The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression

The Frisch–Waugh–Lovell (FWL) (partitioned regression) theorem is essential in regression analysis. This is partly because it is quite useful to derive theoretical results. The lasso regression and the ridge regression, both of which are penalized least-squares regressions, have become popular statistical techniques. This article describes that the FWL theorem remains valid for these penalized least-squares regressions. More precisely, we demonstrate that the covariates corresponding to unpenalized regression parameters in these penalized least-squares regression can be projected out. Some other results related to the FWL theorem in such penalized least-squares regressions are also presented.     

Increasing Competency,Self-Confidence,and Connectedness Among Foster Care Alumni Entering a 4-Year University: Findings from an Early-Start Program

Research shows that few foster care alumni enroll and complete post-secondary education. For those who do enroll, many experience challenges associated with academic and social adjustment and are at risk of dropping out. Many college-based programs are being developed and are available to foster care alumni to support them during their post-secondary education. This study used pre-tests, post-tests, and journal entries of seventeen participants to evaluate a strengths-based, resilience-oriented early-start program for newly enrolled students at a large public university that provides knowledge about the institution, resources (e.g., tutoring), and social support necessary for foster care alumni to make a smooth transition into college life and to increase short and long-term student success. Quantitative and qualitative findings indicate that students who participated in the early-start program showed increased confidence and competency in academic and social adjustment. Findings also showed personal growth (e.g., building resiliency) and an increased connectedness among students who participated in the program. Study findings can inform the development of new on-campus support programs and help enhance existing programming. Future research should address short and long-term outcomes and experiences of students who are former foster youth who have participated in on-campus support programs.     

中国高等教育中的自主招生与人才选拔：来自北大、清华和人大的发现

本文通过对“首都大学生成长追踪调查”中三所精英大学（北京大学、清华大学和中国人民大学）具有代表性样本的数据分析,从教育公平和人才选拔效率两个角度检验了自主招生政策实施的效果。研究结果表明,从教育公平的方面来讲,获得自主招生破格录取的学生更有可能来自父母受过高等教育的家庭、城市家庭和好的重点高中。从人才选拔效率的角度来讲,获得自主招生破格录取学生的学业表现、社会活动能力、非认知能力、毕业后的计划和实际去向与统招学生却并无显著差别。本文的发现对于如何完善自主招生政策、促进教育公平、科学选拔和培养优秀人才等议题具有重要的政策启示意义。     

Effects of Africentric Socialization on Psychosocial Outcomes in Black Girls: The Critical Role of Gender

African American social work scholars recommend rigorous research and evaluation of Africentric interventions as one approach to building culturally appropriate, evidence-based treatments for the Black community. Following this approach, this pilot study evaluates the Imani Rites of Passage program, a 15-week Africentric curriculum with 10 Black adolescent females (mean age = 12.40), comparing their pre- and post-intervention data to that of a no-intervention group of 13 Black males (mean age = 12.08). The program evaluation is based on the degree of correspondence between theory and the measurement model spelled out by the cognitive-cultural view of African-American identity. The findings for Black females were consistent with the cognitive-cultural model in some ways but not in others, and they were more complex than the predictions. Future Africentric interventions guided by the cognitive-cultural model must consider gender differences in the outcomes. Implications for social work research and practice are discussed.     

Through the Ages: Developing Relationships Between the Young and the Old

This article evaluates a program between students at a primary school and aged care residents. The aim of the program was to increase respect and appreciation between the groups. Visiting programs between children and the elderly are well documented, and assumes that the contact will benefit both groups. However the research is contradictory. To ensure that this program was achieving its goals, pre-post test data using the Children’s Perceptions of Aging and Elderly test was collected. Significant improvements in attitude were seen in two items. Overall, there was an improvement in attitude in 12 of the 18 instrument items.     

A Note on High-Dimensional Linear Regression With Interactions

The problem of interaction selection in high-dimensional data analysis has recently received much attention. This note aims to address and clarify several fundamental issues in interaction selection for linear regression models, especially when the input dimension p is much larger than the sample size n. We first discuss how to give a formal definition of “importance” for main and interaction effects. Then we focus on two-stage methods, which are computationally attractive for high-dimensional data analysis but thus far have been regarded as heuristic. We revisit the counterexample of Turlach and provide new insight to justify two-stage methods from the theoretical perspective. In the end, we suggest new strategies for interaction selection under the marginality principle and provide some simulation results.     

Comparison of methods for analyzing binary repeated measures data: A simulation-based study (comparison of methods for binary repeated measures)

In this study, some methods suggested for binary repeated measures, namely, Weighted Least Squares (WLS), Generalized Estimating Equations (GEE), and Generalized Linear Mixed Models (GLMM) are compared with respect to power, type 1 error, and properties of estimates. The results indicate that with adequate sample size, no missing data, the only covariate being time effect, and a relatively limited number of time points, the WLS method performs well. The GEE approach performs well only for large sample sizes. The GLMM method is satisfactory with respect to type I error, but its estimates have poorer properties than the other methods.     

Saddlepoint p-values for group of linear rank tests

Many nonparametric tests in one sample problem, matched pairs, and competingrisks under censoring have the same underlying permutation distribution. This article proposes a saddlepoint approximation to the exact p-values of these tests instead of the asymptotic approximations. The performance of the saddlepoint approximation is assessed by using simulation studies that show the superiority of the saddlepoint methods over the asymptotic approximations in several settings. The use of the saddlepoint to approximate the p-values of class of two sample tests under complete randomized design is also discussed.     

Optimum designs for parameter estimation in a mixture experiment with two correlated responses

In this paper, we investigate a mixture problem with two responses, which are functions of the mixing proportions, and are correlated with known dispersion matrix. We obtain D- and A-optimal designs for estimating the parameters of the response functions, when none or some of the regression coefficients of the two functions are the same. It is shown that when no prior knowledge about the regression coefficients is available, the D-optimal design is independent of the dispersion matrix, while the A-optimal design depends on it, provided the response functions are of different degree. On the other hand, when some of the regression coefficients are known to be the same for both the functions, the D-optimal design depends on the dispersion matrix when the two response functions are not of the same degree.     

An evaluation of the reconstructed coefficient of determination and potential adjustments

Previously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.