Regularized Sandwich Estimators for Analysis of High‐Dimensional Data Using Generalized Estimating Equations

Summary A modification of generalized estimating equations (GEEs) methodology is proposed for hypothesis testing of high‐dimensional data, with particular interest in multivariate abundance data in ecology, an important application of interest in thousands of environmental science studies. Such data are typically counts characterized by high dimensionality (in the sense that cluster size exceeds number of clusters, n>K) and over‐dispersion relative to the Poisson distribution. Usual GEE methods cannot be applied in this setting primarily because sandwich estimators become numerically unstable as n increases. We propose instead using a regularized sandwich estimator that assumes a common correlation matrix R , and shrinks the sample estimate of R toward the working correlation matrix to improve its numerical stability. It is shown via theory and simulation that this substantially improves the power of Wald statistics when cluster size is not small. We apply the proposed approach to study the effects of nutrient addition on nematode communities, and in doing so discuss important issues in implementation, such as using statistics that have good properties when parameter estimates approach the boundary (), and using resampling to enable valid inference that is robust to high dimensionality and to possible model misspecification.     

The multiplier effect: how the accumulation of cultural and social capital explains steep upward social mobility of children of low-educated immigrants

ABSTRACT

We introduce what we have coined the multiplier effect. We explain the steep upward mobility of children of low-educated immigrants by studying how they overcome obstacles on their regular pathway, via alternative routes or through loopholes in the education and labour market system. The idea of the multiplier effect is that they virtually propel themselves forward in their careers. Essential is that each successful step forward offers new possibilities on which they build, thereby accumulating cultural and social capital and multiplying their chances of success. Initial small differences with their less successful co-ethnic peers generate an increasingly wider gap over time. Cultural and social capital theories primarily explain the reproduction of inequalities in society. The multiplier effect explains the breaking of the perpetual cycle of this reproduction, enabling steep upward mobility even when this group does not initially possess the right cultural and social capital to be successful.     

Environmental forcing, invasion and control of ecological and epidemiological systems

Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.     

Machine learning of large‐scale spatial distributions of wild turkeys with high‐dimensional environmental data

Species distribution modeling often involves high‐dimensional environmental data. Large amounts of data and multicollinearity among covariates impose challenges to statistical models in variable selection for reliable inferences of the effects of environmental factors on the spatial distribution of species. Few studies have evaluated and compared the performance of multiple machine learning (ML) models in handling multicollinearity. Here, we assessed the effectiveness of removal of correlated covariates and regularization to cope with multicollinearity in ML models for habitat suitability. Three machine learning algorithms maximum entropy (MaxEnt), random forests (RFs), and support vector machines (SVMs) were applied to the original data (OD) of 27 landscape variables, reduced data (RD) with 14 highly correlated covariates being removed, and 15 principal components (PC) of the OD accounting for 90% of the original variability. The performance of the three ML models was measured with the area under the curve and continuous Boyce index. We collected 663 nonduplicated presence locations of Eastern wild turkeys (Meleagris gallopavo silvestris) across the state of Mississippi, United States. Of the total locations, 453 locations separated by a distance of ≥2 km were used to train the three ML algorithms on the OD, RD, and PC data, respectively. The remaining 210 locations were used to validate the trained ML models to measure ML performance. Three ML models had excellent performance on the RD and PC data. MaxEnt and SVMs had good performance on the OD data, indicating the adequacy of regularization of the default setting for multicollinearity. Weak learning of RFs through bagging appeared to alleviate multicollinearity and resulted in excellent performance on the OD data. Regularization of ML algorithms may help exploratory studies of the effects of environmental factors on the spatial distribution and habitat suitability of wildlife.     

颗粒粒径测量中约束正则CONTIN算法分析

介绍用于光子相关光谱法颗粒粒径分布反演计算的约束正则化方法及基于它的CONTIN算法,通过数值模拟反演理想单峰和双峰分布,分析CONTIN算法的展宽效应、该效应与粒径的关系.利用实验测量比较了指数采样法、非负约束最小二乘法和CONTIN算法的反演结果.研究指出CONTIN的分辨力与粒径有关,总体较弱.合理选择小正则化参数或者缩小反演范围能改善反演质量.     

Precarious legality: regularizing Central American migrants in Mexico

Regularization programmes for undocumented migrants are generally viewed as a form of transition from “illegality” to a secure legal status. Yet, as we argue in this article, in many countries, such as Mexico, this transition is often incomplete and reversible. This article discusses regularization programmes for undocumented migrants in Mexico before and after the introduction of the 2011 Migration Law and illustrates that the status migrants obtain is precarious, that is insecure and conditional upon their ability to meet requirements for status renewal. Focusing on Central Americans in Mexico, we suggest that many migrants have been unable to obtain or renew their status after new procedures were put in place in 2011. Coining the legality granted through Mexico’s regularization process “precarious legality”, we attribute it to the contradiction between Mexico’s stated respect for migrants’ human rights and the de facto commitment to immigration control.     

Bayesian propensity scores for high‐dimensional causal inference: A comparison of drug‐eluting to bare‐metal coronary stents

High‐dimensional data provide many potential confounders that may bolster the plausibility of the ignorability assumption in causal inference problems. Propensity score methods are powerful causal inference tools, which are popular in health care research and are particularly useful for high‐dimensional data. Recent interest has surrounded a Bayesian treatment of propensity scores in order to flexibly model the treatment assignment mechanism and summarize posterior quantities while incorporating variance from the treatment model. We discuss methods for Bayesian propensity score analysis of binary treatments, focusing on modern methods for high‐dimensional Bayesian regression and the propagation of uncertainty. We introduce a novel and simple estimator for the average treatment effect that capitalizes on conjugacy of the beta and binomial distributions. Through simulations, we show the utility of horseshoe priors and Bayesian additive regression trees paired with our new estimator, while demonstrating the importance of including variance from the treatment regression model. An application to cardiac stent data with almost 500 confounders and 9000 patients illustrates approaches and facilitates comparison with existing alternatives. As measured by a falsifiability endpoint, we improved confounder adjustment compared with past observational research of the same problem.