” . Hispanic American Historical Review , 43 : 421 – 48 . argues that the socioracial structure consisted of three groups: Spaniards, Indians, and mixed. Morner's argument (Race Mixture, p. 60) that “the distinction between Mestizos on the one hand, and on the other free Negros, Mulattoes and Zambos is far too important to be ignored” is supported by the marriage patterns analyzed here, except for Antequera and Petorca., On the basis of literary evidence
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• Brading and Wu . “Population Growth” Swann (“Spatial Dimensions,” p. 160) compares spatial differences and attributes them to temporal trends
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• Grubessich , Arturo . 1978 . “Social History of a Colonial Hispanic American City: Valparaiso [Chile] During the Last Quarter of the 18th Century,” , M. A. thesis 63 – 68 . University of Minnesota. . notes that socio-racial declarations at marriage substantially understate the degree of miscegenation
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• Chance . Race and Class 144 – 51 . For a discussion of Antequera's society and economy, If the statistics reported here contradict measures used in our earlier critique of Chance and Taylor's thesis, they support our conclusion on the persisting importance of race as a principle of social stratification in colonial Spanish America. We were misled by our reliance on the poorly fitting simple independence model (McCaa, Schwartz, and Grubessich, “Race and Class,” pp. 424–28). The QS ratios indicate that even in Antequera at the end of the colonial era, choice of marriage Partners was strongly affected by racial considerations. If endogamic propensities were relatively weak for Mestizos and Blacks, they remained quite strong for Spaniards and Indians, declining by only about one-third in a Century. If exogamic preferences were weaker than in the seventeenth Century (a 10 percent decline over a Century), they continue to show the ordered pattern characteristic of more rigid social structures of northern New Spain. If commercial capitalism affected Antequera's marriage patterns, it seems to have done so a Century earlier than Chance and Taylor argue. Already by the end of the seventeenth Century, Antequera had a more open marriage market than any other community studied here
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• Morner . Race Mixture 53
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• Morner , M. 1974 . “Raza y estratificacion social de hispanoamérica hacia 1800,” . In Ibero-Americanax (Latinamerika-Institutet I Stockholm)“Raza y estratificacion social de hispanoamérica hacia 1800,” Vol. 4 , 23 (My translation.)
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• Duncan . “How Destination Depends,” 801 – 2 . notes that finer gradations of categories increase the analytical power of log-linear models. Reynolds H. T. (“Some Comments on the Causal Analysis of Surveys with Log-Linear Models,” American Journal of Sociology 83 [1977]: 127–43) offers a much more general critique than implied by the title
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