Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.

Transformed generalized linear models

The estimation of data transformation is very useful to yield response variables satisfying closely a normal linear model, Generalized linear models enable the fitting of models to a wide range of data types. These models are based on exponential dispersion models. We propose a new class of transformed generalized linear models to extend the Box and Cox models and the generalized linear models. We use the generalized linear model framework to fit these models and discuss maximum likelihood estimation and inference. We give a simple formula to estimate the parameter that index the transformation of the response variable for a subclass of models. We also give a simple formula to estimate the rth moment of the original dependent variable. We explore the possibility of using these models to time series data to extend the generalized autoregressive moving average models discussed by Benjamin er al. [Generalized autoregressive moving average models. J. Amer. Statist. Assoc. 98, 214-223]. The usefulness of these models is illustrated in a Simulation study and in applications to three real data sets. (C) 2009 Elsevier B.V. All rights reserved.

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set. (C) 2008 Elsevier B.V. All rights reserved.

Association between particulate matter from biomass burning and respiratory diseases in the southern region of the Brazilian Amazon

Objective. To investigate the short-term effects of exposure to particulate matter from biomass burning in the Amazon on the daily demand for outpatient care due to respiratory diseases in children and the elderly. Methods. Epidemiologic study with ecologic time series design. Daily consultation records were obtained from the 14 primary health care clinics in the municipality of Alta Floresta, state of Mato Grosso, in the southern region of the Brazilian Amazon, between January 2004 and December 2005. Information on the daily levels of fine particulate matter was made available by the Brazilian National Institute for Spatial Research. To control for confounding factors ( situations in which a non-causal association between exposure and disease is observed due to a third variable), variables related to time trends, seasonality, temperature, relative humidity, rainfall, and calendar effects ( such as occurrence of holidays and weekends) were included in the model. Poisson regression with generalized additive models was used. Results. A 10 mu g/m(3) increase in the level of exposure to particulate matter was associated with increases of 2.9% and 2.6% in outpatient consultations due to respiratory diseases in children on the 6th and 7th days following exposure. Significant associations were not observed for elderly individuals. Conclusions. The results suggest that the levels of particulate matter from biomass burning in the Amazon are associated with adverse effects on the respiratory health of children.

Double generalized linear model for tissue culture proportion data: a Bayesian perspective

Joint generalized linear models and double generalized linear models (DGLMs) were designed to model outcomes for which the variability can be explained using factors and/or covariates. When such factors operate, the usual normal regression models, which inherently exhibit constant variance, will under-represent variation in the data and hence may lead to erroneous inferences. For count and proportion data, such noise factors can generate a so-called overdispersion effect, and the use of binomial and Poisson models underestimates the variability and, consequently, incorrectly indicate significant effects. In this manuscript, we propose a DGLM from a Bayesian perspective, focusing on the case of proportion data, where the overdispersion can be modeled using a random effect that depends on some noise factors. The posterior joint density function was sampled using Monte Carlo Markov Chain algorithms, allowing inferences over the model parameters. An application to a data set on apple tissue culture is presented, for which it is shown that the Bayesian approach is quite feasible, even when limited prior information is available, thereby generating valuable insight for the researcher about its experimental results.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Asymptotic Skewness in Exponential Family Nonlinear Models

In this article, we give an asymptotic formula of order n(-1/2), where n is the sample size, for the skewness of the distributions of the maximum likelihood estimates of the parameters in exponencial family nonlinear models. We generalize the result by Cordeiro and Cordeiro ( 2001). The formula is given in matrix notation and is very suitable for computer implementation and to obtain closed form expressions for a great variety of models. Some special cases and two applications are discussed.

Skovgaard`s adjustment to likelihood ratio tests in exponential family nonlinear models

Likelihood ratio tests can be substantially size distorted in small- and moderate-sized samples. In this paper, we apply Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-321] adjusted likelihood ratio statistic to exponential family nonlinear models. We show that the adjustment term has a simple compact form that can be easily implemented from standard statistical software. The adjusted statistic is approximately distributed as X(2) with high degree of accuracy. It is applicable in wide generality since it allows both the parameter of interest and the nuisance parameter to be vector-valued. Unlike the modified profile likelihood ratio statistic obtained from Cox and Reid [Cox, D.R., Reid, N., 1987. Parameter orthogonality and approximate conditional inference. journal of the Royal Statistical Society B49, 1-39], the adjusted statistic proposed here does not require an orthogonal parameterization. Numerical comparison of likelihood-based tests of varying dispersion favors the test we propose and a Bartlett-corrected version of the modified profile likelihood ratio test recently obtained by Cysneiros and Ferrari [Cysneiros, A.H.M.A., Ferrari, S.L.P., 2006. An improved likelihood ratio test for varying dispersion in exponential family nonlinear models. Statistics and Probability Letters 76 (3), 255-265]. (C) 2008 Elsevier B.V. All rights reserved.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

Use of pleopod morphology to determine sexual dimorphism and maturity in hermit crabs: Isocheles sawayai as a model

In the Anomura, studies on growth patterns are infrequent, possibly because the heterogeneity of the group, especially in terms of morphology, makes it difficult to construct generalized growth models. Particularly hermit crabs are an interesting group to evaluate aspects of growth, because of their unique body. Isocheles sawayai, a hermit crab found only in the western Atlantic Ocean, poorly known with respect to its sexual dimorphism and maturity, was investigated here based on morphometry. Monthly collections (July 2001 through June 2003) were made from a shrimp fishing boat in the Caraguatatuba region on the northern coast of the state of SA o pound Paulo, Brazil. The specimens were measured and weighed, and had their sex checked. Throughout the sampling period, 374 specimens of I. sawayai were collected (11.23% nonovigerous females, 6.69% ovigerous females, 79.41% males and 2.67% intersexes). The size at which morphological sexual maturity was reached by both sexes ranged from 4.0 to 4.3 mm shield length, according to the relative growth and the size of the smallest ovigerous female. Sexual dimorphism was shown by males, which were significantly larger than females, and by differences in growth pattern between the sexes, especially for relationships that involved the pleopods, which is related to their different functions in males and females. The present study is one of the first to use pleopod morphometry to determine sexual maturity and dimorphism in hermit crabs, especially for species with intersexuality such as I. sawayai.

Brood cell size of Apis mellifera modifies the reproductive behavior of Varroa destructor

We undertook a field study to determine whether comb cell size affects the reproductive behavior of Varroa destructor under natural conditions. We examined the effect of brood cell width on the reproductive behavior of V. destructor in honey bee colonies, under natural conditions. Drone and worker brood combs were sampled from 11 colonies of Apis mellifera. A Pearson correlation test and a Tukey test were used to determine whether mite reproduction rate varied with brood cell width. Generalized additive model analysis showed that infestation rate increased positively and linearly with the width of worker and drone cells. The reproduction rate for viable mother mites was 0.96 viable female descendants per original invading female. No significant correlation was observed between brood cell width and number of offspring of V. destructor. Infertile mother mites were more frequent in narrower brood cells.

Rural property size drives patterns of upland and riparian forest retention in a tropical deforestation frontier

Deforestation in Brazilian Amazonia accounts for a disproportionate global scale fraction of both carbon emissions from biomass burning and biodiversity erosion through habitat loss. Here we use field- and remote-sensing data to examine the effects of private landholding size on the amount and type of forest cover retained within economically active rural properties in an aging southern Amazonian deforestation frontier. Data on both upland and riparian forest cover from a survey of 300 rural properties indicated that 49.4% (SD = 29.0%) of the total forest cover was maintained as of 2007. and that property size is a key regional-scale determinant of patterns of deforestation and land-use change. Small properties (<= 150 ha) retained a lower proportion of forest (20.7%, SD = 17.6) than did large properties (>150 ha; 55.6%, SD = 27.2). Generalized linear models showed that property size had a positive effect on remaining areas of both upland and total forest cover. Using a Landsat time-series, the age of first clear-cutting that could be mapped within the boundaries of each property had a negative effect on the proportion of upland, riparian, and total forest cover retained. Based on these data, we show contrasts in land-use strategies between smallholders and largeholders, as well as differences in compliance with legal requirements in relation to minimum forest cover set-asides within private landholdings. This suggests that property size structure must be explicitly considered in landscape-scale conservation planning initiatives guiding agro-pastoral frontier expansion into remaining areas of tropical forest. (C) 2010 Elsevier Ltd. All rights reserved.