Failure Inference From a Marker Process Based on a Bivariate Wiener Model

Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.     

Metropolitan Structure and Neighborhood Attainment: Exploring Intermetropolitan Variation in Racial Residential Segregation

Using data from the 1981, 1991, and 2001 waves of the Panel Study of Income Dynamics and several decennial censuses, we examine how characteristics of metropolitan areas are associated with black and white households’ neighborhood racial composition. Results from hierarchical linear models show that about 20% to 40% of the variation in the percentage of households’ tract population that is non-Hispanic white or non-Hispanic black exists across metropolitan areas. Over time, white households’ exposure to non-Hispanic white neighbors has declined, and their exposure to non-Hispanic black neighbors has increased; the reverse trends are observed for blacks. These trends cannot be attributed to changes in the ecological structure of metropolitan areas. Blacks have fewer white neighbors in large metropolitan areas containing sizable minority populations, and blacks have more white neighbors in metropolitan areas with high government employment. Whites have more black neighbors in metropolitan areas with high levels of government employment and ample new housing; whites have fewer black neighbors in metropolitan areas with a high level of municipal fragmentation. The association between metropolitan-area percentage black and tract percentage black is weaker among whites than among blacks, suggesting that whites are especially motivated to self-segregate in metropolitan areas with large black populations.     

Race,gender, and marriage: destination selection during the great migration

Using historical census microdata, we present a unique analysis of racial and gender disparities in destination selection and an exploration of hypotheses regarding tied migration in the historical context of the Great Migration. Black migrants were more likely to move to metropolitan areas and central cities throughout the period, while white migrants were more likely to locate in nonmetropolitan and farm destinations. Gender differences were largely dependent on marital status. Consistent with the "tied-migration" thesis, married women had destination outcomes that were similar to those of men, whereas single women had a greater propensity to reside in metropolitan locations where economic opportunities for women were more plentiful.     

The Changing Demography of America's Families

We use data from a variety of sources to describe recent dramatic changes in the composition, economic stability, and diversity of American families. The declining prevalence of early marriage, increasing level of marital dissolution, and growing tendency to never marry, especially among some racial and ethnic groups, reflect changes in the relative economic prospects of men and women and support the conclusion that marriage is becoming less valued as a source of economic stability. These developments also imply that relatively more children are born outside of marriage, spend at least part of their childhood in a single‐parent household, and endure multiple changes in family composition. Paralleling these trends have been sharp changes in the economic stability of families, characterized most notably by a growing importance of women's income and increasing economic inequality among American families.     

A Score Test for the Multivariate Burr and Other Weibull Mixture Distributions

The p -variate Burr distribution has been derived, developed, discussed and deployed by various authors. In this paper a score statistic for testing independence of the components, equivalent to testing for p independent Weibull against a p -variate Burr alternative, is obtained. Its null and non-null properties are investigated with and without nuisance parameters and including the possibility of censoring. Two applications to real data are described. The test is also discussed in the context of other Weibull mixture models.     

Analysis of fracture toughness data

In studies of the fracture toughness of irradiated weld metal, specimens are subjected to an increasing load. The test on any one specimen might be terminated by choice or because the specimen ruptures. Prior to termination, ductile tearing might or might not have occurred. The situation is thus basically one of competing risks, with different types of termination, but there are additional features. The major purpose of statistical analysis is to estimate probabilities concerning the values of toughness and crack length. The analysis has been based on a model developed for the joint survivor function of these quantities.     

On repeated measures analysis with misspecified covariance structure

In recent years various sophisticated methods have been developed for the analysis of repeated measures, or longitudinal data. The more traditional approach, based on a normal likelihood function, has been shown to be unsatisfactory, in the sense of yielding asymptotically biased estimates when the covariance structure is misspecified. More recent methodology, based on generalized linear models and quasi-likelihood estimation, has gained widespread acceptance as 'generalized estimating equations'. However, this also has theoretical problems. In this paper a suggestion is made for improving the asymptotic behaviour of estimators by using the older approach, implemented via Gaussian estimation. The resulting estimating equations include the quasi-score function as one component, so the methodology proposed can be viewed as a combination of Gaussian estimation and generalized estimating equations which has a firmer asymptotic basis than either alone has.     

Extended-family resources and racial inequality in the transition to homeownership

We use longitudinal data from the Panel Study of Income Dynamics to examine how access to financial resources in the extended family affects the accumulation of wealth among non-owners and how these resources subsequently affect transitioning into homeownership. Our findings show that economic conditions of the extended family have substantial effects on non-owners’ wealth accumulation and likelihood of becoming homeowners, even after adjusting for individual sociodemographic and economic characteristics. We find significant effects of extended-family wealth for both black and white households, but effects of extended-family income insufficiency for blacks only. Consequently, limited access to wealth and greater level of poverty in the extended family hamper blacks’ transition to homeownership. Our results show that the level of extended-family wealth necessary for black householders to equalize their likelihood of becoming homeowners with whites is very high. In fact, our findings indicate that white householders embedded in extended families with no net wealth are just as likely to make the transition to ownership as are black householders with affluent extended families. These findings support arguments related to the importance of extended-family resources in processes of residential attainment but also point to important racial differences in not only levels but also consequences of these family resources.     

Corrected p-values for tests based on estimated nuisance parameters

In some situations the asymptotic distribution of a random function T _n() that depends on a nuisance parameter is tractable when has known value. In that case it can be used as a test statistic, if suitably constructed, for some hypothesis. However, in practice, often needs to be replaced by an estimator S _n. In this paper general results are given concerning the asymptotic distribution of T _n(S _n) that include special cases previously dealt with. In particular, some situations are covered where the usual likelihood theory is nonregular and extreme values are employed to construct estimators and test statistics.