Numerical solution of likelihood equations for a first-order response surface model for mixture paired comparisons

Summary A simple procedure for numerical solution of the likelihood equations for estimating the regression parameters of a first-order response surface model for the treatment parameters of mixture paired comparison experiments is developed. It is demonstrated that, for defined rotatable designs, those regression parameters are simple functions of the main effect parameters of a corresponding factorial model with no interactions. The maximum likelihood estimators of those main effect parameters, and hence of their corresponding regression parameters, are obtained through using procedures of treatment contrasts, factorial and iterations. A numerical example is given to illustrate applications of the procedures developed in this paper.     

On the wald,lagrangian multiplier and likelihood ratio tests when the information matrix is singular

Summary Modified formulas for the Wald and Lagrangian multiplier statistics are introduced and considered together with the likelihood ratio statistics for testing a typical null hypothesisH ₀ stated in terms of equality constraints. It is demonstrated, subject to known standard regularity conditions, that each of these statistics and the known Wald statistic has the asymptotic chi-square distribution with degrees of freedom equal to the number of equality constraints specified byH ₀ whether the information matrix is singular or nonsingular. The results of this paper include a generalization of the results of Sively (1959) concerning the equivalence of the Wald, Lagrange multiplier and likelihood ratio tests to the case of singular information matrices.     

Asymptotic properties of LS and QML estimators for a class of nonlinear GARCH processes

We consider estimation of a class of power-transformed threshold GARCH models. When the power of the transformation is known, the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) are established under mild conditions. Two sequences of least-squares estimators are also considered in the pure ARCH case, and it is shown that they can be asymptotically more accurate than the QMLE for certain power transformations. In the case where the power of the transformation has to be estimated, the asymptotic properties of the QMLE are proven under the assumption that the noise has a density. The finite-sample properties of the proposed estimators are studied by simulation.     

The effect of computer intervention and task structure on bargaining outcome

This paper reports on a study that examined the impact of computer presentation of suggested solutions during negotiation, in bargaining situations that can be characterized as integrative or distributive. It was found that in the integrative task, the bargainers achieved higher joint outcomes when presented with suggestions. They had a more negative perception of the negotiation atmosphere, however. In the distributive task, the suggestions did not help achieve joint gains, but it lessened negative attitudes of the bargainers. Bargainers who received suggestions felt both they and their partner had been somewhat more flexible, cooperative, considerate, and less suspicious. Thus, regardless of negotiation situation, the suggestions resulted in some benefit to the negotiators.     

Assigning Students to Groups: A Multi-Criteria Decision Support System Approach*

MCADSS is a multi-criteria allocation decision support system for assisting in the task of allocating students to groups. Based on multiple criteria, MCADSS's goal is to maximize the diversity of members within groups, while minimizing the average differences between groups. The project may be viewed from several perspectives: as a multi-criteria decision-making problem, as a “reverse'’clustering problem, or as a personnel assignment problem. The system is currently being used to allocate M.B.A. students into sections and study teams at The European Institute of Business Administration (INSEAD). This paper describes the rationale for MCADSS, design criteria, system methodology, and application results. It also suggests how this approach could be used for further applications.     

From susceptibility to frailty in social networks: The case of obesity

The obesity pandemic is represented by a discrete-time Hopfield Boolean network embedded in continuous-time population dynamics. The influence of the social environment passes through a system of differential equations, whereby obesity spreads by imitation of the most influential neighbors, those who have the highest centrality indices in the network. This property is called “homophily.” Susceptibility and frailty are redefined using network properties. Projections of the spread of obesity are validated on data collected in a French high school.