Carlos Alberto Ribeiro Diniz

On the impact of disproportional samples in credit scoring models: An application to a Brazilian bank data

Statistical methods have been widely employed to assess the capabilities of credit scoring classification models in order to reduce the risk of wrong decisions when granting credit facilities to clients. The predictive quality of a classification model can be evaluated based on measures such as sensitivity, specificity, predictive values, accuracy, correlation coefficients and information theoretical measures, such as relative entropy and mutual information. In this paper we analyze the performance of a naive logistic regression model (Hosmer & Lemeshow, 1989) and a logistic regression with state-dependent sample selection model (Cramer, 2004) applied to simulated data. Also, as a case study, the methodology is illustrated on a data set extracted from a Brazilian bank portfolio. Our simulation results so far revealed that there is no statistically significant difference in terms of predictive capacity between the naive logistic regression models and the logistic regression with state-dependent sample selection models. However, there is strong difference between the distributions of the estimated default probabilities from these two statistical modeling techniques, with the naive logistic regression models always underestimating such probabilities, particularly in the presence of balanced samples.

Bayesian analysis of a correlated binomial model

In this paper a Bayesian approach is applied to the correlated binomial model, CB(n,p,ρ), proposed by Luceno (Comput. Statist. Data Anal. 20 (1995) 511–520). The data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. MCMC methods, including Gibbs sampling and Metropolis within Gibbs, are applied to estimate the posterior marginal for the probability of success p and for the correlation coefficient ρ. The sensitivity of the posterior is studied taking into account several reference priors and it is shown that the posterior characteristics appear not to be influenced by these prior distributions. The article is motivated by a study of plant selection.

Correlated binomial regression models

In this paper, a class of correlated binomial regression models is proposed. The model is based on the generalized binomial distribution proposed by Luceno (1995) and Luceno and Ceballos (1995). The regression structure is modeled by using four different link functions and the dependence between the Bernoulli trials is modeled by using three different correlation functions. A data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. A Bayesian method for inference is developed for the proposed model which relies on both the data augmentation scheme and the MCMC algorithms to obtain the posterior estimate for the parameters. Two types of Bayesian residuals and a local influence measure from a Bayesian perspective are proposed to check the underlying model assumptions, as well as to identify the presence of outliers and/or influential observations. Simulation studies are presented in order to illustrate the performance of the developed methodology. A real data set is analyzed by using the proposed models.

A Generalized Approach to the Modeling of the Species-Area Relationship

This paper proposes a statistical generalized species-area model (GSAM) to represent various patterns of species-area relationship (SAR), which is one of the fundamental patterns in ecology. The approach enables the generalization of many preliminary models, as power-curve model, which is commonly used to mathematically describe the SAR. The GSAM is applied to simulated data set of species diversity in areas of different sizes and a real-world data of insects of Hymenoptera order has been modeled. We show that the GSAM enables the identification of the best statistical model and estimates the number of species according to the area.

Determinação do limiar de anaerobiose de idosos saudáveis: comparação entre diferentes métodos

OBJECTIVE: To determine the anaerobic threshold by the graphic visual ventilatory method and the Hinkley and heteroscedastic mathematical models, applied to heart rate, myoelectric root mean square (RMS) signal and VCO2 datasets, and to compare the anaerobic threshold obtained by the three methods. METHOD: Nine active elderly subjects were studied (aged 61.4 ± 1.8 years) during a ramp-load continuous dynamic physical exercise test on a cycle ergometer, with power ranging from 10 to 15 Watts/min. Beat-to-beat heart rate data, electromyographic data from the surface of the vastus lateralis muscle, and breath-to-breath ventilatory data were collected. After applying mathematical models and identifying the behavioral shift points, these power levels, heart rates and VO2 values were noted and these were compared and correlated with those obtained by the graphic visual model (gold standard). The Friedman test for multiple comparisons and the Spearman correlation test were utilized (significance level: 5%). RESULTS: No significant differences were found in relation to the gold standard, between the power levels, VO2 values and heart rates at the anaerobic threshold identified by the different models. Significant correlations were found between the heart rates identified by the mathematical models, between the VO2 values identified by the heart rates, and between power rates only when identified by the Hinkley model applied to myoelectric RMS signal data. CONCLUSION: In this study group, the mathematical models were shown to be adequate for non-invasively determining the anaerobic threshold. Both models worked best on the heart rate data, followed by VCO2 and RMS.

Statistical monitoring of a web server for error rates: a bivariate time-series copula-based modeling approach

ABSTRACT The monitoring of web servers through statistical frameworks is of utmost important in order to verify possible suspicious anomalies in network traffic or misuse actions that compromise integrity, confidentiality, and availability of information. In this paper, by considering the Plackett copula function, we propose a bivariate beta-autoregressive moving average time-series model for proportion data over time, which is the case for variables present in web server monitoring such as error rates. To illustrate the proposed methodology, we monitor a Brazilian web servers rate of connection synchronization and rejection errors in a web system, with error logging rate in the past 10 min. In essence, the entire methodology may be generalized to any number of time-series of error rates.

CREDIT SCORING MODELING WITH STATE-DEPENDENT SAMPLE SELECTION: A COMPARISON STUDY WITH THE USUAL LOGISTIC MODELING

Statistical methods have been widely employed to assess the capabilities of credit scoring classification models in order to reduce the risk of wrong decisions when granting credit facilities to clients. The predictive quality of a classification model can be evaluated based on measures such as sensitivity, specificity, predictive values, accuracy, correlation coefficients and information theoretical measures, such as relative entropy and mutual information. In this paper we analyze the performance of a naive logistic regression model, a logistic regression with state-dependent sample selection model and a bounded logistic regression model via a large simulation study. Also, as a case study, the methodology is illustrated on a data set extracted from a Brazilian retail bank portfolio. Our simulation results so far revealed that there is nostatistically significant difference in terms of predictive capacity among the naive logistic regression models, the logistic regression with state-dependent sample selection models and the bounded logistic regression models. However, there is difference between the distributions of the estimated default probabilities from these three statistical modeling techniques, with the naive logistic regression models and the boundedlogistic regression models always underestimating such probabilities, particularly in the presence of balanced samples. Which are common in practice.

Skew-normal distribution for growth curve models in presence of a heteroscedasticity structure

In general, growth models are adjusted under the assumptions that the error terms are homoscedastic and normally distributed. However, these assumptions are often not verified in practice. In this work we propose four growth models (Morgan–Mercer–Flodin, von Bertalanffy, Gompertz, and Richards) considering different distributions (normal, skew-normal) for the error terms and three different covariance structures. Maximum likelihood estimation procedure is addressed. A simulation study is performed in order to verify the appropriateness of the proposed growth curve models. The methodology is also illustrated on a real dataset.

Bayesian residual analysis for beta-binomial regression models

The beta-binomial regression model is an alternative model to the sum of any sequence of equicorrelated binary variables with common probability of success p. In this work a Bayesian perspective of this model is presented considering different link functions and different correlation structures. A general Bayesian residual analysis for this model, a issue which is often neglected in Bayesian analysis, using the residuals based on the predicted values obtained by the conditional predictive ordinate [1], the residuals based on the posterior distribution of the model parameters [2] and the Bayesian deviance residual [3] are presented in order to check the assumptions in the model.

The use of several link functions on a beta regression model: a Bayesian approach

By using a reparametrization that translates the beta distribution parameters in a location‐scale form, this paper presents a beta regression model in the presence of three different link functions in order to provide a relationship between the covariates and the response variable. A Bayesian approach is used to estimate the regression coefficients.