Robust Designs in Generalized Linear Models: A Quantile Dispersion Graphs Approach

This article studies design selection for generalized linear models (GLMs) using the quantile dispersion graphs (QDGs) approach in the presence of misspecification in the link and/or linear predictor. The uncertainty in the linear predictor is represented by a unknown function and estimated using kriging. For addressing misspecified link functions, a generalized family of link functions is used. Numerical examples are shown to illustrate the proposed methodology.     

Correlated random effects regression analysis for a log-normally distributed variable

In regression analysis, it is assumed that the response (or dependent variable) distribution is Normal, and errors are homoscedastic and uncorrelated. However, in practice, these assumptions are rarely satisfied by a real data set. To stabilize the heteroscedastic response variance, generally, log-transformation is suggested. Consequently, the response variable distribution approaches nearer to the Normal distribution. As a result, the model fit of the data is improved. Practically, a proper (seems to be suitable) transformation may not always stabilize the variance, and the response distribution may not reduce to Normal distribution. The present article assumes that the response distribution is log-normal with compound autocorrelated errors. Under these situations, estimation and testing of hypotheses regarding regression parameters have been derived. From a set of reduced data, we have derived the best linear unbiased estimators of all the regression coefficients, except the intercept which is often unimportant in practice. Unknown correlation parameters have been estimated. In this connection, we have derived a test rule for testing any set of linear hypotheses of the unknown regression coefficients. In addition, we have developed the confidence ellipsoids of a set of estimable functions of regression coefficients. For the fitted regression equation, an index of fit has been proposed. A simulated study illustrates the results derived in this report.     

Enrollment,Educational Expenditures and Work Among One-Parent Children in India

In this study, I examined the effect of single parenthood due to death, separation, divorce, or migration of spouse on educational inputs among school-age children in India. I used the nationally representative India Human Development Survey to study the implications of different types of parenthood on educational expenditure among children ages 6 to 11 and 12 to 18 years and work participation among the older age group. The study finds that the separated or divorced mothers on average spend less on education and older children of widows are more likely to work because of resource constraints associated with single parenthood. The results highlight the need for public policies that would support widows as well as separated or divorced mothers.     

Comparing Social Work Students’ Perceptions of Risk Using Online Discussion Fora: Lessons Learned from a European Pilot Project

Comparisons of international child welfare systems have identified two basic orientations to practice; a ‘child protection’ orientation and a ‘child welfare’ orientation, which are founded upon fundamentally different values and assumptions regarding the family, the origins of childcare problems, and the proper role of the state in relation to the family. This paper describes a project which sought to compare how undergraduate social work students from three European Universities perceive risk in referrals about the welfare of children and to explore the impact of different cultural, ideological and educational contexts on the way in which risk is constructed by students. Students from Northern Ireland, Germany and Poland examined three vignettes via 10 online discussion fora each of which provided a narrative summary of their discussion. The paper presents some findings from the analysis of the qualitative data emerging from the student discussions and draws out the lessons learned in terms of how the project was designed and implemented using online discussion fora.     

Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups

The use of covariates in block designs is necessary when the covariates cannot be controlled like the blocking factor in the experiment. In this paper, we consider the situation where there is some flexibility for selection in the values of the covariates. The choice of values of the covariates for a given block design attaining minimum variance for estimation of each of the parameters has attracted attention in recent times. Optimum covariate designs in simple set-ups such as completely randomised design (CRD), randomised block design (RBD) and some series of balanced incomplete block design (BIBD) have already been considered. In this paper, optimum covariate designs have been considered for the more complex set-ups of different partially balanced incomplete block (PBIB) designs, which are popular among practitioners. The optimum covariate designs depend much on the methods of construction of the basic PBIB designs. Different combinatorial arrangements and tools such as orthogonal arrays, Hadamard matrices and different kinds of products of matrices viz. Khatri–Rao product, Kronecker product have been conveniently used to construct optimum covariate designs with as many covariates as possible.     

An infinite class of PBIB designs

In this paper, an infinite class of partially balanced incomplete block (PBIB) designs of m+1 associate classes is constructed through the use of a series of row-orthogonal matrices known as partially balanced orthogonal designs (PBOD) of m-associate classes. For the purpose, a series of PBOD is obtained through a method described herein. An infinite class of regular GD designs is also reported.     

Cultural perspectives of death,grief, and bereavement

The cultural makeup of the United States continues to change rapidly, and as minority groups continue to grow, these groups' beliefs and customs must be taken into account when examining death, grief, and bereavement. This article discusses the beliefs, customs, and rituals of Latino, African American, Navajo, Jewish, and Hindu groups to raise awareness of the differences health care professionals may encounter among their grieving clients. Discussion of this small sample of minority groups in the United States is not intended to cover all of the degrees of acculturation within each group. Cultural groups are not homogeneous, and individual variation must always be considered in situations of death, grief, and bereavement. However, because the customs, rituals, and beliefs of the groups to which they belong affect individuals' experiences of death, grief, and bereavement, health care professionals need to be open to learning about them to better understand and help.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.     

ON RESOLVABLE INCOMPLETE BLOCK DESIGNS1

A method of constructing resolvable incomplete block designs for v(=ks, 2 ≤ k ≤ s - 1) treatments in blocks of size k using mutually orthogonal Latin squares is proposed. It has been seen in particular that when the number of replications is s — 1 (or s), which is feasible if s is a prime or a prime power, the method gives PBIB (3) (or semi-regular GD) designs. The analysis of such designs has also been discussed.