We propose a new model for regression and dependence analysis when addressing spatial data with possibly heavy tails and an asymmetric marginal distribution. We first propose a stationary process with t marginals obtained through scale mixing of a Gaussian process with an inverse square root process with Gamma marginals. We then generalize this construction by considering a skew‐Gaussian process, thus obtaining a process with skew‐t marginal distributions. For the proposed (skew) t process, we study the second‐order and geometrical properties and in the t case, we provide analytic expressions for the bivariate distribution. In an extensive simulation study, we investigate the use of the weighted pairwise likelihood as a method of estimation for the t process. Moreover we compare the performance of the optimal linear predictor of the t process versus the optimal Gaussian predictor. Finally, the effectiveness of our methodology is illustrated by analyzing a georeferenced dataset on maximum temperatures in Australia.
In this article, we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatiotemporal dependence. Specifically, we propose to consider stochastic processes obtained through a monotone transformation of scaled version of 2 random processes. The latter is well known in the specialized literature and originates by summing independent copies of a squared Gaussian process. However, their use as stochastic models and related inference has not been much considered. Motivated by a spatiotemporal analysis of wind speed data from a network of meteorological stations in the Netherlands, we exemplify our modeling strategy by means of a nonstationary process with Weibull marginal distributions. For the proposed Weibull process we study the second-order and geometrical properties and we provide analytic expressions for the bivariate distribution. Since the likelihood is intractable, even for a relatively small data set, we suggest adopting the pairwise likelihood as a tool for inference. Moreover, we tackle the prediction problem and we propose to use a linear prediction. The effectiveness of our modeling strategy is illustrated by analyzing the aforementioned Netherland wind speed data that we integrate with a simulation study. The proposed method is implemented in the R package GeoModels.
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and mathematical tractability. However, this assumption seems to be restrictive when dealing with counting data. To deal with this situation, we propose a random field with a Poisson marginal distribution by considering a sequence of independent copies of a random field with an exponential marginal distribution as 'inter-arrival times' in the counting renewal processes framework. Our proposal can be viewed as a spatial generalization of the Poisson process.Unlike the classical hierarchical Poisson Log-Gaussian model, our proposal generates a (non)-stationary random field that is mean square continuous and with Poisson marginal distributions. For the proposed Poisson spatial random field, analytic expressions for the covariance function and the bivariate distribution are provided. In an extensive simulation study, we investigate the weighted pairwise likelihood as a method for estimating the Poisson random field parameters.Finally, the effectiveness of our methodology is illustrated by an analysis of reindeer pellet-group survey data, where a zero-inflated version of the proposed model is compared with zero-inflated Poisson Log-Gaussian and Poisson Gaussian copula models. Supplementary materials for this article, include technical proofs and R code for reproducing the work, are available as an online supplement.
En este artículo se abordarán dos temas relevantes; el primero de ellos se refiere a las causas que explicarían el bajo impacto de la investigación educativa (IE) en la práctica docente (PD) y el segundo, relacionado con la generación de un índice que mida el impacto que tiene la investigación sobre la docencia usando el índice de Fornell. Para lo anterior, se contempló una muestra de 179 individuos, 62 universitarios y 117 docentes no universitarios. Mediante un análisis secundario, y producto de la utilización de ecuaciones estructurales, se identifica un modelo que mostró que la percepción sobre el diagnóstico del impacto de la investigación educativa sobre la práctica de los docentes (IE-PD), explicaba en forma directa la comprensión del fenómeno impacto. El índice de impacto de la IE-PD fue de un 60,23% en contra, que muestra una tendencia de los docentes a considerar no sustantivo el aporte de la Investigación Educativa para su práctica docente. This article will discuss two important subjects. The first is the model of the impact of educational research on teaching practice. The second is the creation of an index that measures the impact of educational research on teaching practice, using structural equation modeling. This study looked at a sample of 179 individuals, of which 62 were university teachers and 117 were non-university teachers. Through a secondary analysis of the data, the different stages of construct validity were developed and structural equation modeling, obtaining a model covered by three constructs represented by 15 items. The model showed that the perception of the diagnosis of the impact of educational research on the practice of teachers directly explained the understanding of the impact phenomenon. The impact index EI-PD was 60.23%, showing that teachers do not substantially consider the contribution of educational research on teaching practice.
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