Robust logistic regression modelling via the elastic net-type regularization and tuning parameter selection

The penalized logistic regression is a useful tool for classifying samples and feature selection. Although the methodology has been widely used in various fields of research, their performance takes a sudden turn for the worst in the presence of outlier, since the logistic regression is based on the maximum log-likelihood method which is sensitive to outliers. It implies that we cannot accurately classify samples and find important factors having crucial information for classification. To overcome the problem, we propose a robust penalized logistic regression based on a weighted likelihood methodology. We also derive an information criterion for choosing the tuning parameters, which is a vital matter in robust penalized logistic regression modelling in line with generalized information criteria. We demonstrate through Monte Carlo simulations and real-world example that the proposed robust modelling strategies perform well for sparse logistic regression modelling even in the presence of outliers.     

A two-sample test for mean functions with increasing number of projections

We propose a test for equality of two means when data are functions and obtain the asymptotic properties of the test statistic as data dimension increases with the sample size. We also derive the asymptotic power of the test under some local alternatives and show that the test statistic is root-n consistent. A simulation study is conducted to evaluate the performance of the test numerically and to compare the proposed test with other existing four popular tests.     

Envelope Theorems for Arbitrary Choice Sets

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function. We also provide conditions for the value function to be, variously, absolutely continuous, left‐ and right‐differentiable, or fully differentiable. These results are applied to mechanism design, convex programming, continuous optimization problems, saddle‐point problems, problems with parameterized constraints, and optimal stopping problems.     

ANOVA-like analysis of matched series of studies with a common structure

It is shown how to condense the information contained in a series of studies, each constituted by an objects by variables matrix and a pair of weight matrices, into a structure vector and a sum of sums of squares of residuals. Based on this condensation we propose to carry out ANOVA-like inference for matched series of studies associated with the level combinations of some factors. It is shown how to validate the assumptions underlying the inference. An application to the results of local elections in Portugal is given.     

Mechanisms Behind the Negative Influence of Single Parenthood on School Performance: Lower Teaching and Learning Conditions?

We take a first step toward unravelling the mechanisms behind the negative influence of single parenthood and the proportion of single-parent families on school performance, using 2012 international Program for International Student Assessment (PISA) data. We find that individual truancy of pupils fully explains the relationship between living in a single-mother family and math performance (after controlling for confounding factors, such as parental socioeconomic status). School-level measures of classroom disruption and truancy and individual truancy explain some of the negative effect of the school’s concentration of students from single-parent families on individual students’ math performance. However, the effect of a school’s proportion of single-parent families remains significantly negative on individual performance.     

Power comparison of data depth-based nonparametric tests for testing equality of locations

In the recent years, the notion of data depth has been used in nonparametric multivariate data analysis since it gives natural ‘centre-outward’ ordering of multivariate data points with respect to the given data cloud. In the literature, various nonparametric tests are developed for testing equality of location of two multivariate distributions based on data depth. Here, we define two nonparametric tests based on two different test statistic for testing equality of locations of two multivariate distributions. In the present work, we compare the performance of these tests with the tests developed by Li and Liu [New nonparametric tests of multivariate locations and scales using data depth. Statist Sci. 2004;(1):686–696] for testing equality of locations of two multivariate distributions. Comparison in terms of power is done for multivariate symmetric and skewed distributions using simulation for three popular depth functions. Application of tests to real life data is provided. Conclusion and recommendations are also provided.     

Factors Influencing STEM Career Aspirations of Underrepresented High School Students

A shortage of female and minority students pursuing science, technology, engineering, and mathematics (STEM) careers has prompted researchers and policy makers to examine the current STEM supply pipeline. This study examined factors influencing STEM career aspirations of a nationally representative sample of 9th‐grade students (N = 21,444). Characteristics of students who aspired to STEM careers and non‐STEM careers were examined. Guided by the career aspirations model (Mau & Bikos, 2000 ), the authors conducted logistic regression analyses to investigate variables predicting STEM career aspirations. Results indicated that race, gender, socioeconomic status, math interest, and science self‐efficacy were the most important predictors of STEM career aspirations. Counselors in school and related career services contexts are encouraged to consider these important factors in identifying high school students who are interested in STEM career choices, as well as in planning career interventions to facilitate their career paths. Future researchers could test the applicability of this model with middle school students or adults.