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.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

Some restriction tests in a new class of regression models for proportions

The main purpose of this work is to study the behaviour of Skovgaard`s [Skovgaard, I.M., 2001. Likelihood asymptotics. Scandinavian journal of Statistics 28, 3-32] adjusted likelihood ratio statistic in testing simple hypothesis in a new class of regression models proposed here. The proposed class of regression models considers Dirichlet distributed observations, and the parameters that index the Dirichlet distributions are related to covariates and unknown regression coefficients. This class is useful for modelling data consisting of multivariate positive observations summing to one and generalizes the beta regression model described in Vasconcellos and Cribari-Neto [Vasconcellos, K.L.P., Cribari-Neto, F., 2005. Improved maximum likelihood estimation in a new class of beta regression models. Brazilian journal of Probability and Statistics 19,13-31]. We show that, for our model, Skovgaard`s adjusted likelihood ratio statistics have a simple compact form that can be easily implemented in standard statistical software. The adjusted statistic is approximately chi-squared distributed with a high degree of accuracy. Some numerical simulations show that the modified test is more reliable in finite samples than the usual likelihood ratio procedure. An empirical application is also presented and discussed. (C) 2009 Elsevier B.V. All rights reserved.

Influence of education and depressive symptoms on cognitive function in the elderly

Objective: The purpose of the present study was to investigate the influence that education and depression have on the performance of elderly people in neuropsychological tests. Methods: The study was conducted at the Institute of Psychiatry, University of Sao Paulo School of Medicine, Hospital das Clinicas. All of the individuals evaluated were aged 60 or older. The study sample consisted of 59 outpatients with depressive disorders and 51 healthy controls. We stratified the sample by level of education: low = 1-4 years of schooling; high = 5 or more years of schooling. Evaluations consisted of psychiatric assessment, cognitive assessment, laboratory tests and cerebral magnetic resonance imaging. Results: We found that level of education influenced all the measures of cognitive domains investigated (intellectual efficiency, processing speed, attention, executive function and memory) except the Digit Span Forward and Fuld Object Memory Evaluation (immediate and delayed recall), whereas depressive symptoms influenced some measures of memory, attention, executive function and processing speed. Although the combination of a low level of education and depression had a significant negative influence on Stroop Test part B, Trail Making Test part B and Logical Memory (immediate recall), we found no other significant effects of the interaction between level of education and depression. Conclusion: The results of this study underscore the importance of considering the level of education in the analysis of cognitive performance in depressed elderly patients, as well as the relevance of developing new cognitive function tests in which level of education has a reduced impact on the results.

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.

In vitro tests to establish LC(50) and discriminating concentrations for fipronil against Rhipicephalus (Boophilus) microplus (Acari: Ixodidae) and their standardization

Laboratory test was carried out on larvae and adults of the cattle tick, Rhipicephalus (Boophilus) microplus, to determine fipronil toxicity. Adult immersion test (AIT, N = 26), larval immersion test (LIT, N = 71) and larval packet test (LPT, N = 41) were standardized using susceptible strain (Mozo). Dose-response curves were compared with a fipronil resistant strain. Four variables were analyzed from AIT results: mortality, weight of eggs on day 7 and on day 14, index of fertility, and index of fecundity. For larval test, dose mortality curves were analyzed. In spite of the high LC(50) variability, all variables determined for AIT were appropriate to discriminate both strains. AIT and LIT had more sensitivity than LPT, with larger resistance factors. It was used two times LC(99.9) as discriminating doses (DCs) following FAO suggestion. For mortality by AIT, LIT and LPT the DCs were estimated: 4.98 ppm, 7.64 ppm and 2365.8 ppm, respectively, for Mozo strain. DCs mortality values estimated for resistant strain by AIT, LIT and LPT were: 6.96 x 10(5) ppm, 343.26 ppm and 5.7 x 10(3) ppm, respectively and their respective resistant factors were: 202.4, 5.36 and 1.52. Protocols for AIT, LIT and LPT have been presented in this paper. (C) 2009 Elsevier B.V. All rights reserved.

Removal of metal ions from aqueous solution by chelating polymeric hydrogel

Polysaccharide natural seed coat from the tree Magonia pubescens, in the form of hydrogel was used to remove metals in aqueous solution. Swelling tests indicate that seed coat presents hydrogel behavior, with maximum water absorption of 292 g water/g. Adsorption experiments performed using Na(+), Mg(2+), K(+), Ca(2+), Cr(3+), Fe(3+) and Zn(2+) demonstrated that the polysaccharide structure has a high capacity to extract these ions from the aqueous solution. Scanning electron microscopy revealed significant morphological changes of the material before and after water contact. Differential scanning calorimetry measurements indicate a signal shift of the water evaporation temperature in the material with adsorbed zinc. X-ray photoelectron spectroscopy analysis combined with theoretical studies by the density functional theory and on Hartree-Fock (HF) level evidence that the metallic ions were adsorbed through coordination with hydroxyl groups of polysaccharide. In the case of Zn(2+) the lowest HF energy was observed for the tetracoordination mode, where Zn(2+) is coordinated by two hydroxyl groups and two water molecules.

Characterization and Identification of Proteolytic Bacteria From the Gut of the Velvetbean Caterpillar (Lepidoptera: Noctuidae)

The characterization and identification of proteolytic bacteria from the gut of the velvetbean caterpillar (Anticarsia gemmatalis) were the objectives of this study. Twelve aerobic and anaerobic isolates of proteolytic bacteria were obtained from the caterpillar gut in calcium caseinate agar. The number of colony forming units (CFUs) of proteolytic bacteria was higher when the bacteria were extracted from caterpillars reared on artificial diet rather than on soybean leaves (1.73 +/- 0.35 X 10(3) and 0.55 +/- 0.22 X 10(3) CFU/mg gut, respectively). The isolated bacteria were divided into five distinct groups, according to their polymerase chain reaction restriction fragment-length polymorphism profiles. After molecular analysis, biochemical tests and fatty acid profile determination, the bacteria were identified as Bacillus subtilis, Bacillus cereus, Enterococcus gallinarum, Enterococcus mundtii, and Staphylococcus xylosus. Bacterial proteolytic activity was assessed through in vitro colorimetric assays for (general) proteases, serine proteases, and cysteine proteases. The isolated bacteria were able of hydrolyzing all tested substrates, except Staphylococcus xylosus, which did not exhibit serine protease activity. This study provides support for the hypothesis that gut proteases from velvetbean caterpillar are not exclusively secreted by the insect cells but also by their symbiotic gut bacteria. The proteolytic activity from gut symbionts of the velvetbean caterpillar is suggestive of their potential role minimizing the potentially harmful consequences of protease inhibitors from some of this insect host plants, such as soybean, with implications for the management of this insect pest species.