Algorithms for optimal design with application to multiple polynomial regression

The approximate theory of optimal linear regression design leads to specific convex extremum problems for numerical solution. A conceptual algorithm is stated, whose concrete versions lead us from steepest descent type algorithms to improved gradient methods, and finally to second order methods with excellent convergence behaviour. Applications are given to symmetric multiple polynomial models of degree three or less, where invariance structures are utilized. A final section is devoted to the construction of efficientexact designs of sizeN from the optimal approximate designs. For the multifactor cubic model and some of the most popular optimality criteria (D-, A-, andI-criteria) fairly efficient exact designs are obtained, even for small sample sizeN. AMS Subject Classification: 62K05.Abbreviated Title: Algorithms for Optimal Design.Invited paper presented at the International Conference on Mathematical Statistics,ProbaStat '94, Smolenice, Slovakia.     

Totally positive regression: E-optimal designs

E-optimality of approximate designs in linear regression models is paired with a dual problem of nonlinear Chebyshev approximation. When the regression functions form a totally positive system, then the information matrices of designs for subparameters turn out to be “almost” totally positive, a property which allows to solve the nonlinear Chebyshev problem. Thereby we obtain explicit formulae for E-optimal designs in terms of equi-oscillating generalized polynomials. The considerations unify and generalize known results on E-optimality for particular regression setups.     

Optimality and efficiency of circular neighbor balanced designs for correlated observations

The purpose of this paper is to apply the Kunert and Martins (2000b) method for finding optimal designs into the case of dependence. Using this method we study optimality of circular neighbor balanced designs at distances 1 and 2 under the one-dimensional interference model with errors correlated according to a circular autoregressive process. We determine the efficiency of binary designs for specified values of correlation coefficient, for which these designs are not optimal.Research partially supported by the KBN Grant Number 5 P03A 041 21.     

Locally D- and c-optimal designs for Poisson and negative binomial regression models

The research on optimal experimental designs for nonlinear regression models is of great interest because these models are used to characterize chemical, biological or agricultural phenomena. Much of them involve an exponential decay. In this paper, locally D- and c-optimal designs are derived analytically for Poisson and negative binomial regression models.     

An application of approximate finite sample results to parameter estimation in a linear errors-in-variables model

In the simple errors-in-variables model the least squares estimator of the slope coefficient is known to be biased towards zero for finite sample size as well as asymptotically. In this paper we suggest a new corrected least squares estimator, where the bias correction is based on approximating the finite sample bias by a lower bound. This estimator is computationally very simple. It is compared with previously proposed corrected least squares estimators, where the correction aims at removing the asymptotic bias or the exact finite sample bias. For each type of corrected least squares estimators we consider the theoretical form, which depends on an unknown parameter, as well as various feasible forms. An analytical comparison of the theoretical estimators is complemented by a Monte Carlo study evaluating the performance of the feasible estimators. The new estimator proposed in this paper proves to be superior with respect to the mean squared error.     

Assessing the relationships between Nationalism, Ethnocentrism, and Individualism in Flanders using Bergstrom's approximate discrete model

Although Nationalism, Ethnocentrism, and Individualism in Flanders have been the subject of several studies before, a longitudinal analysis has not been performed on all three concepts simultaneously nor have their relationships and the direction of their relationships been studied in continuous time. In this study we performed a continuous-time state-space analysis on panel data collected from 1274 subjects, in the years 1991, 1995 and 1999. The LISREL program is used for estimating the approximate discrete model (ADM), and for comparison, also the exact discrete model (EDM) is estimated by means of the Mx program. Details of continuous time modeling, especially the EDM and ADM, are dealt with. Individualism and Ethnocentrism turn out to be connected in a moderately strong feedback relationship with the effect from Individualism towards Ethnocentrism somewhat stronger than that in the opposite direction. Both Individualism and Ethnocentrism have small effects on Nationalism. The autoregression functions, cross-lagged effect functions, and mean predictions are shown.     

Agreement and consensus in a Q-mode research design: an empirical comparison of measures,and an application

Subject of this paper is the analysis of consensus within small groups of respondents, based on a proportionally large number of variables. The target group is researchers who are interested in Q-mode research. Measures of agreement are compared, and an application from a recent project is presented. Cohen’s κ is the preferable measure, Krippendorff’s α is an alternative, which is based on a different concept of expected disagreement. At group level, along with κ and α for multiple raters, additional measures are r _wg, intraclass correlation, and κ _SC. Predictions about level differences between groups can be assessed by a t-test and θ     

重庆动物园笼舍生态丰容设计与实践

通过对重庆动物园涉禽馆、两爬馆、熊猫馆、金鱼馆等动物笼舍的生态化丰容改造,改善了动物圈养生存的环境质量,提高了其生殖率和适应性等生物学功能,增强了福利水平。是动物笼舍自然化、生态化发展做有益的探索。有助于动物的健康和繁殖,也为游客提供良好的视觉享受,提高展出与观赏效果。具有重要的推广应用价值。     

Estimation and testing of crossing‐points in fixed design regression

Many phenomena in the life sciences can be analyzed by using a fixed design regression model with a regression function m that exhibits a crossing‐point in the following sense: the regression function runs below or above its mean level, respectively, according as the input variable lies to the left or to the right of that crossing‐point, or vice versa. We propose a non‐parametric estimator and show weak and strong consistency as long as the crossing‐point is unique. It is defined as maximizing point arg max of a certain marked empirical process. For testing the hypothesis H₀ that the regression function m actually is constant (no crossing‐point), a decision rule is designed for the specific alternative H₁ that m possesses a crossing‐point. The pertaining test‐statistic is the ratio max/argmax of the maximum value and the maximizing point of the marked empirical process. Under the hypothesis the ratio converges in distribution to the corresponding ratio of a reflected Brownian bridge, for which we derive the distribution function. The test is consistent on the whole alternative and superior to the corresponding Kolmogorov–Smirnov test, which is based only on the maximal value max. Some practical examples of possible applications are given where a certain study about dental phobia is discussed in more detail.     

Mixed Methods Studies in Environmental Management Research: Prevalence,Purposes and Designs

Mixed methods research, that is, the combined use of quantitative and qualitative methods in the same study, is a popular approach in several fields. However, its use in the field of environmental management and sustainable development has not been examined. The authors review the application of mixed methods research in the journal Business Strategy and the Environment in the last ten years. A total of 340 articles have been read and reviewed, and 26 mixed methods studies have been identified. The main purposes and mixed methods designs are examined. Suggestions on why and how to use mixed methods research are offered, and recommendations are provided to guide future mixed methods studies to advance our understanding of environmental management topics. Copyright © 2014 John Wiley & Sons, Ltd and ERP Environment