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.

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.

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.

The influence of environmental variables on capybara (Hydrochoerus hydrochaeris: Rodentia, Hydrochoeridae) detectability in anthropogenic environments of southeastern Brazil

Capybaras were monitored weekly from 1998 to 2006 by counting individuals in three anthropogenic environments (mixed agricultural fields, forest and open areas) of southeastern Brazil in order to examine the possible influence of environmental variables (temperature, humidity, wind speed, precipitation and global radiation) on the detectability of this species. There was consistent seasonality in the number of capybaras in the study area, with a specific seasonal pattern in each area. Log-linear models were fitted to the sample counts of adult capybaras separately for each sampled area, with an allowance for monthly effects, time trends and the effects of environmental variables. Log-linear models containing effects for the months of the year and a quartic time trend were highly significant. The effects of environmental variables on sample counts were different in each type of environment. As environmental variables affect capybara detectability, they should be considered in future species survey/monitoring programs.

Cow/calf preweaning efficiency of Nellore and Bos taurus x Bos indicus crosses

The objectives of this study were to determine if percentage Bos taurus (0 or 50%) of the cow had an effect on ME requirements and milk production, and to compare cow/calf efficiency among 3 mating systems. Metabolizable energy requirements were estimated during a feeding trial that encompassed a gestation and lactation feeding trial for each of 2 groups of cows. Cows were 0 or 50% Bos taurus ( 100 or 50% Nellore) breed type: Nellore cows (NL; n = 10) mated to Nellore bulls, NL cows ( n = 9) mated to Angus bulls, Angus x Nellore (ANL; n = 10) and Simmental x Nellore (SNL; n = 10) cows mated to Canchim (5/ 8 Charolais 3/ 8 Zebu) bulls. Cows were individually fed a total mixed diet that contained 11.3% CP and 2.23 Mcal of ME/kg of DM. At 14-d intervals, cows and calves were weighed and the amount of DM was adjusted to keep shrunk BW and BCS of cows constant. Beginning at 38 d of age, corn silage was available to calves ad libitum. Milk production at 42, 98, 126, and 180 d postpartum was measured using the weigh-suckle-weigh technique. At 190 d of age, calves were slaughtered and body composition estimated using 9-10-11th-rib section to obtain energy deposition. Regression of BW change on daily ME intake (MEI) was used to estimate MEI at zero BW change. Increase in percentage Bos taurus had a significant effect on daily ME requirements (Mcal/d) during pregnancy (P < 0.01) and lactation (P < 0.01). Percentage Bos taurus had a positive linear effect on maintenance requirements of pregnant (P = 0.07) and lactating (P < 0.01) cows; during pregnancy, the ME requirements were 91 and 86% of those in lactation (131 +/- 3.5 vs. 145 +/- 3.4 Mcal.kg(-0.75).d(-1)) for the 0 and 50% B. taurus groups, respectively. The 50% B. taurus cows, ANL and SNL, suckling crossbred calves had greater total MEI (4,319 +/- 61 Mcal; P < 0.01) than 0% B. taurus cows suckling NL (3,484 +/- 86 Mcal) or ANL calves (3,600 +/- 91 Mcal). The 0% B. taurus cows suckling ANL calves were more efficient (45.3 +/- 1.6 g/Mcal; P = 0.03) than straightbred NL (35.1 +/- 1.5 g/Mcal) and ANL or SNL pairs (41.0 +/- 1.0 g/Mcal). Under the conditions of this study, crossbreeding improved cow/ calf efficiency and showed an advantage for cows that have lower energy requirements.

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.

Biogas production and valorization by means of a two-step biological process

The scope of this research work was to investigate biogas production and purification by a two-step bench-scale biological system, consisting of fed-batch pulse-feeding anaerobic digestion of mixed sludge, followed by methane enrichment of biogas by the use of the cyanobacterium Arthrospira platensis. The composition of biogas was nearly constant, and methane and carbon dioxide percentages ranged between 70.5-76.0% and 13.2-19.5%, respectively. Biogas yield reached a maximum value (about 0.4 m(biogas)(3)/kgCOD(i)) at 50 days-retention time and then gradually decreased with a decrease in the retention time. Biogas CO(2) was then used as a carbon source for A. platensis cultivation either under batch or fed-batch conditions. The mean cell productivity of fed-batch cultivation was about 15% higher than that observed during the last batch phase (0.035 +/- 0.006 g(DM)/L/d), likely due to the occurrence of some shading effect under batch growth conditions. The data of carbon dioxide removal from biogas revealed the existence of a linear relationship between the rates of A. platensis growth and carbon dioxide removal from biogas and allowed calculating carbon utilization efficiency for biomass production of almost 95%. (C) 2009 Elsevier Ltd. All rights reserved.

Liquid-liquid extraction by mixed micellar systems: A new approach for clavulanic acid recovery from fermented broth

This work is the first attempt to apply aqueous two-phase mixed micellar systems (ATPMS) of the nonionic surfactant Triton X-114 and the anionic one AOT to extract clavulanic acid (CA) from broth fermented by Streptomyces clavuligerus. Cloud points were determined in McIlvane buffer pH 6.5 with or without NaCl, and diagram phases/coexistence curves were constructed. CA partition was investigated following a 2(4)-full factorial design in which AOT (0.022, 0.033 and 0.044% w/w), Triton X-114 (1.0, 3.0 and 5.0% w/w) and NaCl (0, 2.85 and 5.70% w/w) concentrations and temperature (24,26 and 28 degrees C) were selected as independent variables, and CA partition coefficient (K(CA)) and yield in the top phase (eta(CA)) as responses. CA partitioned always to the top, micelle-poor phase. The regression analysis pointed out that NaCl concentration and interaction between temperature and Triton X-114 concentration had statistically significant effects on K(CA), while eta(CA) was mainly influenced by temperature, Triton X-114 concentration and their interaction. Different ATPMS compositions were then needed to maximize these responses, specifically 0.022% (w/w) AOT, 5% (w/w) Triton X-114 for K(CA) (2.08), and 0.044% (w/w) AOT, 1% (w/w) Triton X-114 for eta(CA) (98.7%), both at 24 degrees C without NaCl. Since at 0.022% (w/w) AOT, 1% (w/w) Triton X-114 and 28 degrees C without NaCl the system was able to ensure satisfactory intermediate results (K(CA) = 1.48; eta(CA) = 86.3%), these conditions were selected as the best ones. These preliminary results are of concern for possible industrial application, because CA partition to the dilute phase can simplify the subsequent purification protocol. (C) 2011 Elsevier B.V. All rights reserved.

Effect of inulin on growth and acidification performance of different probiotic bacteria in co-cultures and mixed culture with Streptococcus thermophilus

Inulin was used as a prebiotic to improve the quality and consistency of skim milk fermented by Lactobacillus acidophilus (La), Lactobacillus rhamnosus (Lr), Lactobacillus bulgaricus (Lb) and Bifidobacterium lactis (BI) with Streptococcus thermophilus (St), either in binary co-cultures or in cocktail containing all microorganisms. We compared, either in the presence of 40 mg inulin g(-1) or not, the results of the maximum acidification rate (V(max)) and the times to reach it (t(max)), to reach pH 5.0 (t(PH5.0)) and to complete the fermentation (t(f)). Post-acidification, lactic acid formation and cell counts were also compared after either 1 day (D1) or 7 days of storage at 4 degrees C (N). In co-culture, inulin addition to the milk increased V(max), decreased t(max) and t(f), favored post-acidification and exerted a bifidogenic effect. S. thermophilus proved to stimulate the metabolism of the other lactic bacteria and enhanced the product features. After D7, a significant prebiotic effect of inulin was observed in all co-cultures. Either after D1 or D7, the enumerations of Lr and BI in mixed culture markedly decreased compared to their respective co-cultures because of greater competition for the same substrates. (C) 2008 Elsevier Ltd. All rights reserved.

New Mixed Li/Mg and Li/Mg/Zn Amides for the Chemoselective Metallation of Arenes and Heteroarenes

New mixed Li/Mg and Li/Mg/Zn amides have been synthesized starting from readily prepared secondary amines. They allow a highly chemoselective directed magnesiation or zincation of various polyfunctional aromatics and heteroaromatics. The kinetic basicity, solubility and stability of these new bases have been compared with those of the corresponding 2,2,6,6-tetramethylpiperamide-derived bases. ((c) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2009)