This study demonstrates that the empirical literature on the structural covariates of homicide rates contains inconsistent findings across different time periods and different geographical units. This apparent variance of findings may be due to statistical or methodological artifacts of particular studies, such as different time periods covered, units of analysis, samples, model specifications, and problems of statistical analysis and inference. A baseline regression model using 11 structural covariates is estimated for cities, metropolitan areas, and states in 1960, 1970, and 1980. The empirical estimates of this model exhibit instability because of high levels of collinearity among several regressors. Principal components analysis is applied to simplify the dimensionality of the structural covariate space. Reestimation of the regression model then indicates that the apparent inconsistencies across time and social space are greatly reduced. The theoretical significance of the findings for substantive theories of violent crime are discussed. The past two decades have seen an upsurge in the number of empirical studies that address the question of why some cities, metropolitan areas, ' The research reported here was supported, in part, by National Science Foundation grant SES-8800595. We are grateful to five anonymous A J S referees for stimulating and useful comments on an earlier version of this paper. Requests for reprints should be sent to

This article addresses three issues that are central to the criminal career debate. First, is the life course of individual offending patterns marked by distinctive periods of quiescence? Second, at the level of the individual, do offending rates vary systematically with age? In particular, is the age‐crime curve single peaked or flat? Third, are chronic offenders different from less active offenders? Do offenders themselves differ in systematic ways? Using a new approach to the analysis of individual criminal careers—based on nested, mixed Poisson models in which the mixing distribution is estimated nonparametrically—we analyze a panel data set that tracks a sample of males for more than 20 years. Our results provide empirical evidence in support of some features of criminal propensity theory and some in support of conventional criminal careers theory. In support of latent‐trait criminal propensity theory, the individual‐level average offense rate (per unit of time) varies as a function of observable individual‐level characteristics and unobservable heterogeneity among individuals, and the age trajectory of the offense rate is generally single peaked rather than flat. On the other hand, in support of conventional criminal careers theory, models that incorporate a parameter that permits periods of active as well as inactive offending across age have greater explanatory power than those that do not. In addition, the nonparametric, discrete approximation to the population distribution of unobservable heterogeneity in the individual‐level mean offense rate facilitates identification of four classes of offenders—nonoffenders as well as individual‐level characteristics that are unique to each group. Problems of theoretical explanation and empirical generalizability of these results are described.

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A new approach to the statistical estimation of age-period-cohort (APC) accounting models, called the intrinsic estimator (IE), recently has been developed. This article (1) further describes the IE algebraically, geometrically, and verbally, (2) reviews properties of the IE as a statistical estimator, (3) provides model validation evidence for the IE both from an empirical example and from a simulation exercise, (4) relates the coefficients of the IE to those of conventional constrained APC models using formal definitions of statistical estimability, hypothesis testing, and empirical applications that directly address a criticism that often has been lodged at generalpurpose methods of APC analysis, and (5) introduces computer software for application of the IE that interested users can readily access. The authors conclude that the IE holds the potential for applications not only to APC analysis but also to similar problems of structural underidentification in sociology.

Age-period-cohort (APC) accounting models have long been objects of attention in statistical studies of human populations. It is well known that the identification problem created by the linear dependency of age, period, and cohort (Period ¼ Age þ Cohort or P ¼ A þ C) presents a major methodological challenge to APC analysis, a problem that has been widely addressed in demography, epidemiology, and statistics. This paper compares 75 parameter estimates and model fit statistics produced by two solutions to the identification problem in age-period-cohort models-namely, the conventional demographic approach of constrained generalized linear models Mason 1978, 1985;Mason and Smith 1985) and the intrinsic estimator method recently developed by Fu (2000;Knight and Fu 2000;Fu, Hall, and Rohan 2004). We report empirical analyses of applications of these two methods to population data on U.S. female mortality rates. Comparisons of parameter estimates suggest that both constrained generalized linear models and the intrinsic estimator method can yield similar estimates of age, period, and cohort effects, but estimates obtained by the intrinsic estimator are more direct and do not require prior information to select appropriate model identifying constraints. We also describe three statistical properties of the estimators: (1) finite-time-period bias, (2) relative statistical efficiency, and (3) consistency as the number of periods of observed data increases. These empirical analyses and theoretical results suggest that the intrinsic estimator may well provide a useful alternative to conventional methods for the APC analysis of demographic rates.

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OBJECTIVES:To compare how well frailty measures based on a phenotypic frailty approach proposed in the Cardiovascular Health Study (CHS) and a cumulative deficits approach predict mortality. DESIGN: Cohort study.Corresponding Author: A. Kulminski Center for Population Health and Aging, Duke University Trent Hall, Room 002, Box 90408, Durham, NC 27708. Fax: (919) 684-3861 E-mail: E-mail: Alexander.Kulminski@duke.edu. Alternate Corresponding Author: A. Yashin E-mail: E-mail: aiy@duke.edu. Author contributions: Drs. Kulminski and Yashin are responsible for study design, the accuracy of the analyses, and interpretation of the results. Drs. Kulminski, Ukraintseva, Kulminskaya, Arbeev, and Yashin take responsibility for the data integrity, and drafting the manuscript. Drs. Ukraintseva and Kulminskaya participated in elaboration of the phenotypic frailty and cumulative deficits indices. Dr. Kulminski was responsible for statistical analyses.Financial Disclosure: The research reported in this paper was supported by the grants 1R01 AG028259, 1R01-AG-027019 and 5P01-AG-008761 from the National Institute on Aging (NIA). Conflict of Interest MEASUREMENTS:A phenotypic frailty index (PFI) was defined in the same way as proposed in the CHS: assessing weight loss, exhaustion, low physical activity, slowness, and poor grip strength. A cumulative deficit index (DI) was defined based on 48 elderly deficits (signs, symptoms, impairments, diseases) included in the index, with equal weights. RESULTS:Of the 1,073 frailest individuals with the lowest survival, the PFI, categorized as proposed in the CHS into robust, prefrail, and frail categories, underestimated the risk of death for 720 persons, whereas the DI categorized into the same three frailty categories underestimated the mortality risk for 134 persons. The higher power of the DI for discriminating frail individuals in their susceptibility to death also followed from comparison of quasi-instantaneous values of both indices. The three-level DI identified 219 individuals as frail of 361 individuals identified as frail according to the three-level PFI. CONCLUSIONS:The DI can more precisely evaluate chances of death because it assesses a broader spectrum of disorders than the PFI. Both indices appear to be frailty related. Integration of both approaches is highly promising for increasing the precision of discrimination of the risk of death and especially for identification of the most vulnerable elderly people.