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Weighting lower and upper ranks simultaneously through rank-order correlation coefficients

Publication . Aleixo, Sandra; Teles, Julia

Two new weighted correlation coefficients, that allow to give more weight to the lower and upper ranks simultaneously, are proposed. These indexes were obtained computing the Pearson correlation coefficient with a modified Klotz and modified Mood scores. Under the null hypothesis of independence of the two sets of ranks, the asymptotic distribution of these new coefficients was derived. The exact and approximate quantiles were provided. To illustrate the value of these measures an example, that could mimic several biometrical concerns, is presented. A Monte Carlo simulation study was carried out to compare the performance of these new coefficients with other weighted coefficient, the van der Waerden correlation coefficient, and with two non-weighted indexes, the Spearman and Kendall correlation coefficients. The results show that, if the aim of the study is the detection of correlation or agreement between two sets of ranks, putting emphasis on both lower and upper ranks simultaneously, the use of van der Waerden, signed Klotz and signed Mood rank-order correlation coefficients should be privileged, since they have more power to detect this type of agreement, in particular when the concordance was focused on a lower proportion of extreme ranks. The preference for one of the coefficients should take into account the weight one wants to assign to the extreme ranks.

2018-07-04Conference object

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Bifurcation structures in a 2D exponential diffeomorphism with Allee effect

Publication . Rocha, J. Leonel; Taha, Abdel-Kaddous

An embedding of one-dimensional generic growth functions into a two-dimensional diffeomorphism is considered. This family of unimodal maps naturally incorporates a key item of ecological and biological research: the Allee effect. Consequently, the presence of this species extinction phenomenon leads us to a new definition of bifurcation for this two-dimensional exponential diffeomorphism: Allee’s effect bifurcation. The stability and the nature of the fixed points of the two-dimensional diffeomorphism are analyzed, by studying the corresponding contour lines. Fold and flip bifurcation structures of this exponential diffeomorphism are investigated, in which there are flip codimension-2 bifurcation points and cusp points, when some parameters evolve. Numerical studies are included.

2019-03Journal article

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Stability analysis of Gompertz’s logistic growth equation under strong, weak and no allee effects

Publication . Rocha, J. Leonel

The interest and the relevance of the study of population dynamics and extinction phenomenon are the main motivation to investigate the induction of Allee effects in Gompertz’s logistic growth equation. The stability analysis of the equilibrium points of Gompertz’s logistic growth equation under strong, weak and no Allee effects is presented. Properties and sufficient conditions for the existence of strong, weak and no Allee effects for these new continuous population growth models are provided and discussed. It is established a sufficient condition to prove that the time evolution of the population density to the stable equilibria gets larger, as the Allee effects get stronger. These continuous population growth models subjected to Allee effects take longer time to reach its equilibrium states. The developed models are validated using the Icelandic herring population, with GPDD Id.1765.

2016Journal article

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Homoclinic and big bang bifurcations of an embedding of 1D Allee's functions into a 2D diffeomorphism

Publication . Rocha, J. Leonel; Taha, Abdel-Kaddous; Fournier-Prunaret, D.

In this work a thorough study is presented of the bifurcation structure of an embedding of one-dimensional Allee's functions into a two-dimensional diffeomorphism. A complete classification of the nature and stability of the fixed points, on the contour lines of the two-dimensional diffeomorphism, is provided. A necessary and sufficient condition so that the Allee fixed point is a snapback repeller is established. Sufficient conditions for the occurrence of homoclinic tangencies of a saddle fixed point of the two-dimensional diffeomorphism are also established, associated to the snapback repeller bifurcation of the endomorphism defined by the Allee functions. The main results concern homoclinic and big bang bifurcations of the diffeomorphism as "germinal" bifurcations of the Allee functions. Our results confirm previous predictions of structures of homoclinic and big bang bifurcation curves in dimension one and extend these studies to "local" concepts of Allee effect and big bang bifurcations to this two-dimensional exponential diffeomorphism.

2017-08Journal article

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A spatial econometric analysis of the calls to the Portuguese National Health Line

Publication . Simões, Paula; Carvalho, M. Lucília; Aleixo, Sandra; Gomes, Sérgio; Natário, Isabel

The Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health services. This study aims to describe and evaluate the use of LS24. Since for LS24 data, the location attribute is an important source of information to describe its use, this study analyses the number of calls received, at a municipal level, under two different spatial econometric approaches. This analysis is important for future development of decision support indicators in a hospital context, based on the economic impact of the use of this health line. Considering the discrete nature of data, the number of calls to LS24 in each municipality is better modelled by a Poisson model, with some possible covariates: demographic, socio-economic information, characteristics of the Portuguese health system and development indicators. In order to explain model spatial variability, the data autocorrelation can be explained in a Bayesian setting through different hierarchical log-Poisson regression models. A different approach uses an autoregressive methodology, also for count data. A log-Poisson model with a spatial lag autocorrelation component is further considered, better framed under a Bayesian paradigm. With this empirical study we find strong evidence for a spatial structure in the data and obtain similar conclusions with both perspectives of the analysis. This supports the view that the addition of a spatial structure to the model improves estimation, even in the case where some relevant covariates have been included.

2017-06Journal article

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