Shrinkage inverse regression estimation for model-free variable selection

Summary.  The family of inverse regression estimators that was recently proposed by Cook and Ni has proven effective in dimension reduction by transforming the high dimensional predictor vector to its low dimensional projections. We propose a general shrinkage estimation strategy for the entire inverse regression estimation family that is capable of simultaneous dimension reduction and variable selection. We demonstrate that the new estimators achieve consistency in variable selection without requiring any traditional model, meanwhile retaining the root n estimation consistency of the dimension reduction basis. We also show the effectiveness of the new estimators through both simulation and real data analysis.     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.     

Analysis of robust design experiments with time-dependent ordinal response characteristics: a quality improvement study from the horticulture industry

An approach to the analysis of time-dependent ordinal quality score data from robust design experiments is developed and applied to an experiment from commercial horticultural research, using concepts of product robustness and longevity that are familiar to analysts in engineering research. A two-stage analysis is used to develop models describing the effects of a number of experimental treatments on the rate of post-sales product quality decline. The first stage uses a polynomial function on a transformed scale to approximate the quality decline for an individual experimental unit using derived coefficients and the second stage uses a joint mean and dispersion model to investigate the effects of the experimental treatments on these derived coefficients. The approach, developed specifically for an application in horticulture, is exemplified with data from a trial testing ornamental plants that are subjected to a range of treatments during production and home-life. The results of the analysis show how a number of control and noise factors affect the rate of post-production quality decline. Although the model is used to analyse quality data from a trial on ornamental plants, the approach developed is expected to be more generally applicable to a wide range of other complex production systems.     

A new estimation method for Weibull-type tails based on the mean excess function

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ$\gamma$. The class γ>0$\gamma >0$ corresponds to Pareto-type or heavy tailed distributions, while γ<0$\gamma <0$ indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0$\gamma =0$. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.     

Use of log−log survival function in modeling time-covariate interactions in Cox regression

Plotting of log−log survival functions against time for different categories or combinations of categories of covariates is perhaps the easiest and most commonly used graphical tool for checking proportional hazards (PH) assumption. One problem in the utilization of the technique is that the covariates need to be categorical or made categorical through appropriate grouping of the continuous covariates. Subjectivity in the decision making on the basis of eye-judgment of the plots and frequent inconclusiveness arising in situations where the number of categories and/or covariates gets larger are among other limitations of this technique. This paper proposes a non-graphical (numerical) test of the PH assumption that makes use of log−log survival function. The test enables checking proportionality for categorical as well as continuous covariates and overcomes the other limitations of the graphical method. Observed power and size of the test are compared to some other tests of its kind through simulation experiments. Simulations demonstrate that the proposed test is more powerful than some of the most sensitive tests in the literature in a wide range of survival situations. An example of the test is given using the widely used gastric cancer data.     

R×C ecological inference: bounds, correlations, flexibility and transparency of assumptions

Summary.  Despite its potential pitfalls, ecological inference is an unavoidable part of some quantitative settings, including US voting rights litigation. In such applications, the analyst will typically encounter two-way tables with more than two rows and columns. Although several ecological inference methods are currently available for 2×2 tables, there are fewer options for analysing general R × C tables, and virtually none that model counts as opposed to fractions. We propose a count R × C method that respects the bounds deterministically, that allows for complex relationships between internal cell quantities, that is easily extensible and that results from transparent assumptions. We study the method via simulation, and then apply it to an example that is drawn from the state of Texas relevant to recent redistricting litigation there.     

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.     

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.     

Deconstructing Immigrant Illegality: A Mixed-Methods Investigation of Stress and Health Among Undocumented College Students

Research has established that being undocumented is a risk factor for mental and physical health conditions. Much of this work emphasizes undocumented immigrants’ chronic stress, yet key questions about pathways to health remain. The mere state of being undocumented is viewed as a general stressor, without considering actual levels of stress or identifying dimensions of documentation status that contribute to overall stress levels. Drawing on surveys and interviews with undocumented students at the University of California, we uncover the everyday manifestations of four dimensions of immigrant “illegality”: academic concerns, future concerns, financial concerns, and deportation concerns, and their association with reported stress levels and self-rated health. Survey data establish undocumented students’ high levels of stress and poorer health, in comparison to previous research on other national samples. In a structural equation model, we found academic and future concerns to be significantly associated with higher stress, which was in turn, associated with poorer self-rated health. Financial concerns were not associated with higher perceived stress but were directly associated with poorer self-rated health. Notably, deportation concerns did not have any significant independent associations with stress or health. We use our qualitative data to identify specific stressors embedded within these four dimensions. Our findings inform understandings of the health risks arising from documentation status.     

Multidimensional poverty: An alternative measurement approach for the United States?

International poverty research has increasingly underscored the need to use multidimensional approaches to measure poverty. Largely embraced in Europe and elsewhere, this has not had much impact on the way poverty is measured in the United States. In this paper, I use a comprehensive multidimensional framework including economic well-being, capability, and social inclusion to examine poverty in the US. Data from the 2004 General Social Survey support the interconnectedness among these poverty dimensions, indicating that the multidimensional framework utilizing a comprehensive set of information provides a compelling value added to poverty measurement. The suggested demographic characteristics of the various categories of the poor are somewhat similar between this approach and other traditional approaches. But the more comprehensive and accurate measurement outcomes from this approach help policymakers target resources at the specific groups.