Clarice Garcia Borges Demétrio

Overdispersion: models and estimation

Overdispersion models for discrete data are considered and placed in a general framework. A distinction is made between completely specified models and those with only a mean-variance specification. Different formulations for the overdispersion mechanism can lead to different variance functions which can be placed within a general family. In addition, many different estimation methods have been proposed, including maximum likelihood, moment methods, extended quasi-likelihood, pseudo-likelihood and non-parametric maximum likelihood. We explore the relationships between these methods and examine their application to a number of standard examples for count and proportion data. A simple graphical method using half-normal plots is used to examine different overdispersion models.

A Family of Generalized Linear Models for Repeated Measures with Normal and Conjugate Random Effects

Non-Gaussian outcomes are often modeled using members of the so-called exponential family. Notorious members are the Bernoulli model for binary data, leading to logistic regression, and the Poisson model for count data, leading to Poisson regression. Two of the main reasons for extending this family are (1) the occurrence of overdispersion, meaning that the vari- ability in the data is not adequately described by the models, which often exhibit a prescribed mean-variance link, and (2) the accommodation of hier- archical structure in the data, stemming from clustering in the data which, in turn, may result from repeatedly measuring the outcome, for various mem- bers of the same family, etc. The first issue is dealt with through a variety of overdispersion models, such as, for example, the beta-binomial model for grouped binary data and the negative-binomial model for counts. Clustering is often accommodated through the inclusion of random subject-specific ef- fects. Though not always, one conventionally assumes such random effects to be normally distributed. While both of these phenomena may occur simul- taneously, models combining them are uncommon. This paper proposes a broad class of generalized linear models accommodating overdispersion and clustering through two separate sets of random effects. We place particular emphasis on so-called conjugate random effects at the level of the mean for the first aspect and normal random effects embedded within the linear pre- dictor for the second aspect, even though our family is more general. The binary, count and time-to-event cases are given particular emphasis. Apart from model formulation, we present an overview of estimation methods, and then settle for maximum likelihood estimation with analytic-numerical in- tegration. Implications for the derivation of marginal correlations functions are discussed. The methodology is applied to data from a study in epileptic seizures, a clinical trial in toenail infection named onychomycosis and sur- vival data in children with asthma.

The beta generalized half-normal distribution

For the first time, we propose the so-called beta generalized half-normal distribution, which contains some important distributions as special cases, such as the half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions. We derive expansions for the cumulative distribution and density functions which do not depend on complicated functions. We obtain formal expressions for the moments of the new distribution. We examine the maximum likelihood estimation of the parameters and provide the expected information matrix. The usefulness of the new distribution is illustrated through a real data set by showing that it is quite flexible in analyzing positive data instead of the generalized half-normal, half-normal, Weibull and beta Weibull distributions.

Zero-inflated proportion data models applied to a biological control assay

Biological control of pests is an important branch of entomology, providing environmentally friendly forms of crop protection. Bioassays are used to find the optimal conditions for the production of parasites and strategies for application in the field. In some of these assays, proportions are measured and, often, these data have an inflated number of zeros. In this work, six models will be applied to data sets obtained from biological control assays for Diatraea saccharalis , a common pest in sugar cane production. A natural choice for modelling proportion data is the binomial model. The second model will be an overdispersed version of the binomial model, estimated by a quasi-likelihood method. This model was initially built to model overdispersion generated by individual variability in the probability of success. When interest is only in the positive proportion data, a model can be based on the truncated binomial distribution and in its overdispersed version. The last two models include the zero proportions and are based on a finite mixture model with the binomial distribution or its overdispersed version for the positive data. Here, we will present the models, discuss their estimation and compare the results.

Somatic embryogenesis in Citrus SPP.: Carbohydrate stimulation and histodifferentiation

SummarySomatic embryogenesis from nucellus-derived callus cultures of five cultivars, including three (Caipira, Seleta Vermelha, and Valencia) of sweet oranges (C. sinesis L. Osbeck), Rangpur lime (C. limonia L. Osbeck), and Cleopatra mandarin (C. reticulata Blanco) (lines I and II), were studied. Callus lines maintained on MT medium supplemented with 50 g l−1 sucrose were transferred to MT medium supplemented with different carbohydrate sources: galactose, glucose, lactose, maltose, or sucrose at 18, 37, 75, 110, or 150 mM, or glycerol at 6, 12, 24, 36, or 50 mM. Globular embryos were observed after approximately 4 wk, in several treatments. Cultures of Valencia and Caipira sweet oranges and Cleopatra mandarin (line I) showed high numbers of embryos on medium containing galactose, lactose, and maltose. Histological studies showed somatic embryos in all developmental stages with a normal histodiffeentiation pattern. The other two cultivars (Rangpur lime and Cleopatra mandarin, line II) formed very few embryos, which did not develop further following the globular stage. Some of the abnormalities observed were lack or dedifferentiation of protoderm and absence of apical meristems and procambial strands. Embryos that followed the normal sequence of development were easily converted into plants. Non-embryogenic cultures continued as proliferating callus cultures, eventually forming a few embryos which did not convert into plants. Statistical analyses of the callus response to carbohydrate treatments was done using an overdispersion Poisson model.

A statistical approach to study the dynamics of micropropagation rates, using banana (Musa spp.) as an example

Abstract The use of micropropagation to obtain large numbers of high-quality planting material has increased in recent years. Behavior in culture, mainly in terms of multiplication rate, varies among genotypes, directly affecting plant production planning. To study multiplication rates over time, suckers of banana, Musa spp., cv. Maçã, were collected in the field and the shoot apex introduced in vitro for micropropagation. The number of new shoots produced in each of the six multiplication cycles was recorded and the data analyzed statistically. Variability in total shoot production and differences in multiplication rates was considerable among families, which consisted of the initial explant and its progeny. Moreover, the adjusted Poisson regression models for the number of shoots showed that the multiplication rate in this cultivar tends to decrease with time: after the seventh subculture, new shoots may form at a very low rate. Interpretation of the first and second derivatives of the regression model allowed determination of the maximum speed of multiplication and the time at which the multiplication rate begins to decline.

Contagem de células somáticas e produção de leite em vacas holandesas confinadas

ABSTRACT - The relationship between milk somatic cells count (SCC) and milk yield has been the aim of countless researchesin several countries; however, in Brazil, the literature related to this subject is scarce. Therefore, the objective of this st udy is to verifyif the losses in milk yield due to SCC increase are proportional to the yield, or absolute (independent of it) and starting fro m which SCC,the losses become evident. For this study, 13.725 observations were used, collected monthly from 6 different herds, from Januar y/2001up to June/2002. The analysis model, for lactation curve, was based upon the incomplete gama function, considering the effects of lactationorder, herd and calving season. The SCC entered in that model in two ways: as multiplicative factor (representing relative loss es) andas addictive factor (representing absolute losses). The best model was chosen based on the information criteria of Schwarz (BIC ). It isconcluded that the losses are absolute, becoming evident from 17.000 cells/mL, and they are 238 and 868 mL/day for each increas e ofone unit in the natural logarithm scale, starting from that SCC, respectively, for primiparous and multiparous.Key Words: SCC, subclinical mastitis, bovine mastitis, milk yield

Marginal correlation from an extended random-effects model for repeated and overdispersed counts

Vangeneugden et al. [15] derived approximate correlation functions for longitudinal sequences of general data type, Gaussian and non-Gaussian, based on generalized linear mixed-effects models (GLMM). Their focus was on binary sequences, as well as on a combination of binary and Gaussian sequences. Here, we focus on the specific case of repeated count data, important in two respects. First, we employ the model proposed by Molenberghs et al. [13], which generalizes at the same time the Poisson-normal GLMM and the conventional overdispersion models, in particular the negative-binomial model. The model flexibly accommodates data hierarchies, intra-sequence correlation, and overdispersion. Second, means, variances, and joint probabilities can be expressed in closed form, allowing for exact intra-sequence correlation expressions. Next to the general situation, some important special cases such as exchangeable clustered outcomes are considered, producing insightful expressions. The closed-form expressions are contrasted with the generic approximate expressions of Vangeneugden et al. [15]. Data from an epileptic-seizures trial are analyzed and correlation functions derived. It is shown that the proposed extension strongly outperforms the classical GLMM.

Diferenças em colonização do hospedeiro por isolados de Xylella fastidiosa de citros e cafeeiro em inoculações recíprocas

Citrus variegated chlorosis (CVC) and coffee stem atrophy (CSA) are important diseases in Brazil associated with closely-related strains of Xylella fastidiosa, but little is know about host aoverlappingnd importance of citrus and coffee as inoculum sources of these strains. In this study, reciprocal-inoculation experiments were performed to determine if CVC and CSA isolates are biologically similar within citrus and coffee plants. These two hosts were mechanically inoculated with a CVC and a CSA isolate of X. fastidiosa at four concentrations ranging between103 and 109 colony forming units CFU mL-1. At two, four and eight months after inoculation, the infection efficiency and bacterial populations of the isolates in each host were determined by culturing. The CVC isolate infected both citrus and coffee plants, but developed lower populations in coffee. The CSA isolate did not colonize citrus. Inoculation of coffee plants with the CVC isolate resulted in low rates of infection and required an inoculum concentration ten-fold higher than that necessary to obtain a similar (25%) rate of infection in citrus. The relatively low infection rates and bacterial numbers of the CVC isolate in coffee plants compared with those observed in citrus suggest that coffee is not a suitable host to serve as a source of inoculum of the CVC strain for primary spread to citrus or within coffee plantations.

EFEITO DO MILHO GENETICAMENTE MODIFICADO MON810 SOBRE A LAGARTA-DO-CARTUCHO Spodoptera frugiperda (J. E. SMITH, 1797) (LEPIDOPTERA: NOCTUIDAE)

Com o objetivo de verificar se a posicao da semente na espiga afeta diferentemente a produtividade e outros caracteres da planta e se essa diferenca pode ser ampliada por meio de ciclos seletivos, foi conduzido o presente trabalho. Para isto, na safra 1995/1996, foram semeadas, em lote isolado, cerca de 3.000 plantas da populacao CMS-39 e, por ocasiao da colheita, tomadas 300 espigas ao acaso. De cada espiga, foram coletadas sementes das extremidades e, posteriormente, as sementes da ponta de cada espiga foram misturadas e o mesmo foi realizado com as sementes da base. Esse procedimento foi repetido de modo analogo por cinco ciclos seletivos. As dez subpopulacoes, cinco da ponta e cinco da base, foram avaliadas em experimentos conduzidos nas safras 2000/2001 e 2001/2002. O delineamento utilizado foi o de blocos casualizados, com seis repeticoes, segundo esquema de parcelas subdivididas. Os tratamentos nas parcelas foram os cinco ciclos seletivos e, nas subparcelas, a origem das sementes, ponta ou base. Foram considerados os caracteres numero de dias para o florescimento masculino e feminino, altura de espiga e produtividade de graos. Constatou-se que a origem da semente da ponta ou da base nao alterou a expressao de varios caracteres avaliados e nao foi possivel, com a precisao experimental obtida, detectar efeito da selecao indireta para o vigor de polen pela posicao dos graos na espiga, em todos os caracteres considerados.