A log-extended Weibull regression model

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which has the ability to deal with bathtub-shaped failure rate functions. We use the method of maximum likelihood to estimate the model parameters and some inferential procedures are presented. We reanalyze a real data set under the new model and the log-modified Weibull regression model. We perform a model check based on martingale-type residuals and generated envelopes and the statistics AIC and BIC to select appropriate models. (C) 2009 Elsevier B.V. All rights reserved.

The generalized log-gamma mixture model with covariates: local influence and residual analysis

In a sample of censored survival times, the presence of an immune proportion of individuals who are not subject to death, failure or relapse, may be indicated by a relatively high number of individuals with large censored survival times. In this paper the generalized log-gamma model is modified for the possibility that long-term survivors may be present in the data. The model attempts to separately estimate the effects of covariates on the surviving fraction, that is, the proportion of the population for which the event never occurs. The logistic function is used for the regression model of the surviving fraction. Inference for the model parameters is considered via maximum likelihood. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. Finally, a data set from the medical area is analyzed under the log-gamma generalized mixture model. A residual analysis is performed in order to select an appropriate model.

Bias-corrected Pearson estimating functions for Taylor`s power law applied to benthic macrofauna data

Estimation of Taylor`s power law for species abundance data may be performed by linear regression of the log empirical variances on the log means, but this method suffers from a problem of bias for sparse data. We show that the bias may be reduced by using a bias-corrected Pearson estimating function. Furthermore, we investigate a more general regression model allowing for site-specific covariates. This method may be efficiently implemented using a Newton scoring algorithm, with standard errors calculated from the inverse Godambe information matrix. The method is applied to a set of biomass data for benthic macrofauna from two Danish estuaries. (C) 2011 Elsevier B.V. All rights reserved.

Different Approaches for Modeling Grouped Survival Data: A Mango Tree Study

Interval-censored survival data, in which the event of interest is not observed exactly but is only known to occur within some time interval, occur very frequently. In some situations, event times might be censored into different, possibly overlapping intervals of variable widths; however, in other situations, information is available for all units at the same observed visit time. In the latter cases, interval-censored data are termed grouped survival data. Here we present alternative approaches for analyzing interval-censored data. We illustrate these techniques using a survival data set involving mango tree lifetimes. This study is an example of grouped survival data.

Log-modified Weibull regression models with censored data: Sensitivity and residual analysis

This paper proposes a regression model considering the modified Weibull distribution. This distribution can be used to model bathtub-shaped failure rate functions. Assuming censored data, we consider maximum likelihood and Jackknife estimators for the parameters of the model. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and we also present some ways to perform global influence. Besides, for different parameter settings, sample sizes and censoring percentages, various simulations are performed and the empirical distribution of the modified deviance residual is displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for a martingale-type residual in log-modified Weibull regression models with censored data. Finally, we analyze a real data set under log-modified Weibull regression models. A diagnostic analysis and a model checking based on the modified deviance residual are performed to select appropriate models. (c) 2008 Elsevier B.V. All rights reserved.

Regression models for grouped survival data: Estimation and sensitivity analysis

In this study, regression models are evaluated for grouped survival data when the effect of censoring time is considered in the model and the regression structure is modeled through four link functions. The methodology for grouped survival data is based on life tables, and the times are grouped in k intervals so that ties are eliminated. Thus, the data modeling is performed by considering the discrete models of lifetime regression. The model parameters are estimated by using the maximum likelihood and jackknife methods. To detect influential observations in the proposed models, diagnostic measures based on case deletion, which are denominated 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 those measures, the local influence and the total influential estimate are also employed. Various simulation studies are performed and compared to the performance of the four link functions of the regression models for grouped survival data for different parameter settings, sample sizes and numbers of intervals. Finally, a data set is analyzed by using the proposed regression models. (C) 2010 Elsevier B.V. All rights reserved.

The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

A Model for comparing reduced impact logging with conventional logging for an Eastern Amazonian Forest

Using data from a logging experiment in the eastern Brazilian Amazon region, we develop a matrix growth and yield model that captures the dynamic effects of harvest system choice on forest structure and composition. Multinomial logistic regression is used to estimate the growth transition parameters for a 10-year time step, while a Poisson regression model is used to estimate recruitment parameters. The model is designed to be easily integrated with an economic model of decisionmaking to perform tropical forest policy analysis. The model is used to compare the long-run structure and composition of a stand arising from the choice of implementing either conventional logging techniques or more carefully planned and executed reduced-impact logging (RIL) techniques, contrasted against a baseline projection of an unlogged forest. Results from log and leave scenarios show that a stand logged according to Brazilian management requirements will require well over 120 years to recover its initial commercial volume, regardless of logging technique employed. Implementing RIL, however, accelerates this recovery. Scenarios imposing a 40-year cutting cycle raise the possibility of sustainable harvest volumes, although at significantly lower levels than is implied by current regulations. Meeting current Brazilian forest policy goals may require an increase in the planned total area of permanent production forest or the widespread adoption of silvicultural practices that increase stand recovery and volume accumulation rates after RIL harvests. Published by Elsevier B.V.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Modeling soil organic carbon dynamics in Oxisols of Ibiruba (Brazil) with the Century Model

introduction of conservation practices in degraded agricultural land will generally recuperate soil quality, especially by increasing soil organic matter. This aspect of soil organic C (SOC) dynamics under distinct cropping and management systems can be conveniently analyzed with ecosystem models such as the Century Model. In this study, Century was used to simulate SOC stocks in farm fields of the Ibiruba region of north central Rio Grande do Sul state in Southern Brazil. The region, where soils are predominantly Oxisols, was originally covered with subtropical woodlands and grasslands. SOC dynamics was simulated with a general scenario developed with historical data on soil management and cropping systems beginning with the onset of agriculture in 1900. From 1993 to 2050, two contrasting scenarios based on no-tillage soil management were established: the status quo scenario, with crops and agricultural inputs as currently practiced in the region and the high biomass scenario with increased frequency of corn in the cropping system, resulting in about 80% higher biomass addition to soils. Century simulations were in close agreement with SOC stocks measured in 2005 in the Oxisols with finer texture surface horizon originally under woodlands. However, simulations in the Oxisols with loamy surface horizon under woodlands and in the grassland soils were not as accurate. SOC stock decreased from 44% to 50% in fields originally under woodland and from 20% to 27% in fields under grasslands with the introduction of intensive annual grain crops with intensive tillage and harrowing operations. The adoption of conservation practices in the 1980s led to a stabilization of SOC stocks followed by a partial recovery of native stocks. Simulations to 2050 indicate that maintaining status quo would allow SOC stocks to recover from 81% to 86% of the native stocks under woodland and from 80% to 91 % of the native stocks under grasslands. Adoption of a high biomass scenario would result in stocks from 75% to 95% of the original stocks under woodlands and from 89% to 102% in the grasslands by 2050. These simulations outcomes underline the importance of cropping system yielding higher biomass to further increase SOC content in these Oxisols. This application of the Century Model could reproduce general trends of SOC loss and recovery in the Oxisols of the Ibiruba region. Additional calibration and validation should be conducted before extensive usage of Century as a support tool for soil carbon sequestration projects in this and other regions can be recommended. (C) 2009 Elsevier B.V. All rights reserved.

Deciphering the weathering processes using environmental mineralogy and geochemistry: Towards an integrated model of laterite and podzol genesis in the Upper Amazon Basin

This article reports major results from collaborative research between France and Brazil on soil and water systems, carried out in the Upper Amazon Basin. It reveals the weathering processes acting in the partly inundated, low elevation plateaus of the Basin, mostly covered by evergreen forest. Our findings are based on geochemical data and mineral spectroscopy that probe the crystal chemistry of Fe and Al in mineral phases (mainly kaolinite, Al- and Fe-(hydr)oxides) of tropical soils (laterites). These techniques reveal crystal alterations in mineral populations of different ages and changes of metal speciation associated with mineral or organic phases. These results provide an integrated model of soil formation and changes (from laterites to podzols) in distinct hydrological compartments of the Amazon landscapes and under altered water regimes. (C) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.

Parametric correlation functions to model the structure of permanent environmental (co)variances in milk yield random regression models

The objective of the present study was to estimate milk yield genetic parameters applying random regression models and parametric correlation functions combined with a variance function to model animal permanent environmental effects. A total of 152,145 test-day milk yields from 7,317 first lactations of Holstein cows belonging to herds located in the southeastern region of Brazil were analyzed. Test-day milk yields were divided into 44 weekly classes of days in milk. Contemporary groups were defined by herd-test-day comprising a total of 2,539 classes. The model included direct additive genetic, permanent environmental, and residual random effects. The following fixed effects were considered: contemporary group, age of cow at calving (linear and quadratic regressions), and the population average lactation curve modeled by fourth-order orthogonal Legendre polynomial. Additive genetic effects were modeled by random regression on orthogonal Legendre polynomials of days in milk, whereas permanent environmental effects were estimated using a stationary or nonstationary parametric correlation function combined with a variance function of different orders. The structure of residual variances was modeled using a step function containing 6 variance classes. The genetic parameter estimates obtained with the model using a stationary correlation function associated with a variance function to model permanent environmental effects were similar to those obtained with models employing orthogonal Legendre polynomials for the same effect. A model using a sixth-order polynomial for additive effects and a stationary parametric correlation function associated with a seventh-order variance function to model permanent environmental effects would be sufficient for data fitting.

Leaf area index estimation with MODIS reflectance time series and model inversion during full rotations of Eucalyptus plantations

The leaf area index (LAI) of fast-growing Eucalyptus plantations is highly dynamic both seasonally and interannually, and is spatially variable depending on pedo-climatic conditions. LAI is very important in determining the carbon and water balance of a stand, but is difficult to measure during a complete stand rotation and at large scales. Remote-sensing methods allowing the retrieval of LAI time series with accuracy and precision are therefore necessary. Here, we tested two methods for LAI estimation from MODIS 250m resolution red and near-infrared (NIR) reflectance time series. The first method involved the inversion of a coupled model of leaf reflectance and transmittance (PROSPECT4), soil reflectance (SOILSPECT) and canopy radiative transfer (4SAIL2). Model parameters other than the LAI were either fixed to measured constant values, or allowed to vary seasonally and/or with stand age according to trends observed in field measurements. The LAI was assumed to vary throughout the rotation following a series of alternately increasing and decreasing sigmoid curves. The parameters of each sigmoid curve that allowed the best fit of simulated canopy reflectance to MODIS red and NIR reflectance data were obtained by minimization techniques. The second method was based on a linear relationship between the LAI and values of the GEneralized Soil Adjusted Vegetation Index (GESAVI), which was calibrated using destructive LAI measurements made at two seasons, on Eucalyptus stands of different ages and productivity levels. The ability of each approach to reproduce field-measured LAI values was assessed, and uncertainty on results and parameter sensitivities were examined. Both methods offered a good fit between measured and estimated LAI (R(2) = 0.80 and R(2) = 0.62 for model inversion and GESAVI-based methods, respectively), but the GESAVI-based method overestimated the LAI at young ages. (C) 2010 Elsevier Inc. All rights reserved.

A Log-Linear Regression Model for the Beta-Weibull Distribution

We introduce the log-beta Weibull regression model based on the beta Weibull distribution (Famoye et al., 2005; Lee et al., 2007). We derive expansions for the moment generating function which do not depend on complicated functions. The new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We employ a frequentist analysis, a jackknife estimator, and a parametric bootstrap for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Further, for different parameter settings, sample sizes, and censoring percentages, several simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We define martingale and deviance residuals to evaluate the model assumptions. The extended regression model is very useful for the analysis of real data and could give more realistic fits than other special regression models.

Hyaluronidase Behavior at the Air/Liquid and Air/Lipid Interfaces and Improved Enzymatic Activity by Its Immobilization in a Biomembrane Model

Bovine testicular hyalurphidase (BT-HAase), a tetrameric enzyme responsible for randomly hyaluronic acid, catalytic hydrolysis, was successfully immobilized on Langmuir- Blodgett films prepared with the sodium salt of dihexadacylphosphoric acid, (DHP-Zn(II)) ending with dipalmitoylphosphatidylcholine, DPPC. Data of protein, adsorption at the air-liquid interface by means of pendant drop shipe analysis and interaction of the protein with Langmuir monolayers of DPPC, using a Langmuir trough, have provided information. about the conditions to be used in the protein immobilization. The dynamic surface pressure curves obtained from pendant drop experiments for the enzyme in buffer solutions indicate that, within the range of concentration investigated in this study, the enzyme exhibits the largest induction time at 5 mu g L(-1) attributed to diffusion processes. Nevertheless, it seems that, at this concentration, the most probable conformation should be the one which occupies the smallest area at pi -> 0. The surface pressure (pi) area curves obtained for BT-HAase and mixed DPPC- BT-HAase monolayers reveal the presence of the enzyme at the air-lipid interface up to 45 mN m(-1). Tests of enzymatic activity, using hyaluronic acid, HA, as the substrate, showed an increase of activity compared to the homogeneous medium. A simplified model of protein insertion into the lipid matrix is used to explain the obtained results.