Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Can neuroimaging be used as a support to diagnosis of borderline personality disorder? An approach based on computational neuroanatomy and machine learning

Several recent studies in literature have identified brain morphological alterations associated to Borderline Personality Disorder (BPD) patients. These findings are reported by studies based on voxel-based-morphometry analysis of structural MRI data, comparing mean gray-matter concentration between groups of BPD patients and healthy controls. On the other hand, mean differences between groups are not informative about the discriminative value of neuroimaging data to predict the group of individual subjects. In this paper, we go beyond mean differences analyses, and explore to what extent individual BPD patients can be differentiated from controls (25 subjects in each group), using a combination of automated-morphometric tools for regional cortical thickness/volumetric estimation and Support Vector Machine classifier. The approach included a feature selection step in order to identify the regions containing most discriminative information. The accuracy of this classifier was evaluated using the leave-one-subject-out procedure. The brain regions indicated as containing relevant information to discriminate groups were the orbitofrontal, rostral anterior cingulate, posterior cingulate, middle temporal cortices, among others. These areas, which are distinctively involved in emotional and affect regulation of BPD patients, were the most informative regions to achieve both sensitivity and specificity values of 80% in SVM classification. The findings suggest that this new methodology can add clinical and potential diagnostic value to neuroimaging of psychiatric disorders. (C) 2012 Elsevier Ltd. All rights reserved.

The polysurvival model with long-term survivors

Long-term survival models have historically been considered for analyzing time-to-event data with long-term survivors fraction. However, situations in which a fraction (1 - p) of systems is subject to failure from independent competing causes of failure, while the remaining proportion p is cured or has not presented the event of interest during the time period of the study, have not been fully considered in the literature. In order to accommodate such situations, we present in this paper a new long-term survival model. Maximum likelihood estimation procedure is discussed as well as interval estimation and hypothesis tests. A real dataset illustrates the methodology.

Temporal Trends of Asthma Mortality Rates in Brazil from 1980 to 2010

Objective. Mortality from asthma has varied among countries during the last several decades. This study aimed to identify temporal trends of asthma mortality in Brazil from 1980 to 2010. Method. We analyzed 6840 deaths of patients aged 5-34 years that occurred in Brazil with the underlying cause of asthma. We applied a log-linear model using Poisson regression to verify peaks and trends. We also calculated the point estimation and 95% confidence interval (CI 95%) of the annual percent change (APC) of the mortality rates, and the average annual percent change (AAPC) for 2001-2010. Results. A decline was observed from 1980 to 1992 [APC = -3.4 (-5.0 to -1.8)], followed by a nonsignificant rise until 1996 [APC = 6.8 (-1.4 to 15.6)], and a new downward trend from 1997 to 2010 [APC = -2.7 (-3.9 to -1.6)]. The APCs varied according to age strata: 5-14 years from 1980 to 2010 [-0.3 (-1.1 to 0.5)]; 15-24 years from 1980 to 1991 [-2.1 (-5.0 to 0.9)], from 1992 to 1996 [6.8 (-6.7 to 22.2)], and from 1997 to 2010 [-3.9 (-5.7 to -2.0)]; 24-25 years from 1980 to 1992 [-2.5 (-4.6 to -0.3)], from 1993 to 1995 [12.0 (-21.1 to 59.1)], and from 1996-2010 [-1.7 (-3.0 to -0.4)]. AAPC from 2001 to 2010 was -1.7 (-3.0 to -0.4); the decline for this period was significant for patients over 15 years old, women, and those living in the Southeast region. Conclusion. Asthma mortality rates in Brazil have been declining since the late 1990s.

Suitability of distance metrics as indexes of home-range size in tropical rodent species

Estimators of home-range size require a large number of observations for estimation and sparse data typical of tropical studies often prohibit the use of such estimators. An alternative may be use of distance metrics as indexes of home range. However, tests of correlation between distance metrics and home-range estimators only exist for North American rodents. We evaluated the suitability of 3 distance metrics (mean distance between successive captures [SD], observed range length [ORL], and mean distance between all capture points [AD]) as indexes for home range for 2 Brazilian Atlantic forest rodents, Akodon montensis (montane grass mouse) and Delomys sublineatus (pallid Atlantic forest rat). Further, we investigated the robustness of distance metrics to low numbers of individuals and captures per individual. We observed a strong correlation between distance metrics and the home-range estimator. None of the metrics was influenced by the number of individuals. ORL presented a strong dependence on the number of captures per individual. Accuracy of SD and AD was not dependent on number of captures per individual, but precision of both metrics was low with numbers of captures below 10. We recommend the use of SD and AD instead of ORL and use of caution in interpretation of results based on trapping data with low captures per individual.

Influence diagnostics for elliptical semiparametric mixed models

In this paper we extend semiparametric mixed linear models with normal errors to elliptical errors in order to permit distributions with heavier and lighter tails than the normal ones. Penalized likelihood equations are applied to derive the maximum penalized likelihood estimates (MPLEs) which appear to be robust against outlying observations in the sense of the Mahalanobis distance. A reweighed iterative process based on the back-fitting method is proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to study the sensitivity of the MPLEs. Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering some appropriate elliptical errors. The local influence approach is used to compare the sensitivity of the model estimates.