Simplex Regression Research Articles

The simplex regression model as a methodology of actuarial analysis

The risk management business evolves rapidly, so actuaries are faced with the need for new analysis methodologies. However, the use of incorrect methodologies for actuarial modeling can have serious implications for strategic decision making. This study aims to introduce the simplex regression model as a suitable methodology for actuarial modeling of data whose values belong to the unit interval. Using a risk management data set, the linear model with normal distribution and the proposed regression model were compared. The evaluation of the models presented concluded by the quality of the modeling through simplex regression, indicating the quality of this method as a new analysis tool for the actuarial context.

Improved Likelihood Ratio Tests for Varying Dispersion Simplex Regression Models

AbstractThe simplex regression model is tailored to response variables that assume values in the standard unit interval, such as rates and proportions. The estimation of the parameters that index the model is performed by maximum likelihood, and test inferences are commonly reached using the likelihood ratio test. Such a test is based on an asymptotic approximation, and thus the resulting inferences may be misleading when the sample size is not large. In this paper, Bartlett‐corrected likelihood ratio tests are obtained for varying dispersion simplex regressions. Monte Carlo simulations are performed to compare the finite sample behavior of the corrected tests to that of standard likelihood ratio. The numerical results show that one of the corrected tests displays excellent control of the type I error frequency. An empirical application is presented and discussed.

Bootstrap-based inferential improvements to the simplex nonlinear regression model.

In this paper we evaluate the performance of point and interval estimators based on the maximum likelihood(ML) method for the nonlinear simplex regression model. Inferences based on traditional maximum likelihood estimation have good asymptotic properties, but their performance in small samples may not be satisfactory. At out set we consider the maximum likelihood estimation for the parameters of the nonlinear simplex regression model, and so we introduced a bootstrap-based correction for such estimators of this model. We also develop the percentile and bootstrapt confidence intervals for those parameters as competitors to the traditional approximate confidence interval based on the asymptotic normality of the maximum likelihood estimators (MLEs). We then numerically evaluate the performance of these different methods for estimating the simplex regression model. The numerical evidence favors inference based on the bootstrap method, in special the bootstrapt interval, which was decisive in an application to real data.

Testing distributional assumption of unit-Lindley regression model

This paper proposes smooth goodness of fit test statistic and its components to test the distributional assumption of the unit-Lindley regression model, which is useful for describing data measured between zero and one. Orthonormal polynomials on the unit-Lindley distribution, score functions and Fisher's information matrix are provided for the smooth test. Deviance and Pearson's chi-square tests are also adapted to the unit-Lindley regression model. A parametric bootstrap simulation study is conducted to compare type I errors and powers of the tests under different scenarios. Empirical findings demonstrate that the first smooth component, deviance, and chi-square tests have undesirable behavior for the unit-Lindley regression model. A real data set is analyzed by using the developed tests to show the adequacy of the unit-Lindley regression model. Model selection criteria and residual analysis prove that the unit-Lindley regression model provides a better fit than the Beta and simplex regression models for the real data set.

SimBetaReg Web-Tool: The Easiest Way to Implement the Beta and Simplex Regression Models

When the response variable is defined on the (0,1) interval, the beta and simplex regression models are commonly used by researchers. However, there is no software support for these models to make their implementation easy for researchers. In this study, we developed a web-tool, named SimBetaReg, to help researchers who are not familiar with programming to implement the beta and simplex regression models. The developed application is free and works independently from the operating systems. Additionally, we model the incidence ratios of COVID-19 with educational and civic engagement indicators of the OECD countries using the SimBetaReg web-tool. Empirical findings show that when the educational attainment, years in education, and voter turnout increase, the incidence ratios of the countries decrease.

Beta regression model nonlinear in the parameters with additive measurement errors in variables.

We propose in this paper a general class of nonlinear beta regression models with measurement errors. The motivation for proposing this model arose from a real problem we shall discuss here. The application concerns a usual oil refinery process where the main covariate is the concentration of a typically measured in error reagent and the response is a catalyst’s percentage of crystallinity involved in the process. Such data have been modeled by nonlinear beta and simplex regression models. Here we propose a nonlinear beta model with the possibility of the chemical reagent concentration being measured with error. The model parameters are estimated by different methods. We perform Monte Carlo simulations aiming to evaluate the performance of point and interval estimators of the model parameters. Both results of simulations and the application favors the method of estimation by maximum pseudo-likelihood approximation.

Use of an Unmanned Aerial Vehicle (UAV) to Document Vegetation Coverage Rate in Managed Grasslands Following a Historic River Flood

Abstract Our objective was to document the vegetation coverage rate of grasslands impacted by a historic flood event that occurred May and June 2019 within the Arkansas river valley. Primary flooding within the observation area lasted 21 d with a maximum water depth of 3m above flood stage. Three cooperator fields were monitored. Aerial images were captured at 7, 14, 33, and 48 d following water recession. Geo-referenced images were captured at 76.2 m above ground level using an UAV fitted with an integrated camera and a secondary camera with a near infrared filter. Images were stitched and aligned prior to vegetation indexing. Two vegetation indices were calculated: green leaf index (GLI, using the integrated camera color bands) and normalized difference vegetative index (NDVI, using the secondary camera color bands). Image pixels were classified as green vegetation or non-vegetation based on a threshold for each processed image’s indices. The estimated proportion green vegetation was modeled as a dependent variable with day (post water recession) and index method as fixed covariates. A simplex regression model (simplexreg package for R) was chosen for analyzing longitudinal proportion data. Both day (P < 0.001) and index method (P = 0.002) were significant with NDVI predicting less vegetation than GLI. The estimated daily coverage rate was 0.02 ± 0.003. Although fields achieved 90% coverage in 45 d, each cooperator experienced different outcomes in plant community. A d 48 field inventory indicated 38 to 77% undesirable species. The field with the greatest percentage undesirable species was covered with barnyardgrass. Assessment of residual statistics suggests NDVI likely under-estimated vegetation cover of this field on d 48. At inventory, this grass’ growth appeared very erect, with sufficient plant spacing that soil may have influenced NDVI more than GLI. These results demonstrate green vegetation coverage can be estimated without specialized UAV cameras. The UAV was helpful in that it accounted for the entire field at high resolution and images could be captured on cloudy days. Documented flood impacts will be useful in future events.

A structural enriched functional network: An application to predict brain cognitive performance.

The structure-function coupling in brain networks has emerged as an important research topic in modern neuroscience. The structural network could provide the backbone of the functional network. The integration of the functional network with structural information can help us better understand functional communication in the brain. This paper proposed a method to accurately estimate the brain functional network enriched by the structural network from diffusion magnetic resonance imaging. First, we adopted a simplex regression model with graph-constrained Elastic Net to construct the functional networks enriched by the structural network. Then, we compared the constructed network characteristics of this approach with several state-of-the-art competing functional network models. Furthermore, we evaluated whether the structural enriched functional network model improves the performance for predicting the cognitive-behavioral outcomes. The experiments have been performed on 218 participants from the Human Connectome Project database. The results demonstrated that our network model improves network consistency and its predictive performance compared with several state-of-the-art competing functional network models.

The beta and simplex regression models to explain homicides in state capitals of Brazil

The intentional killing of one human being by its own kind is considered the worst of the crimes. Therefore, homicide prevention is a major concern for policy makers in both developing and developed countries. We propose regression modeling for the homicide rates in Brazil along with appropriately chosen distributions for these responses that are in agreement with the restriction of values to the unit interval. We adopt the beta and simplex regression models with systematic components for the mean and dispersion parameters to explain the homicide rates in 27 state capitals of Brazil from the following explanatory variables: time, Gini coefficient, municipal human development index (MHDI), illiteracy and poverty rates. We employ standard likelihood techniques, perform influence and residual analysis and calculate goodness-of-fit statistics to select the best regression to explain homicides rates in these capitals. We perform the computations in the R package. The main results suggest the following: the mean homicide rate is increasing over time; there is a negative correlation between MHDI and murder rate; the poverty has a quite small negative impact on the mean homicide rates in the beta regression. The Gini coefficient and the illiteracy and poverty rates explain the dispersion of the homicide rates.

A simplex dispersion model for improving precision in the odds ratio confidence interval in mixture experiments

A new approach to data analysis in mixture experiments is proposed using the simplex regression, that is in the class of dispersion models family. The advantages of this approach are illustrated in an experiment studying the mixture effect of fat, carbohydrate, and fiber on tumors’ proportion in mammary glands of rats. Model was evaluated by goodness of fit criteria, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals. The simplex regression model showed better quality of fit and smaller odds ratio confidence intervals.

Structural Connectivity Enriched Functional Brain Network using Simplex Regression with GraphNet.

The connectivity analysis is a powerful technique for investigating a hard-wired brain architecture as well as flexible, functional dynamics tied to human cognition. Recent multi-modal connectivity studies had the challenge of combining functional and structural connectivity information into one integrated network. In this paper, we proposed a simplex regression model with graph-constrained Elastic Net (GraphNet) to estimate functional networks enriched by structural connectivity in a biologically meaningful way with a low model complexity. Our model constructed the functional networks using sparse simplex regression framework and enriched structural connectivity information based on GraphNet constraint. We applied our model on the real neuroimaging datasets to show its ability for predicting a clinical score. Our results demonstrated that integrating multi-modal features could detect more sensitive and subtle brain biomarkers than using a single modality.

Zero-one-inflated simplex regression models for the analysis of continuous proportion data

Zero-one-inflated simplex regression models for the analysis of continuous proportion data

Machine learning based on extended generalized linear model applied in mixture experiments

When performing mixture experiments, we observe that maximum likelihood methods present problems related to the collinearity, small sample size, and over/under dispersion. In order to overcome these problems, this investigation proposes a model built in accordance with a machine learning approach. This approach will be called Boosted Simplex Regression, which has been evaluated both in terms of accuracy and precision for the odds ratio. The advantages of this new approach are illustrated in a mixture experiment, which has made us conclude that the model Boosted Simplex Regression has unveiled not only better fit quality but also more precise odds ratio confidence intervals.

Modelos de regressão para dados de proporção: Beta e Simplex com aplicação ao IDHM 2010

O objetivo deste artigo foi investigar o IDHM de 2010 a partir de alguns indicadores de aspecto socioeconômico e espacial, com intuito de averiguar a existência de relações entre eles. Foram aplicadas técnicas de estatística descritiva para visualização do comportamento dos dados e os modelos de regressão Beta e Simplex, que são adequados para a modelagem de taxas e proporções. Os resultados permitiram constatar que os modelos apresentaram estimativas e conclusões bastante similares, quando considerado a modelagem da média. Além disso, verificou-se uma considerável conformidade na relação entre os indicadores sociais selecionados e a variável resposta.

The unit-improved second-degree Lindley distribution: inference and regression modeling

We define a new one-parameter model on the unit interval, called the unit-improved second-degree Lindley distribution, and obtain some of its structural properties. The methods of maximum likelihood, bias-corrected maximum likelihood, moments, least squares and weighted least squares are used to estimate the unknown parameter. The finite sample performance of these methods are investigated by means of Monte Carlo simulations. Moreover, we introduce a new regression model as an alternative to the beta, unit-Lindley and simplex regression models and present a residual analysis based on Pearson and Cox–Snell residuals. The new models are proved empirically to be competitive to the beta, Kumaraswamy, simplex, unit-Lindley, unit-Gamma and Topp–Leone models by means of two real data sets. Empirical findings indicate that the proposed models can provide better fits than other competitive models when the data are close to the boundaries of the unit interval.

Simplex regression models with measurement error

This paper considers the simplex regression model when there is measurement error in the covariate. We consider a structural approach where the measurement error follows a normal or gamma distribution. We apply a Monte Carlo EM algorithm to estimate the parameters using a pseudo-likelihood function. A simulation study is used to investigate the impact of ignoring the measurement error. Finally, the results are illustrated with a data set.

Residual and influence analysis to a general class of simplex regression

In this paper, we propose a residual and local influence analysis for diagnostics in a general class of simplex regression model. Here, we introduce this class in which the predictors involve covariates and nonlinear functions in the parameters. We provide closed-form expressions for the score functions, information matrices, as well a procedure for the choice of initial guesses to be used in the Fisher’s iterative scheme for the estimation by maximum likelihood. All diagnostic techniques were also adjusted for the linear simplex model. We present Monte Carlo simulations to investigate the empirical distribution of the proposed residual and the performance of the starting points scheme. We also performed three applications to real data; one of them explores the features of nonlinear regressions. By performing diagnostic analysis, we compare the beta and simplex fits to two datasets. The applications results favor the simplex regression to fit data close to the boundaries of the unit interval. Indeed, the simplex regression can present estimation by maximum likelihood procedure more robust to influential cases than the beta regression.

A semiparametric Bayesian approach to simplex regression model with heterogeneous dispersion

ABSTRACTSimplex regression model is often employed to analyze continuous proportion data in many studies. In this paper, we extend the assumption of a constant dispersion parameter (homogeneity) to varying dispersion parameter (heterogeneity) in Simplex regression model, and present the B-spline to approximate the smoothing unknown function within the Bayesian framework. A hybrid algorithm combining the block Gibbs sampler and the Metropolis-Hastings algorithm is presented for sampling observations from the posterior distribution. The procedures for computing model comparison criteria such as conditional predictive ordinate statistic, deviance information criterion, and averaged mean squared error are presented. Also, we develop a computationally feasible Bayesian case-deletion influence measure based on the Kullback-Leibler divergence. Several simulation studies and a real example are employed to illustrate the proposed methodologies.

The Development of the Mozambican Banking Sector and Strategic Fit of Mergers and Acquisitions: A Two‐Stage DEA Approach

AbstractThis paper examines the strategic fit of mergers and acquisitions (M&A) in Mozambican banks, using a two‐stage data envelopment analysis (DEA) approach to compute the impact of contextual variables on efficiency scores and returns to scale of the resulting virtual merged banks. In an ‘M&A DEA’ model, different pairs of bidder and target companies are considered. In the first stage an M&A DEA model is used. Simplex regression is adopted in the second stage. The results reveal that ownership (public or foreign) impacts virtual efficiency levels. However, the findings also show that care must be exercised with M&A because the resultant banking organization could be oversized when foreign ownership is predominant, especially when public ownership is low. Given the relative sizes of the markets in terms of productive resources, M&A involving Mozambican banks can easily lead to decreasing returns to scale. Thus, a greater emphasis should be given to merging purely public banks with foreign ones and vice versa.

Efficiency in Latin American airlines: A two-stage approach combining Virtual Frontier Dynamic DEA and Simplex Regression

This paper presents an efficiency assessment of Latin American airlines, using VDRAM-DEA (Virtual Frontier Dynamic Range Adjusted Model - Data Envelopment Analysis). In VDRAM, the reference and DMU evaluation sets are different, thus allowing higher discrimination of scoring. In this research, the VDRAM model is used first in a two-stage approach. In the second stage, Simplex Regression is adopted to handle skewed and asymmetrical efficiency scores. The results corroborate previous studies and reveal that the impact of fleet mix and public ownership cannot be overlooked in Latin American airlines, which seem to be affected by insufficient load factors and hub and spoke systems. For the same reasons, although low cost carriers are an emerging trend in the region, it was not possible to confirm their higher efficiency levels. Besides, to some extent, these findings also show the absence of a learning curve in Latin American airlines.