We introduce and study the Box-Cox symmetric class of distributions, which is useful for modeling positively skewed, possibly heavy-tailed, data. The new class of distributions includes the Box-Cox t, Box-Cox Cole-Green (or Box-Cox normal), Box-Cox power exponential distributions, and the class of the log-symmetric distributions as special cases. It provides easy parameter interpretation, which makes it convenient for regression modeling purposes. Additionally, it provides enough flexibility to handle outliers. The usefulness of the Box-Cox symmetric models is illustrated in a series of applications to nutritional data.
The growth of a tree or a forest settlement is of great value to a forest enterprise, because many decisions are directly dependent of this information, for instance, determining the optimal cutting age. This study aims to apply a new class of models to fit growth curves for diameter and height of Eucalyptus grandis X Eucalyptus urophylla seedling data. Data were collected from a trial conducted in a green house at the Natural Resources Department at School of Agriculture, Botucatu, São Paulo, Brazil. The experiment's design was completely randomized with eight treatments and four replications. In this trial, the growth variables referring to the height and the diameter were evaluated, being measured five and four times, respectively. The methodology was carried in a mixed longitudinal model using a new approach based on Box-Cox Normal (BCN) distribution, and comparisons with this model were made assuming normality of the data. The results revealed that the BCN mixed model provided similar results to the standard model in order to estimate growth curves; however, the BCN model was the best result according to Akaike criterion, considering the slight asymmetry in the data set. This approach is of great interest in case of outliers and robust procedures for parameter estimation.
Physical activity has been scientifically discussed as fundamental in the process of healthy ageing. Hence, this study aimed at determining the factors that influence older people to perform physical activities. The complete IPAQ (International Physical Activity Questionnaire) was applied to a population-based sample consisting of 364 elderly persons in the city of Botucatu, São Paulo, Brazil. Days of physical activity performed by the older people were considered by taking into account household and leisure activities. Models for count data were fitted by including socio-demographic variables as well as those related to life satisfaction. It was shown that housework physical-activity performance is associated with female, who predominantly showed to be more active in all levels. Male seemed to be more predisposed to perform lighter recreation, sports and leisure-time physical activities, such as walking. Additionally, poor schooling showed to be decisive for not performing physical activities both at home and during leisure.
One of the main interests in the nutrition field is to estimate the distribution of usual nutrient intake. Data from vitamin intake generally present high asymmetry mainly to the presence of outliers. This can occur due to the variability of the diet and, in this case, robust estimation to get the distribution of the data can be required. Then, the aim of paper is to propose an alternative approach for estimating usual intake through asymmetric distributions with random effects applied to data set 10 vitamins obtained from a dietetic survey for 368 older people from Botucatu city, São Paulo, Brazil. In general, these asymmetric distributions include parameters related to mean, median, dispersion measures and such parameters provide good estimates for the intake distribution. In order to make some comparisons, a model fitted by National Cancer Institute (NCI) method with only for amount of nutrient intake was established using Akaike Information Criteria (AIC). NCI method is based on a Box-Cox transformation coupled with normal distribution but in case of asymmetric data, this transformation can be not useful. It was observed that, in the presence of outliers, the asymmetric models provided a better fit than the NCI method in the major of the cases. Then, these models can be an alternative method to estimate the distribution of nutrient intake mainly because a transformation for the data is no necessary and all the information can be obtained directly from the parameters.
many environmental factors, including food availability, the ability to purchase and preparation of food and the numerous advertisements of products [6]. Then, the option of analyzing eating patterns can provide better benefits in proposing effective measures to promote health through food, which is the focus of nutritional epidemiology [7].Then, the aim of the study was to describe dietary patterns of the olders and associate with central and abdominal obesity as well as with the macronutrient intake. MethodologyThen, in the year of 2011, a cross-sectional study was carried out in Botucatu city, São Paulo, Brazil, in which anthropometric measures were obtained and a sociodemographic and a validated frequency food questionnaire (FFQ) were applied in a representative sample 355 older people. The sample size was calculating based on the number of items in the FFQ (71 food items). Following the recommendation of this sort of research, we considered five subjects for each item, totalizing the mentioned sample size. Results and discussionResults showed that 15.95% of men and 30.20% of female had general obesity and 42.94% of men and 74.47% of females had central obesity elderly. The highest prevalence regarding morbidities was hypertension (55.92%), triglycerides (38.49%) and diabetes mellitus (20.72%). Major of them are married (60.6%) and retired (75%). The
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