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For the problem of percentile estimation of a quantal response curve, the authors determine multiobjective designs which are robust with respect to misspecifications of the model assumptions. They propose a maximin approach based on efficiencies which leads to designs that are simultaneously efficient with respect to various choices of link functions and parameter regions. Furthermore, the authors deal with the problems of designing model and percentile robust experiments. They give various examples of such designs, which are calculated numerically. /// Préoccupés par l'estimation des centiles d'une courbe de réponse quantale, les auteurs identifient des plans d'expérience multi-objectifs qui s'avèrent robustes même si les postulats du modèle ont été mal spécifiés. Ils proposent une approche maximin à base d'efficacités qui conduit à des plans efficaces à la fois pour divers choix de fonctions de lien et d'ensembles de valeurs pour les paramètres. Les auteurs abordent aussi la conception de modèles et de plans d'expérience robustes pour l'estimation des centiles. Ils fournissent plusieurs exemples de tels plans, obtenus numériquement.

Scientists commonly ask questions about the relative importance of processes and then turn to statistical models for answers. Standardized coefficients are typically used in such situations, with the goal being to compare effects on a common scale. Traditional approaches to obtaining standardized coefficients were developed with idealized Gaussian variables in mind. When responses are binary, complications arise that impact standardization methods. In this paper, we review, evaluate, and propose new methods for standardizing coefficients from models that contain binary outcomes. We first consider the interpretability of unstandardized coefficients and then examine two main approaches to standardization. One approach, which we refer to as the latent‐theoretical (LT) method, assumes that underlying binary observations, there exists a latent, continuous propensity linearly related to the coefficients. A second approach, which we refer to as the observed‐empirical (OE) method, assumes responses are purely discrete and estimates error variance empirically via reference to a classical R2 estimator. We also evaluate the standard formula for calculating standardized coefficients based on standard deviations. Criticisms of this practice have been persistent, leading us to propose an alternative formula that is based on user‐defined “relevant ranges.” Finally, we implement all of the above in an open‐source package for the statistical software R. Results from simulation studies show that both the LT and OE methods of standardization support a similarly broad range of coefficient comparisons. The LT method estimates effects that reflect underlying latent‐linear propensities, while the OE method computes a linear approximation for the effects of predictors on binary responses. The contrast between assumptions for the two methods is reflected in persistently weaker standardized effects associated with OE standardization. Reliance on standard deviations for standardization (the traditional approach) is critically examined and shown to introduce substantial biases when predictors are non‐Gaussian. The use of relevant ranges in place of standard deviations has the capacity to place LT and OE standardized coefficients on a more comparable scale. As ecologists address increasingly complex hypotheses, especially those that comparing the influences of different controlling factors (e.g., top‐down vs. bottom‐up or biotic vs. abiotic controls), comparable coefficients become necessary for evaluations.

In this paper the results of Radloff and Schwabe (Stat Papers 60:165–177, 2019) will be extended for a special class of symmetrical intensity functions. This includes binary response models with logit and probit link. To evaluate the position and the weights of the two non-degenerated orbits on the k-dimensional ball usually a system of three equations has to be solved. The symmetry allows to reduce this system to a single equation. As a further result, the number of support points can be reduced to the minimal number. These minimally supported designs are highly efficient. The results can be generalized to arbitrary ellipsoidal design regions.

D-optimality is a well-known concept in experimental design that seeks to select an optimal set of design points to estimate the unknown parameters of a statistical model with a minimum variance. In this paper, we focus on proving a conjecture made by Ford, Torsney and Wu regarding the existence of a class of D-optimal designs for binary and weighted linear regression models. Our concentration is on models with one design variable. The conjecture states that, for any given level of precision, there exists a two-level factorial design that is D-optimal for these models. To prove this conjecture, we use an intuitive approach that explores various link functions in the generalised linear model context to establish the veracity of the conjecture. We also present explicit and clear plots of various functions wherever deemed necessary and appropriate to further strengthen the proofs. Our results establish the existence of D-optimal designs for binary and weighted linear regression models with one design variable, which have important implications for the efficient design of experiments in various fields. These findings contribute to the development of optimal experimental designs for studying binary and weighted linear regression models and provide a foundation for future research in this area.

Binary response data arise naturally in applications. In general, the well-known logistic and probit regression models form the basis for analyzing binary data in practice. These regression models make use of symmetric link functions (logit and probit links). However, many authors have emphasized the need of asymmetric links in modeling binary response data. In this paper, we consider a broad class of parametric link functions that contains as special cases both symmetric as well as asymmetric links. Furthermore, this class of links is quite flexible and simple, and may be an interesting alternative to the usual regression models for binary data. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. We also propose residuals for the link models to assess departures from model assumptions as well as to detect outlying observations. Additionally, the local influence method is discussed, and the normal curvatures for studying local influence are derived under two specific perturbation schemes. Finally, an application to the coca leaf cultivation in Peru is considered to show the usefulness of the proposed link models in practice.

In Chile, the native forest has suffered anthropic pressure that has resulted in the reduction in its surface and increased degradation, which has led to the development of public policies to reverse this scenario and encourage its sustainable management and conservation. This study examines the socioeconomic variables that influence the area increase in native forests in southern Chile, based on the analysis of 154 properties in the regions of Los Ríos, La Araucanía and Los Lagos. Georeferenced information from the 2015 SIMEF program survey and the Cadastre and Evaluation of Native Vegetation Resources of Chile were used. A Probit regression model was implemented, which associates a traceable increase in the native forest area with the variables regarding the owner: location, gender, age, schooling, management plan and technical advisory; and regarding the exploitation: farm size, percentage of native forest, scrub and forest plantations of the property and number of animal units. The econometric results show that smaller farms and those located in Los Lagos presented less probability of increasing their native forests. In the same way, an increase in the share of forest plantations area decreases the probability. Conversely, the scrub area share is related to the recovery of native forests in the sample. No significant effects of the variables associated with the implementation of management plans and technical assistance were found.

In this article, we consider the estimation of a panel data binary response model with a weak restriction imposed on the individual specific effects. Our estimator is -consistent and asymptotically normal under reasonable regularity conditions. Furthermore, we allow the error terms to be heteroscedastic over time. The proposed estimator has a closed form expression and thus is very easy to compute. Simulations and the empirical illustration demonstrate the usefulness of our proposed estimator.

The original Risk-Metrics method is underpinned by the assumption that daily asset returns are conditional Gaussian independently identically distributed (iid) random variables with a mean of zero. In this paper, a new method to calculate Value at Risk (VaR) was suggested to overcome the shortcoming of Risk-Metrics by employing binary response models to compute probability forecasts of the portfolio return by exceeding a grid of candidate quantile values. From those values, the VaR quantile value was selected. The proposed model was called BRV (Binary Response VaR method). Consistent application of BRV to the Dow Jones Industrial Average (INDEXDJX: DJI) and Dow Jones U.S. Marine Transportation Index (DJUSMT) time series proved that it was more accurate than the Risk-Metric system. This method not only worked similar to quantile regression but had the advantage that conventional maximum likelihood methods could be used for parameter estimation and inference. The BRV method was the best performing method for computing the daily VaR at both the 95% and 99% confidence levels over the period 02/01/06–31/12/08. The BRV and the QR (quantile regression) methods performed similarly, but the BRV method had the practical advantage that conventional maximum likelihood (ML) technique could be used for parameter estimation and robust inference.

We develop nearly unbiased maximum likelihood estimators for a new class of asymmetric link functions proposed recently in the statistic literature by Lemonte and Bazán (TEST 27, 597–617 2018). These authors have introduced a broad class of parametric link functions in binary regression that contains as special cases both symmetric as well as asymmetric links. We discuss maximum likelihood estimation for the model parameters and derive a closed-form expression for the second order bias of these estimators. The second order bias can be easily computed as an ordinary weighted leastsquares regression and is then used to define bias corrected maximum likelihood estimators. Monte Carlo simulation experiments are conducted in order to investigate the performance of the corrected estimators. The numerical results reveal that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Empirical applications are considered for illustrative purposes.