Regression,Self-Disclosure,and the Teach or Treat Dilemma: Implications of a Relational Approach for Social Work Supervision

This paper presents a brief review of a relational approach to clinical supervision and argues for its application in social work settings. Although an integral and essential part of practice, clinical supervision is underrepresented in the practice literature. Given this paucity of writings on supervision, the recent book by Mary Gail Frawley-O'Dea and Joan Sarnat, The Supervisory Relationship: A Contemporary Psychodynamic Approach, stands out as a seminal contribution because the authors present a fully developed relational model of supervision that fills a major gap in the development of contemporary relational theory and practice. We selectively review the basic concepts and principles of Frawley-O'Dea and Sarnat's model and apply this supervisory approach to current social work practice. Our focus will be on exploring three controversial and much-debated topics: self-disclosure, regression, and the teach or treat dilemma. Case vignettes from two supervisory experiences will serve to illustrate how a relational approach enhances both the treatment and the supervisory relationship.     

Properties of the mixed regression estimator when disturbances are not necessarily normal

Small-disturbance approximations for the bias vector and mean squared error matrix of the mixed regression estimator for the coefficients in a linear regression model are derived and efficiency with respect to least squares estimator is examined.     

Survival trees with time-dependent covariates: Application to estimating changes in the incubation period of AIDS

Tree-structured methods for exploratory data analysis have previously been extended to right-censored survival data. We further extend these methods to allow for truncation and time-dependent covariates. We apply the new methods to a data set on incubation times of acquired immunodeficiency syndrome (AIDS), using calendar time as a time-dependent covariate. Contrary to expectation, we find that rates of progression to AIDS appear to be faster after August 1989 than before.     

回归分析在短跑教学中的应用

针对教学中学生100m跑的具体情况,采用逐步回归分析方法建立了回归方程;在此基础上,分别以各相关因素、100 m跑成绩作为因变量与自变量建立了多项式回归方程,并依据正态分布理论制定了各因素平衡发展的标准.上述方法在指导短跑教学中取得了较好的效果.     

Robust estimation for linear regression with asymmetric errors

The authors propose a new class of robust estimators for the parameters of a regression model in which the distribution of the error terms belongs to a class of exponential families including the log‐gamma distribution. These estimates, which are a natural extension of the MM‐estimates for ordinary regression, may combine simultaneously high asymptotic efficiency and a high breakdown point. The authors prove the consistency and derive the asymptotic normal distribution of these estimates. A Monte Carlo study allows them to assess the efficiency and robustness of these estimates for finite samples.     

JAMES-STEIN RULE ESTIMATORS IN LINEAR REGRESSION MODELS WITH MULTIVARIATE-t DISTRIBUTED ERROR

This paper considers estimation of β in the regression model y =Xβ+μ, where the error components in μ have the jointly multivariate Student-t distribution. A family of James-Stein type estimators (characterised by nonstochastic scalars) is presented. Sufficient conditions involving only X are given, under which these estimators are better (with respect to the risk under a general quadratic loss function) than the usual minimum variance unbiased estimator (MVUE) of β. Approximate expressions for the bias, the risk, the mean square error matrix and the variance-covariance matrix for the estimators in this family are obtained. A necessary and sufficient condition for the dominance of this family over MVUE is also given.     

Protection against outliers in empirical bayes estimation

The proven optimality properties of empirical Bayes estimators and their documented successful performance in practice have made them popular. Although many statisticians have used these estimators since the landmark paper of James and Stein (1961), relatively few have proposed techniques for protecting them from the effects of outlying observations or outlying parameters. One notable series of studies in protection against outlying parameters was conducted by Efron and Morris (1971, 1972, 1975). In the fully Bayesian case, a general discussion on robust procedures can be found in Berger (1984, 1985). Here we implement and evaluate a different approach for outlier protection in a random-effects model which is based on appropriate specification of the prior distribution. When unusual parameters are present, we estimate the prior as a step function, as suggested by Laird and Louis (1987). This procedure is evaluated empirically, using a number of simulated data sets to compare the effects of the step-function prior with those of the normal and Laplace priors on the prediction of small-area proportions.     

Testing for and against a set of linear inequality constraints in a multinomial setting

There are numerous situations in categorical data analysis where one wishes to test hypotheses involving a set of linear inequality constraints placed upon the cell probabilities. For example, it may be of interest to test for symmetry in k × k contingency tables against one-sided alternatives. In this case, the null hypothesis imposes a set of linear equalities on the cell probabilities (namely p_ij = P_ji ×i > j), whereas the alternative specifies directional inequalities. Another important application (Robertson, Wright, and Dykstra 1988) is testing for or against stochastic ordering between the marginals of a k × k contingency table when the variables are ordinal and independence holds. Here we extend existing likelihood-ratio results to cover more general situations. To be specific, we consider testing H_t,0 against H₁ - H₀ and H₁ against H₂ - H ₁ when H₀:k × i=1 p_ix_ji = 0, j = 1,…, s, H₁:k × i=1 p_ix_ji × 0, j = 1,…, s, and does not impose any restrictions on p. The x_ji's are known constants, and s × k - 1. We show that the asymptotic distributions of the likelihood-ratio tests are of chi-bar-square type, and provide expressions for the weighting values.     

Efficient score tests for heteroskedasticity in micro-economics

This paper develops an artificial regression that can be employed to obtain efficient score test statistics for heteroskedasticity in the context of a variety of micro-econometric models