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.

Patterns of food acquisition in Brazilian households and associated factors: a population-based survey

Objective: To identify food acquisition patterns in Brazil and relate them to the sociodemographic characteristics of the household. Design: A cross-sectional national Household Budget Survey (HBS). Principal component factor analysis was used to derive food patterns (factors) on the basis of the acquisition of food classified into thirty-two food groups. Setting: The source of data originates from the 2002-2003 HBS carried out by the Brazilian Institute of Geography and Statistics between June 2002 and July 2003 using a representative sample of all Brazilian households. Subject: A total of 48 470 households allocated into 443 strata of households that were geographically and socio-economically homogeneous as a study unit. Results: We identified two patterns of food acquisition. The first, named `dual`, was characterized by dairy, fruit, fruit juice, vegetables, processed meat, soft drinks, sweets, bread and margarine, and by inverse correlations with Brazilian staple foods. In contrast, the second pattern, named `traditional`, was characterized by rice, beans, manioc, flour, milk and sugar. The `dual` pattern was associated with higher household educational level, income and the average age of adults on the strata, whereas the `traditional` presented higher loadings in less-educated households and in the rural setting. Conclusions: Dietary patterns described here suggest that policies and programmes to promote healthy eating need to consider that healthy and non-healthy foods may be integral in the same pattern.

Random walks systems with killing on Z

We study random walks systems on Z whose general description follows. At time zero, there is a number N >= 1 of particles at each vertex of N, all being inactive, except for those placed at the vertex one. Each active particle performs a simple random walk on Z and, up to the time it dies, it activates all inactive particles that it meets along its way. An active particle dies at the instant it reaches a certain fixed total of jumps (L >= 1) without activating any particle, so that its lifetime depends strongly on the past of the process. We investigate how the probability of survival of the process depends on L and on the jumping probabilities of the active particles.