A note on the equality of the OLSE and the BLUE of the parametric function in the general Gauss–Markov model

In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the original Gauss–Markov model.      

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

Estimation of a relative potency of two preparations with correlated responses

Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new tuberculins with respect to some international standards tested in experiments on guinea-pigs.     

A re-evaluation of random-effects meta-analysis

Summary.  Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of 'set shifting' ability in people with eating disorders.     

Using relative utility curves to evaluate risk prediction

Summary.  Because many medical decisions are based on risk prediction models that are constructed from medical history and results of tests, the evaluation of these prediction models is important. This paper makes five contributions to this evaluation: the relative utility curve which gauges the potential for better prediction in terms of utilities, without the need for a reference level for one utility, while providing a sensitivity analysis for misspecification of utilities, the relevant region, which is the set of values of prediction performance that are consistent with the recommended treatment status in the absence of prediction, the test threshold, which is the minimum number of tests that would be traded for a true positive prediction in order for the expected utility to be non-negative, the evaluation of two-stage predictions that reduce test costs and connections between various measures of performance of prediction. An application involving the risk of cardiovascular disease is discussed.     

Automating and evaluating reversible jump MCMC proposal distributions

The reversible jump Markov chain Monte Carlo (MCMC) sampler (Green in Biometrika 82:711–732, 1995) has become an invaluable device for Bayesian practitioners. However, the primary difficulty with the sampler lies with the efficient construction of transitions between competing models of possibly differing dimensionality and interpretation. We propose the use of a marginal density estimator to construct between-model proposal distributions. This provides both a step towards black-box simulation for reversible jump samplers, and a tool to examine the utility of common between-model mapping strategies. We compare the performance of our approach to well established alternatives in both time series and mixture model examples.     

Bullying and Victimization Among Young Elementary School Children: The Role of Child Ethnicity and Ethnic School Composition

School-aged children with an ethnic minority background are relatively often involved in bullying and victimization, but the role of ethnic composition of schools in this context remains unclear. This study examined the relation between ethnic minority background, ethnic school composition, and bullying behaviour around primary school entry in the Netherlands. The study was based on a 2008/2009 school survey in Rotterdam, a Dutch city where about 50 % of children have a non-Dutch background. For 8523 children, teacher reports of bullying behaviour at age 5–6 years were available. Children with a non-Dutch background had higher odds of being a victim (adjusted OR 1.41, 95 % CI 1.11, 1.80), bully (OR 1.38, 95 % CI 1.20, 1.58) or bully-victim (OR 1.38, 95 % CI 1.19, 1.62) than children of Dutch national origin. Ethnic diversity in schools increased children’s risk of bullying behaviour (e.g. OR_victim per 0.1 increase in 0–1 diversity range = 1.06, 95 % CI 1.00, 1.13), with children of both Dutch and non-Dutch national origin relatively more often involved in bullying in ethnically diverse schools. The proportion of same-ethnic peers in school reduced the risk of bullying among children of Dutch national origin (e.g. OR_victim per 10 % more same-ethnic children = 0.90, 95 % CI 0.83, 0.98), but not among non-Dutch children. In conclusion, ethnic minority background and ethnic diversity within schools are risk factors for bullying among 5–6 year olds. Plausibly, reductions in absolute numbers of bullying events may be obtained with tailor-made interventions in ethnically diverse schools. Such interventions should preferably be offered early in the school curriculum.     

Wealth Inequality in Black and White: Cultural and Structural Sources of the Racial Wealth Gap

Using data from the 2013 Survey of Consumer Finances, this research examines competing and complementary cultural and structural explanations of the sources of racial differences in wealth. We use OLS regression and quantile regression to identify the major individual-level sources of wealth differences between African Americans and whites. Whites have more favorable wealth characteristics than do African Americans on all of the variables in the analysis: gender of household head, bankruptcies, spending patterns, stock ownership, business ownership, home ownership, inheritance, educational attainment, income, occupation, age, and number of children. Cultural factors, having a female-headed family, spending patterns, and inheritance account for little of the racial wealth gap. Racial differences in income, stock ownership, and business ownership account for much of the explained racial wealth gap. Moreover, compared with whites, African Americans receive significantly lower wealth returns to education, age, income, stock ownership, and business ownership. We discuss the implications of our findings.     

Variations in Citizenship Profiling by Generational Status: Individual and Neighborhood Characteristics of Latina/os Questioned by Law Enforcement About Their Legal Status

Although racial profiling is widely studied, the related issue of citizenship profiling by law enforcement has received little scholarly attention. In this study we begin to address citizenship profiling, which may be highly salient in light of the increasing policing of immigration in the United States through Secure Communities and other federal, state and local efforts to localize the enforcement of immigration laws. Using a sample of 563 Latina/o adults residing in 46 neighborhoods in El Paso County, Texas, USA, we assess the impacts of a variety of individual and neighborhood characteristics on the likelihood of being questioned about citizenship status by law enforcement. Results using hierarchical generalized linear models (HGLMs) show that, at the individual-level, first-generation Latina/o immigrants and second-Latina/os are more likely to be questioned about citizenship status than third- and later-generation Latina/os. At the neighborhood-level, living in a neighborhood with a mid-level of Latina/o immigrant characteristics increased the probability of being questioned. The implications of these findings for citizenship profiling are discussed.     

Living a Deportation Threat: Anticipatory Stressors Confronted by Undocumented Mexican Immigrant Women

Previous sociological research shows that exposure to stress varies by individuals’ social statuses and is a central mechanism in producing mental health disparities. This line of research suggests that ethnoracial groups are more exposed to racial discrimination, thus negatively impacting their mental health. There has also been a growing literature showing how legal status impacts the mental health of immigrants and their families. However, the sociology of mental health and migration literature has largely remained disparate. This paper bridges these literatures to highlight how living a deportation threat manifests itself as an anticipatory stressor that negatively impacts undocumented Mexican migrant women’s access to resources, social relationships, and social roles. Based on 30 semi-structured in-depth interviews with undocumented Mexican immigrant women from Houston, Texas, my findings reveal living a deportation threat is a perpetual anticipatory stressor that intensifies the effects of avoiding authorities, family fragmentation, and economic uncertainty. I argue this anticipatory stressor transforms into a chronic stressor that undocumented Mexican women confront daily. By situating this study within an anti-immigrant social context, it highlights the social processes and mechanisms that exacerbate the stressors undocumented Mexican immigrant women confront.