Accounting for Uncertainty in Heteroscedasticity in Nonlinear Regression

Toxicologists and pharmacologists often describe toxicity of a chemical using parameters of a nonlinear regression model. Thus estimation of parameters of a nonlinear regression model is an important problem. The estimates of the parameters and their uncertainty estimates depend upon the underlying error variance structure in the model. Typically, a priori the researcher would not know if the error variances are homoscedastic (i.e., constant across dose) or if they are heteroscedastic (i.e., the variance is a function of dose). Motivated by this concern, in this paper we introduce an estimation procedure based on preliminary test which selects an appropriate estimation procedure accounting for the underlying error variance structure. Since outliers and influential observations are common in toxicological data, the proposed methodology uses M-estimators. The asymptotic properties of the preliminary test estimator are investigated; in particular its asymptotic covariance matrix is derived. The performance of the proposed estimator is compared with several standard estimators using simulation studies. The proposed methodology is also illustrated using a data set obtained from the National Toxicology Program.     

A modified LGB method for detecting significant effects based on a half-normal probability plot

In analyzing data from unreplicated factorial designs, the half-normal probability plot is commonly used to screen for the ‘vital few’ effects. Recently, many formal methods have been proposed to overcome the subjectivity of this plot. Lawson (1998) (hereafter denoted as LGB) suggested a hybrid method based on the half-normal probability plot, which is a blend of Lenth (1989) and Loh (1992) method. The method consists of fitting a simple least squares line to the inliers, which are determined by the Lenth method. The effects exceeding the prediction limits based on the fitted line are candidates for the vital few effects. To improve the accuracy of partitioning the effects into inliers and outliers, we propose a modified LGB method (hereafter denoted as the Mod_LGB method), in which more outliers can be classified by using both the Carling’s modification of the box plot (Carling, 2000) and Lenth method. If no outlier exists or there is a wide range in the inliers as determined by the Lenth method, more outliers can be found by the Carling method. A simulation study is conducted in unreplicated $2^4$ designs with the number of active effects ranging from 1 to 6 to compare the efficiency of the Lenth method, original LGB methods, and the proposed modified version of the LGB method.     

Hierarchical likelihood approach to non-Gaussian factor analysis

Factor models, structural equation models (SEMs) and random-effect models share the common feature that they assume latent or unobserved random variables. Factor models and SEMs allow well developed procedures for a rich class of covariance models with many parameters, while random-effect models allow well developed procedures for non-normal models including heavy-tailed distributions for responses and random effects. In this paper, we show how these two developments can be combined to result in an extremely rich class of models, which can be beneficial to both areas. A new fitting procedures for binary factor models and a robust estimation approach for continuous factor models are proposed.     

Learning discrete decomposable graphical models via constraint optimization

Statistical model learning problems are traditionally solved using either heuristic greedy optimization or stochastic simulation, such as Markov chain Monte Carlo or simulated annealing. Recently, there has been an increasing interest in the use of combinatorial search methods, including those based on computational logic. Some of these methods are particularly attractive since they can also be successful in proving the global optimality of solutions, in contrast to stochastic algorithms that only guarantee optimality at the limit. Here we improve and generalize a recently introduced constraint-based method for learning undirected graphical models. The new method combines perfect elimination orderings with various strategies for solution pruning and offers a dramatic improvement both in terms of time and memory complexity. We also show that the method is capable of efficiently handling a more general class of models, called stratified/labeled graphical models, which have an astronomically larger model space.     

Farmers' Contribution to Agricultural Social Capital: Evidence from Southern Spain

Social capital is the whole set of shared norms, values, attitudes, and beliefs that promote cooperation among individuals within the community and that has proved to be a key factor in explaining development processes. This article aims to provide an analytically reliable notion of social capital within the farming sector and a methodological tool for empirically measuring how social capital is accumulated at the farmer level. The theoretical framework proposed is based on the multidimensionality of the complex concept of social capital. Thus, to develop a comprehensive index for social capital, we identify three dimensions of the concept, structural, relational, and cognitive social capital, each one also comprising several subdimensions. This integrative approach permits creation of a composite indicator of the agricultural social capital accumulated at the farmer level, further identifying socioeconomic factors that influence its accumulation at that level. We empirically apply this methodological approach to farmers in Andalusia in southern Spain as a case study. This research provides an interesting starting point for informing policymakers about social capital and helping them implement the necessary programs to facilitate sustainable development in the agricultural sector.     

On second-order improved estimation of a gamma scale parameter

This paper concludes our comprehensive study on point estimation of model parameters of a gamma distribution from a second-order decision theoretic point of view. It should be noted that efficient estimation of gamma model parameters for samples ‘not large’ is a challenging task since the exact sampling distributions of the maximum likelihood estimators and its variants are not known. Estimation of a gamma scale parameter has received less attention from the earlier researchers compared to shape parameter estimation. What we have observed here is that improved estimation of the shape parameter does not necessarily lead to improved scale estimation if a natural moment condition (which is also the maximum likelihood restriction) is satisfied. Therefore, this work deals with the gamma scale parameter estimation as a separate new problem, not as a by-product of the shape parameter estimation, and studies several estimators in terms of second-order risk.     

How publics’ active and passive communicative behaviors affect their tornado responses: An integration of STOPS and SMCC

During imminent threat crises, such as natural disasters, publics have minutes to decide how to respond after receiving a warning. This study advances understanding of publics’ crisis communicative and noncommunicative behaviors in the context of tornadoes through combining and extending two theories: the social-mediated crisis communication (SMCC) model and the situational theory of problem solving (STOPS). Findings from a survey of Southeast U.S. residents (n = 1,585) indicate that STOPS is internally consistent and accurate at measuring its intended outcomes of communicative action in problem solving. However, the STOPS measures do not have a significant relationship with the desirable outcome for imminent threat crisis communication: individuals following government’s protective action guidance about tornadoes. In comparison, the expanded SMCC model predicts individuals’ self-reported compliance. Finally, variables from the SMCC model and tornado-specific variables were integrated into the STOPS model to explain individuals’ communicative engagement. Implications for theory and public relations practice are discussed.     

Intensive management reduces butterfly diversity over time in urban green spaces

Urban Ecosystems - Loss and fragmentation of semi-natural grasslands have had negative consequences for grassland biodiversity, such as butterflies. Urban parks and other urban green spaces have so...