Fortunato Silva de Menezes

Information criteria: How do they behave in different models?

The choice of the best model is crucial in modeling data, and parsimony is one of the principles that must guide this choice. Despite their broad use in model selection, the foundations of the Akaike information criterion (AIC), the corrected Akaike criterion (AICc) and the Bayesian information criterion (BIC) are, in general, poorly understood. The AIC, AICc and BIC penalize the likelihoods in order to select the simplest model. These criteria are based upon concepts of information and entropy, which are explained in this work, by focusing on a statistical approach. The three criteria are compared through Monte Carlo simulations, and the applications of these criteria are investigated in the selection of normal models, the selection of biological growth models and selection of time series models. For the simulation with normal models, all three criteria exhibited poor performance for a small sample size N=100 (particularly, when the variances are slightly different). For biological growth model simulations with a very small sample size N=13 the AIC and AICc showed better performance in comparison to the BIC. The simulation based on time series models produced results similar to the normal model simulations. For these simulations, the BIC exhibited superior performance, in some cases, in comparison to the other two information criteria (AIC and AICc) for a small sample size N=100, but in other cases, the BIC performed poorly, as did the AIC and AICc.

Data classification with binary response through the Boosting algorithm and logistic regression

Abstract The task of classifying is natural to humans, but there are situations in which a person is not best suited to perform this function, which creates the need for automatic methods of classification. Traditional methods, such as logistic regression, are commonly used in this type of situation, but they lack robustness and accuracy. These methods do not not work very well when the data or when there is noise in the data, situations that are common in expert and intelligent systems. Due to the importance and the increasing complexity of problems of this type, there is a need for methods that provide greater accuracy and interpretability of the results. Among these methods, is Boosting, which operates sequentially by applying a classification algorithm to reweighted versions of the training data set. It was recently shown that Boosting may also be viewed as a method for functional estimation. The purpose of the present study was to compare the logistic regressions estimated by the maximum likelihood model (LRMML) and the logistic regression model estimated using the Boosting algorithm, specifically the Binomial Boosting algorithm (LRMBB), and to select the model with the better fit and discrimination capacity in the situation of presence(absence) of a given property (in this case, binary classification). To illustrate this situation, the example used was to classify the presence (absence) of coronary heart disease (CHD) as a function of various biological variables collected from patients. It is shown in the simulations results based on the strength of the indications that the LRMBB model is more appropriate than the LRMML model for the adjustment of data sets with several covariables and noisy data. The following sections report lower values of the information criteria AIC and BIC for the LRMBB model and that the Hosmer–Lemeshow test exhibits no evidence of a bad fit for the LRMBB model. The LRMBB model also presented a higher AUC, sensitivity, specificity and accuracy and lower values of false positives rates and false negatives rates, making it a model with better discrimination power compared to the LRMML model. Based on these results, the logistic model adjusted via the Binomial Boosting algorithm (LRMBB model) is better suited to describe the problem of binary response, because it provides more accurate information regarding the problem considered.

Determination of prediction intervals for a future number of failures: a statistical and Monte Carlo approach

In this work, we present a new procedure, called sub-sampling, to obtain data concerning time of failure in trials without replacement, (NRT). With this data it is possible to determine the prediction interval (PI) for the future number of failures. We also present an alternative way to evaluate the coverage probability of the prediction interval (PI). The results presented show that the method proposed is reliable and can be useful for the statistical analyses of quality control of processes.

Ridge Path in Mixtures Experiments: Optimal Result with Restriction on Prediction of Variance

In order to evaluate a methodology applied to the ridge analysis in mixing experiments with linear constraints, this article proposes through the construction of a ridge path to obtain the maximum or minimum value of the predicted response under a prediction variance conditioned to a restriction. For this purpose, we considered two experiments mixtures with variables with a lower or upper bound limit. The results were compared with the ones obtained by other methods available in the literature in industrial application. According to the degree of multicollinearity of the variables in each experiment, it was observed that the proposed methodology was efficient to provide predicted response with the value higher than the maximum obtained by existing methods and variance reduced prediction

Resíduos generalizados de Cox-Snell na avaliação do ajuste de modelos

Varios tipos de residuos tem sido propostos para modelos de sobrevivencia, sendo os mais adequados resultado dos residuos generalizados de Cox e Snell (1968). O objetivo com este trabalho e avaliar a adequacidade de modelos por meio de graficos de diagnosticos gerados a partir dos residuos generalizados de Cox-Snell. Para ilustrar a teoria, foram feitas tres aplicacoes. A primeira aplicacao visou a ilustrar a logica existente entre a plotagem dos residuos ordenados de tres distribuicoes, normal (0,1), logistica (0,1) e valor extremo (0,1) versus as estatisticas de ordem esperadas desses residuos de acordo com as distribuicoes assumidas. Para a segunda aplicacao, foram utilizados dados de tempo de vida de isolantes, obtidos em Nelson (1990). A partir da verificacao por meio dos graficos de diagnosticos utilizando-se os residuos generalizados de Cox-Snell, encontrou-se que o modelo apropriado para o tempo de vida dos isolantes era o log-normal. Para a terceira aplicacao, foram analisados dados censurados referentes ao tempo de vida de pacientes, obtidos em Collett (1994). Avaliou-se a adequacidade de varios modelos por meio dos residuos de Cox-Snell adaptados para dados de sobrevivencia. Pelos resultados constatou-se que o modelo Weibull foi o mais adequado.