Formulating Mixed Models for Experiments, Including Longitudinal Experiments

Mixed models have become important in analyzing the results of experiments, particularly those that require more complicated models (e.g., those that involve longitudinal data). This article describes a method for deriving the terms in a mixed model. Our approach extends an earlier method by Brien and Bailey to explicitly identify terms for which autocorrelation and smooth trend arising from longitudinal observations need to be incorporated in the model. At the same time we retain the principle that the model used should include, at least, all the terms that are justified by the randomization. This is done by dividing the factors into sets, called tiers, based on the randomization and determining the crossing and nesting relationships between factors. The method is applied to formulate mixed models for a wide range of examples. We also describe the mixed model analysis of data from a three-phase experiment to investigate the effect of time of refinement on Eucalyptus pulp from four different sources. Cubic smoothing splines are used to describe differences in the trend over time and unstructured covariance matrices between times are found to be necessary.

Influence diagnostics for polyhazard models in the presence of covariates

In this paper, we present various diagnostic methods for polyhazard models. Polyhazard models are a flexible family for fitting lifetime data. Their main advantage over the single hazard models, such as the Weibull and the log-logistic models, is to include a large amount of nonmonotone hazard shapes, as bathtub and multimodal curves. Some influence methods, such as the local influence and total local influence of an individual are derived, analyzed and discussed. A discussion of the computation of the likelihood displacement as well as the normal curvature in the local influence method are presented. Finally, an example with real data is given for illustration.

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.

On estimation and influence diagnostics for zero-inflated negative binomial regression models

The zero-inflated negative binomial model is used to account for overdispersion detected in data that are initially analyzed under the zero-Inflated Poisson model A frequentist analysis a jackknife estimator and a non-parametric bootstrap for parameter estimation of zero-inflated negative binomial regression models are considered In addition an EM-type algorithm is developed for performing maximum likelihood estimation Then the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and some ways to perform global influence analysis are derived In order to study departures from the error assumption as well as the presence of outliers residual analysis based on the standardized Pearson residuals is discussed The relevance of the approach is illustrated with a real data set where It is shown that zero-inflated negative binomial regression models seems to fit the data better than the Poisson counterpart (C) 2010 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.

A positive growth response to NaCl applications in Eucalyptus plantations established on K-deficient soils

Contrasting responses of Eucalyptus trees to K fertilizer applications have been reported on soils with low K contents. A complete randomized block experiment was set up in Brazil to test the hypothesis that large atmospheric deposits of NaCl in coastal regions might lead to a partial substitution of K by Na in Eucalyptus physiology and enhance tree growth. Treatments with application of 1.5, 3.0, 4.5 kmol K ha(-1) (K(1.5), K(3.0), 1(4.5, respectively) as KCl, 3.0 kmol K ha(-1) applied as K(2)SO(4), 3.0 kmol Na ha(-1) (Na(3.0)) as NaCl commercialized for cattle feeding, and a mixture of 1.5 kmol K + 1.5 kmol Na ha(-1) (K(1.5) + Na(1.5)) were compared to a control treatment (C) with no K and Na applications. All the plots were fertilized with large amounts of the other nutrients. A positive effect of NaCl applications on the growth of E. grandis trees was observed. NaCl and KCl additions in treatments Na(3.0) and K(3.0) increased above-ground biomass by 56% and 130% three years after planting, respectively, in comparison with the C treatment. By contrast, accumulated litterfall up to age 3 years was not significantly modified. NaCl applications in the Na(3.0) treatment significantly increased Na accumulation in above-ground tree components but did not modify K accumulation, whatever the sampling age. A partial substitution of K by Na in tree physiology, as observed for various agricultural crops, might explain this behaviour. Our results suggest the possibility of applying inexpensive K fertilizers, which are less purified in Na, and explain why high yields are achieved without K fertilizer applications in areas with large dry depositions of marine aerosols. Further investigations are necessary to identify the processes involving Na in Eucalyptus tree physiology. (C) 2009 Elsevier B.V. All rights reserved.

Native tree seedling growth when fertilized with different amounts of dry sewage sludge and mineral fertilizer

The increasing volume of urban sewage nowadays generates considerable amount of sludge to be disposed of. One environmentally adequate destination could be the application of treated and stabilized sludge (biosolids) to forest plantations as fertilizer and soil conditioner. The purpose of this study was to analyze the feasibility of applying sewage sludge, evaluating its effects on native tree seedlings. The species evaluated were aroeira-pimenteira (Schinus terebinthifolia Raddi), cabreuva-vermelha (Myroxy-Ion peruiferum L. f.), pau-de-viola (Cytarexyllum myrianthum Cham), unha-de-vaca (Bauhinia forficata Link), which are usually planted in forest restoration. Seedlings were cultivated in pots, containing a volume of 4 dm(3) of soil, within a greenhouse. The study was developed in the proximity of Campinas, SP, Brazil, and installed in November, 2003. The design was entirely randomized including seven treatments: control; mineral fertilization; and different doses of sewage sludge (biosolids) complemented with potassium, due to the low concentration of this element in the sludge produced by the wastewater treatment plant of Barueri (Metropolitan region of Sao Paulo city). The results showed that the application of different dosages of biosolids promoted different responses in stem height and biomass production. The treatment with 20 g/dm(3) of dry sewage sludge promoted both the highest growth and the highest seedling biomass production, compared to the control treatment. All native tree species treated with the highest dosage of sewage sludge showed a growth similar to that of mineral fertilization. The seedlings of aroeira-pimenteira, pau-de-viola, and unha-de-vaca, all typical species of the initial succession in natural forest ecosystems, grew and produced more biomass than cabreuva-vermelha, a typical species of the final forest succession.

Bioinsecticidal activity of Talisia esculenta reserve protein on growth and serine digestive enzymes during larval development of Anticarsia gemmatalis

Plants synthesize a variety of molecules to defend themselves against an attack by insects. Talisin is a reserve protein from Talisia esculenta seeds, the first to be characterized from the family Sapindaceae. In this study, the insecticidal activity of Talisin was tested by incorporating the reserve protein into an artificial diet fed to the velvetbean caterpillar Anticarsia gemmatalis, the major pest of soybean crops in Brazil. At 1.5% (w/w) of the dietary protein, Talisin affected larval growth, pupal weight, development and mortality, adult fertility and longevity, and produced malformations in pupae and adult insects. Talisin inhibited the trypsin-like activity of larval midgut homogenates. The trypsin activity in Talisin-fed larvae was sensitive to Talisin, indicating that no novel protease-resistant to Talisin was induced in Talisin-fed larvae. Affinity chromatography showed that Talisin bound to midgut proteinases of the insect A. gemmatalis, but was resistant to enzymatic digestion by these larval proteinases. The transformation of genes coding for this reserve protein could be useful for developing insect resistant crops. (C) 2010 Elsevier Inc. All rights reserved.

Adenanthera pavonina TRYPSIN INHIBITOR RETARD GROWTH OF Anagasta kuehniella (LEPIDOPTERA: PYRALIDAE)

Anagasta kuehniella is a polyphagous pest that feeds on a wide variety of stored products. The possible roles suggested for seed proteinase inhibitors include the function as a part of the plant defensive system against pest via inhibition of their proteolytic enzymes. In this study, a trypsin inhibitor (ApTI) was purified from Adenanthera pavonina seed and was tested for insect growth regulatory effect. The chronic ingestion of ApTI did result in a significant reduction in larval survival and weight. Larval and pupal developmental time of larvae fed on ApTI diet at 1% was significantly longer; the larval period was extended by 5 days and pupal period was 10 days longer, therefore delaying by up to 20 days and resulting in a prolonged period of development from larva to adult. As a result, the ApTI diet emergence rate was only 28% while the emergence rate of control larvae was 80%. The percentage of surviving adults (%S) decreased to 62%. The fourth instar larvae reared on a diet containing 1% ApTI showed a decrease in tryptic activity of gut and that no novel proteolytic form resistant to ApTI was induced. In addition, the tryptic activity in ApTI -fed larvae was sensitive to ApTI. These results suggest that ApTI have a potential antimetabolic effect when ingested by A. kuehniella. (C) 2010 Wiley Periodicals, Inc.

Spatial portability of numerical models of leaf wetness duration based on empirical approaches

Leaf wetness duration (LWD) models based on empirical approaches offer practical advantages over physically based models in agricultural applications, but their spatial portability is questionable because they may be biased to the climatic conditions under which they were developed. In our study, spatial portability of three LWD models with empirical characteristics - a RH threshold model, a decision tree model with wind speed correction, and a fuzzy logic model - was evaluated using weather data collected in Brazil, Canada, Costa Rica, Italy and the USA. The fuzzy logic model was more accurate than the other models in estimating LWD measured by painted leaf wetness sensors. The fraction of correct estimates for the fuzzy logic model was greater (0.87) than for the other models (0.85-0.86) across 28 sites where painted sensors were installed, and the degree of agreement k statistic between the model and painted sensors was greater for the fuzzy logic model (0.71) than that for the other models (0.64-0.66). Values of the k statistic for the fuzzy logic model were also less variable across sites than those of the other models. When model estimates were compared with measurements from unpainted leaf wetness sensors, the fuzzy logic model had less mean absolute error (2.5 h day(-1)) than other models (2.6-2.7 h day(-1)) after the model was calibrated for the unpainted sensors. The results suggest that the fuzzy logic model has greater spatial portability than the other models evaluated and merits further validation in comparison with physical models under a wider range of climate conditions. (C) 2010 Elsevier B.V. All rights reserved.

Root Water Extraction under Combined Water and Osmotic Stress

Using a numerical implicit model for root water extraction by a single root in a symmetric radial flow problem, based on the Richards equation and the combined convection-dispersion equation, we investigated some aspects of the response of root water uptake to combined water and osmotic stress. The model implicitly incorporates the effect of simultaneous pressure head and osmotic head on root water uptake, and does not require additional assumptions (additive or multiplicative) to derive the combined effect of water and salt stress. Simulation results showed that relative transpiration equals relative matric flux potential, which is defined as the matric flux potential calculated with an osmotic pressure head-dependent lower bound of integration, divided by the matric flux potential at the onset of limiting hydraulic conditions. In the falling rate phase, the osmotic head near the root surface was shown to increase in time due to decreasing root water extraction rates, causing a more gradual decline of relative transpiration than with water stress alone. Results furthermore show that osmotic stress effects on uptake depend on pressure head or water content, allowing a refinement of the approach in which fixed reduction factors based on the electrical conductivity of the saturated soil solution extract are used. One of the consequences is that osmotic stress is predicted to occur in situations not predicted by the saturation extract analysis approach. It is also shown that this way of combining salinity and water as stressors yields results that are different from a purely multiplicative approach. An analytical steady state solution is presented to calculate the solute content at the root surface, and compared with the outputs of the numerical model. Using the analytical solution, a method has been developed to estimate relative transpiration as a function of system parameters, which are often already used in vadose zone models: potential transpiration rate, root length density, minimum root surface pressure head, and soil theta-h and K-h functions.

Effect of Calcium on the in vitro Growth of Aechmea blanchetiana (Baker) L. B. Smith Plantlets

This work investigated the influence of different concentrations of calcium on the growth of plantlets of the bromeliad Aechmea blanchetiana cultured in vitro. Seedlings of A. blanchetiana were axenically cultured in liquid Murashige and Skoog basal medium supplemented with different concentrations of calcium (Ca; 1.5, 3, 4.5, 6, or 12 mM) without growth regulators. The resulting plantlets were cultured under 93 mol m-2 s-1 illumination, 12 hour photoperiod regime and 25C 1 for 120 days with subculture to fresh identical media every 30 days. The addition of calcium at 9.38 mM to MS modified medium increased the production of fresh and dry mass of plantlets, whilst chlorine from calcium chloride dehydrate (CaCl2 2 H2O) in excess (3.35 mM) decreased both the fresh and dry mass of plantlets.

Alternative Analytical Expressions for the General van Genuchten-Mualem and van Genuchten-Burdine Hydraulic Conductivity Models

The van Genuchten expressions for the unsaturated soil hydraulic properties, first published in 1980, are used frequently in various vadose zone flow and transport applications assuming a specific relationship between the m and n soil hydraulic parameters. By comparison, probably because of the complexity of the hydraulic conductivity equations, the more general solutions with independent m and n values are rarely used. We expressed the general van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity equations in terms of hypergeometric functions, which can be approximated by infinite series that converge rapidly for relatively large values of the van Genuchten-Mualem parameter n but only very slowly when n is close to one. Alternative equations were derived that provide very close approximations of the analytical results. The newly proposed equations allow the use of independent values of the parameters m and n in the soil water retention model of van Genuchten for subsequent prediction of the van Genuchten-Mualem and van Genuchten-Burdine hydraulic conductivity models, thus providing more flexibility in fitting experimental pressure-head-dependent water content, theta(h), and hydraulic conductivity, K(h), or K(theta) data.

Annual and polyetic progression of citrus canker on trees protected with copper sprays

The effects of copper sprays on annual and polyetic progress of citrus canker, caused by Xanthomonas citri subsp. citri, in the presence of the Asian citrus leafminer (Phyllocnistis citrella), were evaluated in a study conducted in a commercial orchard in northwest Parana state, Brazil, where citrus canker is endemic. Nonlinear monomolecular, logistic and Gompertz models were fitted to monthly disease incidence data (proportion of leaves with symptoms) for each treatment for three seasons. The logistic model provided the best estimate of disease progress for all years and treatments evaluated and logistic parameter estimates were used to describe polyetic disease dynamics. Although citrus canker incidence increased during each of the seasons studied, it decreased over the whole study period, more so in copper-treated trees than in water-sprayed controls. Copper treatment reduced disease incidence compared with controls in every year, especially 2004-2005, when incidence was ca. 10-fold higher in controls than in treated plots (estimated asymptote values 0 center dot 82 and 0 center dot 07, respectively). Copper treatment also reduced estimated initial disease incidence and epidemic growth rates every year.

Atmospheric Absorption of Fluoride by Cultivated Species. Leaf Structural Changes and Plant Growth

Fluoride (F) is an air pollutant that causes phytotoxicity. Besides the importance of this, losses of agricultural crops in the vicinity of F polluting industries in Brazil have been recently reported. Injuries caused to plant leaf cell structures by excess F are not well characterized. However, this may contribute to understanding the ways in which plant physiological and biochemical processes are altered. A study evaluated the effects of the atmospheric F on leaf characteristics and growth of young trees of sweet orange and coffee exposed to low (0.04 mol L(-1)) or high (0.16 mol L(-1)) doses of HF nebulized in closed chamber for 28 days plus a control treatment not exposed. Gladiolus and ryegrass were used as bioindicators in the experiment to monitor F exposure levels. Fluoride concentration and dry mass of leaves were evaluated. Leaf anatomy was observed under light and electron microscopy. High F concentrations (similar to 180 mg kg(-1)) were found in leaves of plants exposed at the highest dose of HF. Visual symptoms of F toxicity in leaves of citrus and coffee were observed. Analyses of plant tissue provided evidence that F caused degeneration of cell wall and cytoplasm and disorganization of bundle sheath, which were more evident in Gladiolus and coffee. Minor changes were observed for sweet orange and ryegrass. Increase on individual stomatal area was also marked for the Gladiolus and coffee, and which were characterized by occurrence of opened ostioles. The increased F absorption by leaves and changes at the structural and ultrastructural level of leaf tissues correlated with reduced plant growth.