Bayesian analysis of discrete time warranty data

Summary.  The analysis of warranty claim data, and their use for prediction, has been a topic of active research in recent years. Field data comprising numbers of units returned under guarantee are examined, covering both situations in which the ages of the failed units are known and in which they are not. The latter case poses particular computational problems for likelihood-based methods because of the large number of feasible failure patterns that must be included as contributions to the likelihood function. For prediction of future warranty exposure, which is of central concern to the manufacturer, the Bayesian approach is adopted. For this, Markov chain Monte Carlo methodology is developed.     

A Multivariate Model for Repeated Failure Time Measurements

A parametric multivariate failure time distribution is derived from a frailty-type model with a particular frailty distribution. It covers as special cases certain distributions which have been used for multivariate survival data in recent years. Some properties of the distribution are derived: its marginal and conditional distributions lie within the parametric family, and association between the component variates can be positive or, to a limited extent, negative. The simple closed form of the survivor function is useful for right-censored data, as occur commonly in survival analysis, and for calculating uniform residuals. Also featured is the distribution of ratios of paired failure times. The model is applied to data from the literature     

Influence of Proximity to Kin on Residential Mobility and Destination Choice: Examining Local Movers in Metropolitan Areas

A growing body of research has examined how family dynamics shape residential mobility, highlighting the social—as opposed to economic—drivers of mobility. However, few studies have examined kin ties as both push and pull factors in mobility processes or revealed how the influence of kin ties on mobility varies across sociodemographic groups. Using data on local residential moves from the Panel Study of Income Dynamics (PSID) from 1980 to 2013, we find that location of noncoresident kin influences the likelihood of moving out of the current neighborhood and the selection of a new destination neighborhood. Analyses of out-mobility reveal that parents and young adult children living near each other as well as low-income adult children living near parents are especially deterred from moving. Discrete-choice models of neighborhood selection indicate that movers are particularly drawn to neighborhoods close to aging parents, white and higher-income households tend to move close to parents and children, and lower-income households tend to move close to extended family. Our results highlight the social and economic trade-offs that households face when making residential mobility decisions, which have important implications for broader patterns of inequality in residential attainment.     

Metropolitan Heterogeneity and Minority Neighborhood Attainment: Spatial Assimilation or Place Stratification?

Using geo-referenced data from the Panel Study of Income Dynamics, in conjunction with decennial census data, this research examines metropolitan-area variation in the ability of residentially mobile blacks, Hispanics, and whites to convert their income into two types of neighborhood outcomes-neighborhood racial composition and neighborhood socioeconomic status. For destination tract racial composition, we find strong and near-universal support for the "weak version" of place stratification theory; relative to whites, the effect of individual income on the percent of the destination tract population that is non-Hispanic white is stronger for blacks and Hispanics, but even the highest earning minority group members move to tracts that are "less white" than the tracts that the highest-earning whites move to. In contrast, for moves into neighborhoods characterized by higher levels of average family income, we find substantial heterogeneity across metropolitan areas in minorities' capacity to convert income into neighborhood quality. A slight majority of metropolitan areas evince support for the "strong version" of place stratification theory, in which blacks and Hispanics are less able than whites to convert income into neighborhood socioeconomic status. However, a nontrivial number of metropolitan areas also evince support for spatial assimilation theory, where the highest-earning minorities achieve neighborhood parity with the highest-earning whites. Several metropolitan-area characteristics, including residential segregation, racial and ethnic composition, immigrant population size, poverty rates, and municipal fragmentation, emerge as significant predictors of minority-white differences in neighborhood attainment.     

Models and estimation for systems with recurrent events and usage processes

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.     

Residential segregation of West Indians in the New York/New Jersey metropolitan area: the roles of race and ethnicity

"To assess the relative roles of race and ethnicity in shaping patterns of residential segregation, this article utilizes indices of segregation and a geographic mapping strategy to examine the residential patterns of West Indian blacks in the greater New York City area. The socioeconomic characteristics of neighborhoods occupied by West Indian blacks are also examined and compared to those of areas occupied by African Americans. The results indicate that, on one hand, West Indians are largely denied access to residential areas occupied predominantly by whites and are confined to areas of large black concentrations. On the other hand, West Indians appear to have carved out somewhat separate residential enclaves within these largely black areas...."     

Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure

The gamma process is a natural model for degradation processes in which deterioration is supposed to take place gradually over time in a sequence of tiny increments. When units or individuals are observed over time it is often apparent that they degrade at different rates, even though no differences in treatment or environment are present. Thus, in applying gamma-process models to such data, it is necessary to allow for such unexplained differences. In the present paper this is accomplished by constructing a tractable gamma-process model incorporating a random effect. The model is fitted to some data on crack growth and corresponding goodness-of-fit tests are carried out. Prediction calculations for failure times defined in terms of degradation level passages are developed and illustrated.     

Metropolitan influences on migration into poor and nonpoor neighborhoods

Data from the Panel Study of Income Dynamics and three decennial US censuses are used to examine the influence of metropolitan-area characteristics on black and white households’ propensity to move into poor versus nonpoor neighborhoods. We find that a nontrivial portion of the variance in the odds of moving to a poor rather to a nonpoor neighborhood exists between metropolitan areas. Net of established individual-level predictors of inter-neighborhood migration, black and white households are more likely to move to a poor or extremely poor tract rather than to a nonpoor tract in metropolitan areas containing many poor neighborhoods and a paucity of recently-built housing in nonpoor areas. Blacks are especially likely to move to a poor tract in metropolitan areas characterized by high levels of racial residential segregation and in which poor tracts have a sizeable concentration of blacks. White households are more likely to move to a poor than to a nonpoor tract in metropolitan areas that have comparatively few African Americans.