Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

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.

Finite-size corrections of the entanglement entropy of critical quantum chains

Using the density matrix renormalization group, we calculated the finite-size corrections of the entanglement alpha-Renyi entropy of a single interval for several critical quantum chains. We considered models with U(1) symmetry such as the spin-1/2 XXZ and spin-1 Fateev-Zamolodchikov models, as well as models with discrete symmetries such as the Ising, the Blume-Capel, and the three-state Potts models. These corrections contain physically relevant information. Their amplitudes, which depend on the value of a, are related to the dimensions of operators in the conformal field theory governing the long-distance correlations of the critical quantum chains. The obtained results together with earlier exact and numerical ones allow us to formulate some general conjectures about the operator responsible for the leading finite-size correction of the alpha-Renyi entropies. We conjecture that the exponent of the leading finite-size correction of the alpha-Renyi entropies is p(alpha) = 2X(epsilon)/alpha for alpha > 1 and p(1) = nu, where X-epsilon denotes the dimensions of the energy operator of the model and nu = 2 for all the models.

Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data

In this paper, we propose nonlinear elliptical models for correlated data with heteroscedastic and/or autoregressive structures. Our aim is to extend the models proposed by Russo et al. [22] by considering a more sophisticated scale structure to deal with variations in data dispersion and/or a possible autocorrelation among measurements taken throughout the same experimental unit. Moreover, to avoid the possible influence of outlying observations or to take into account the non-normal symmetric tails of the data, we assume elliptical contours for the joint distribution of random effects and errors, which allows us to attribute different weights to the observations. We propose an iterative algorithm to obtain the maximum-likelihood estimates for the parameters and derive the local influence curvatures for some specific perturbation schemes. The motivation for this work comes from a pharmacokinetic indomethacin data set, which was analysed previously by Bocheng and Xuping [1] under normality.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.

Pollination services at risk: Bee habitats will decrease owing to climate change in Brazil

Native bees are important providers of pollination services, but there are cumulative evidences of their decline. Global changes such as habitat losses, invasions of exotic species and climate change have been suggested as the main causes of the decline of pollinators. In this study, the influence of climate change on the distribution of 10 species of Brazilian bees was estimated with species distribution modelling. We used Maxent algorithm (maximum entropy) and two different scenarios, an optimistic and a pessimistic, to the years 2050 and 2080. We also evaluated the percentage reduction of species habitat based on the future scenarios of climate change through Geographic Information System (GIS). Results showed that the total area of suitable habitats decreased for all species but one under the different future scenarios. The greatest reductions in habitat area were found for Melipona bicolor bicolor and Melipona scutellaris, which occur predominantly in areas related originally to Atlantic Moist Forest. The species analysed have been reported to be pollinators of some regional crops and the consequence of their decrease for these crops needs further clarification. (C) 2012 Elsevier B.V. All rights reserved.

Local power and size properties of the LR, Wald, score and gradient tests in dispersion models

We derive asymptotic expansions for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the class of dispersion models, under a sequence of Pitman alternatives. The asymptotic distributions of these statistics are obtained for testing a subset of regression parameters and for testing the precision parameter. Based on these nonnull asymptotic expansions, the power of all four tests, which are equivalent to first order, are compared. Furthermore, in order to compare the finite-sample performance of these tests in this class of models, Monte Carlo simulations are presented. An empirical application to a real data set is considered for illustrative purposes. (C) 2012 Elsevier B.V. All rights reserved.

Assessing malaria transmission in a low endemicity area of north-western Peru

Background Where malaria endemicity is low, control programmes need increasingly sensitive tools for monitoring malaria transmission intensity (MTI) and to better define health priorities. A cross-sectional survey was conducted in a low endemicity area of the Peruvian north-western coast to assess the MTI using both molecular and serological tools. Methods Epidemiological, parasitological and serological data were collected from 2,667 individuals in three settlements of Bellavista district, in May 2010. Parasite infection was detected using microscopy and polymerase chain reaction (PCR). Antibodies to Plasmodium vivax merozoite surface protein-119 (PvMSP119) and to Plasmodium falciparum glutamate-rich protein (PfGLURP) were detected by ELISA. Risk factors for exposure to malaria (seropositivity) were assessed by multivariate survey logistic regression models. Age-specific antibody prevalence of both P. falciparum and P. vivax were analysed using a previously published catalytic conversion model based on maximum likelihood for generating seroconversion rates (SCR). Results The overall parasite prevalence by microscopy and PCR were extremely low: 0.3 and 0.9%, respectively for P. vivax, and 0 and 0.04%, respectively for P. falciparum, while seroprevalence was much higher, 13.6% for P. vivax and 9.8% for P. falciparum. Settlement, age and occupation as moto-taxi driver during previous year were significantly associated with P. falciparum exposure, while age and distance to the water drain were associated with P. vivax exposure. Likelihood ratio tests supported age seroprevalence curves with two SCR for both P. vivax and P. falciparum indicating significant changes in the MTI over time. The SCR for PfGLURP was 19-fold lower after 2002 as compared to before (λ1 = 0.022 versus λ2 = 0.431), and the SCR for PvMSP119 was four-fold higher after 2006 as compared to before (λ1 = 0.024 versus λ2 = 0.006). Conclusion Combining molecular and serological tools considerably enhanced the capacity of detecting current and past exposure to malaria infections and related risks factors in this very low endemicity area. This allowed for an improved characterization of the current human reservoir of infections, largely hidden and heterogeneous, as well as providing insights into recent changes in species specific MTIs. This approach will be of key importance for evaluating and monitoring future malaria elimination strategies.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

Evolution of extrafloral nectaries: adaptive process and selective regime changes from forest to savanna

Much effort has been devoted to understanding the function of extrafloral nectaries (EFNs) for antplantherbivore interactions. However, the pattern of evolution of such structures throughout the history of plant lineages remains unexplored. In this study, we used empirical knowledge on plant defences mediated by ants as a theoretical framework to test specific hypotheses about the adaptive role of EFNs during plant evolution. Emphasis was given to different processes (neutral or adaptive) and factors (habitat change and trade-offs with new trichomes) that may have affected the evolution of antplant associations. We measured seven EFN quantitative traits in all 105 species included in a well-supported phylogeny of the tribe Bignonieae (Bignoniaceae) and collected field data on antEFN interactions in 32 species. We identified a positive association between ant visitation (a surrogate of ant guarding) and the abundance of EFNs in vegetative plant parts and rejected the hypothesis of phylogenetic conservatism of EFNs, with most traits presenting K-values < 1. Modelling the evolution of EFN traits using maximum likelihood approaches further suggested adaptive evolution, with static-optimum models showing a better fit than purely drift models. In addition, the abundance of EFNs was associated with habitat shifts (with a decrease in the abundance of EFNs from forest to savannas), and a potential trade-off was detected between the abundance of EFNs and estipitate glandular trichomes (i.e. trichomes with sticky secretion). These evolutionary associations suggest divergent selection between species as well as explains K-values < 1. Experimental studies with multiple lineages of forest and savanna taxa may improve our understanding of the role of nectaries in plants. Overall, our results suggest that the evolution of EFNs was likely associated with the adaptive process which probably played an important role in the diversification of this plant group.

THE LOG-BURR XII REGRESSION MODEL FOR GROUPED SURVIVAL DATA

The log-Burr XII regression model for grouped survival data is evaluated in the presence of many ties. The methodology for grouped survival data is based on life tables, where the times are grouped in k intervals, and we fit discrete lifetime regression models to the data. The model parameters are estimated by maximum likelihood and jackknife methods. To detect influential observations in the proposed model, diagnostic measures based on case deletion, so-called global influence, and influence measures based on small perturbations in the data or in the model, referred to as local influence, are used. In addition to these measures, the total local influence and influential estimates are also used. We conduct Monte Carlo simulation studies to assess the finite sample behavior of the maximum likelihood estimators of the proposed model for grouped survival. A real data set is analyzed using a regression model for grouped data.