The residential distribution of status groups in Puerto Rico’s metropolitan areas

The purpose of this paper is to investigate the pattern of residential segregation of status groups in Puerto Rico’s three metropolitan areas. The findings showed that in all three areas: (1) as the social status distance between groups increases so too does the degree of dissimilarity of their residential distributions; (2) the status groups most residentially segregated are those at the top and at the bottom of the status pyramid; (3) the pattern of residential centralization of status groups for Ponce and Mayaguez are such that the highest status groups are the most centralized while the lowest status groups are the most decentralized, but in San Juan it is the highest status groups that are the most decentralized and the lowest status groups that are the most centralized. The data are from the 1960 census. Indicators of status employed are education, occupation, and income. Differences in findings about centralization between San Juan and the other cities are explained in terms of differential economic development.     

Bounds on minimum mean squared error in ridge regression

The minimum MSE (mean squared error) of ridge regression coefficient estimates (for a given set of eigenvalues and variance) is a function of the transformed coefficient vector. In this paper, the authors prove that the minimum MSE is bounded, for a given coefficient vector length, by the two cases corresponding to the signal completely contained in the component associated with the smallest or largest eigenvalue. The implication for evaluating proposed estimators of the ridge regression biasing parameter is discussed.     

The expansion of religious affiliation: An explanation of the growth of church participation in the United States 1850–1930

This paper focuses on the period in U.S. history that experienced the most rapid rate of increase of church membership—the decades between 1850 and 1930—in order to explain synchronic and diachronic variation in those rates. Using pooled cross-sectional time series analysis, different predictions are derived and tested from theories of secularization/social control, comparative disadvantage, resource mobilization, and pluralism. The effects of spatial diffusion and the momentum of religious tradition also are estimated. Our conclusion is that religious monopoly—not diversity—fuels religious expansion. This finding is bolstered by the complementary result that ethnic homogeneity is also conducive to religious expansion. Together these results highlight the importance for mobilization of religious and ethnocultural dominance in a particular niche.     

MULTIVARIATE NORMALITY AND A BOND RATING DECISION MODEL*

An assumption of multivariate normality for a decision model is validated in this paper. Measurements for the independent variables of a bond rating model were taken from a sample of municipal bonds. Three methods for examining both univariate and multivariate normality (including normal probability plots) are described and applied to the bond data. The results imply, after applying normalizing transformations to four of the variables, that the data reasonably approximate multivariate normality, thereby validating a distributional requirement of the discriminant-analysis-based decision model. The methods described in the paper may also be used by others interested in examining multivariate normality assumptions of decision models.