Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach

The exact density distribution of the non‐linear least squares estimator in the one‐parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the non‐linear regression with an arbitrary number of linear parameters and one intrinsically non‐linear parameter. For a very special non‐linear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieler almost a century ago, unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the non‐linear least squares are illustrated, such as non‐existence and/or multiple solutions, as major factors contributing to poor density approximation. The non‐linear Markov–Gauss theorem is formulated on the basis of the near exact EE density approximation.     

On multivariate confidence regions and simultaneous confidence limits for ratios

Convenient general linear model computational procedures are presented for constructing multivariate confidence regions and simultaneous confidence limits for ratios of linear combinations of the parameters. The practical consequence is that a single general linear model computer program, capable of validating the underlying model and estimating the parameters, can (after slight modification) also construct the confidence regions, and even determine their precise analytic form (ellipsoid, hyperboloid, etc.). The text is deliberately factual while the appendices extend and help clarify earlier work by Henry Scheffe. As an example, a confidence ellipse and simultaneous confidence limits are constructed for several relative potencies in a classical multiple parallel line bioassay.     

A confidence region with multiple intervals in multivariate bioassay

The exact confidence region for log relative potency resulting from likelihood score methods (Williams (1988) An exact confidence interval for the relative potency estimated from a multivariate bioassay, Biometrics, 44:861-868) will very likely consist of two disjoint confidence intervals. The two methods proposed by Williams which aim to select just one (the same) confidence interval from the confidence region are nearly – but not completely – consistent. The likelihood score interval and likelihood ratio interval are asymptotically equivalent. Williams's very strong claim concerning the confidence coefficient in the second selection method is still theoretically unproved; yet, simulations show that it is true for a wide range of practical experimental situations.     

Supervised access: A judicial alternative to noncompliance with visitation arrangements following divorce

Visitation of children after divorce by noncustodial parents is a “natural” right, generally regarded to be in the best interest of children. Custodial parents frequently refuse to allow visitation, even when ordered to do so by the court. The purpose of this report is twofold: (a) to review issues and problems related to visitation; and (b) to describe a program, developed under family court sponsorship, which provides mediation to families in visitation disputes, and supervised visitation when more reasonable access is frustrated by noncompliant parents or when there is concern for the safety and well-being of visited children.     

Probabilistic text understanding

We discuss a new framework for text understanding. Three major design decisions characterize this approach. First, we take the problem of text understanding to be a particular case of the general problem of abductive inference. Second, we use probability theory to handle the uncertainty which arises in this abductive inference process. Finally, all aspects of natural language processing are treated in the same framework, allowing us to integrate syntactic, semantic and pragmatic constraints. In order to apply probability theory to this problem, we have developed a probabilistic model of text understanding. To make it practical to use this model, we have devised a way of incrementally constructing and evaluating belief networks. We have written a program,wimp3, to experiment with this framework. To evaluate this program, we have developed a simple single-blind testing method.     

Numerical computation of bridge probabilities

This paper contains an analysis of the problem of computing the joint probability density of the honor card point count in each of four hands in the game of bridge. Efficient representation of the data is considered. Computational algorithms are given for dealing with a compressed form of the density. From the joint density, the densities of the point count in the best and worst hands are obtained. Also obtained is the conditional distribution that a partnership has m points given that one of the partners has n1 points.     

Learning in organizations: HR implications and considerations

This paper looks at learning in organizations as one response to competitive pressure and accelerating environmental change. Two approaches, the learning organization and HRD, are examined in the light of new models of management and learning and a move towards the integration of work, learning, and strategy. The significance of employee participation is considered in relation to learning and some benefits and drawbacks discussed. The development of a learning orientation is seen as an organization-wide responsibility but HR practitioners can play a key role in the promotion of learning by gearing the more traditional HR activities towards the achievement of organizational goals.     

The influence of follower mood on leader mood and task performance: An affective,follower-centric perspective of leadership

Based on the notion that leadership involves affective exchange (Dasborough, Ashkanasy, Tee & Tse, 2009), we hypothesize that a leader's mood and task performance can be determined in part by follower mood displays. In two laboratory experiments, leaders supervised teams where the team members were confederates instructed to display positive or negative moods. Results were that followers' mood influenced leader mood and task performance. Moreover, leaders of positive mood followers were judged to have performed more effectively and expediently than leaders of followers who expressed negative mood states. We replicated these findings in Study 2 and found further that leaders high on neuroticism performed less effectively than their low neuroticism counterparts when interacting with negative-mood followers. Collectively, by demonstrating that follower moods influence leader affect and behaviors, our studies provide support for a core element of the Dasborough et al. (2009) reciprocal affect theory of leadership.