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.

Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

Concordant Phylogeographies of 2 Malaria Vectors Attest to Common Spatial and Demographic Histories

The phylogeography of South American lineages is a topic of heated debate. Although a single process is unlikely to describe entire ecosystems, related species, which incur similar habitat limitations, can inform the history for a subsection of assemblages. We compared the phylogeographic patterns of the cytochrome oxidase I marker from Anopheles triannulatus (N = 72) and previous results for A. darlingi (N = 126) in a broad portion of their South American distributions. Both species share similar population subdivisions, with aggregations northeast of the Amazon River, in southern coastal Brazil and 2 regions in central Brazil. The average (ST) between these groups was 0.39 for A. triannulatus. Populations northeast of the Amazon and in southeastern Brazil are generally reciprocally monophyletic to the remaining groups. Based on these initial analyses, we constructed the a priori hypothesis that the Amazon and regions of high declivity pose geographic barriers to dispersal in these taxa. Mantel tests confirmed that these areas block gene flow for more than 1000 km for both species. The efficacy of these impediments was tested using landscape genetics, which could not reject our a priori hypothesis but did reject simpler scenarios. Results form summary statistics and phylogenetics suggest that both lineages originated in central Amazonia (south of the Amazon River) during the late Pleistocene (579 000 years ago) and that they followed the same paths of expansion into their contemporary distributions. These results may have implications for other species sharing similar ecological limitations but probably are not applicable as a general paradigm of Neotropical biogeography.

Recent Trends in Maternal, Newborn, and Child Health in Brazil: Progress Toward Millennium Development Goals 4 and 5

We analyzed Brazil`s efforts in reducing child mortality, improving maternal and child health, and reducing socioeconomic and regional inequalities from 1990 through 2007. We compiled and reanalyzed data from several sources, including vital statistics and population-based surveys. We also explored the roles of broad socioeconomic and demographic changes and the introduction of health sector and other reform measures in explaining the improvements observed. Our findings provide compelling evidence that pro-active measures to reduce health disparities accompanied by socioeconomic progress can result in measurable improvements in the health of children and mothers in a relatively short interval. Our analysis of Brazil`s successes and remaining challenges to reach and surpass Millennium Development Goals 4 and 5 can provide important lessons for other low- and middle-income countries. (Am J Public Health. 2010;100:1877-1889. doi:10.2105/AJPH.2010.196816)

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

The exponentiated generalized inverse Gaussian distribution

The modeling and analysis of lifetime data is an important aspect of statistical work in a wide variety of scientific and technological fields. Good (1953) introduced a probability distribution which is commonly used in the analysis of lifetime data. For the first time, based on this distribution, we propose the so-called exponentiated generalized inverse Gaussian distribution, which extends the exponentiated standard gamma distribution (Nadarajah and Kotz, 2006). Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters. The usefulness of the new model is illustrated by means of a real data set. (c) 2010 Elsevier B.V. All rights reserved.

The beta-Birnbaum-Saunders distribution An improved distribution for fatigue life modeling

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies For the first time based on this distribution the so-called beta-Birnbaum-Saunders distribution is proposed for fatigue life modeling Various properties of the new model including expansions for the moments moment generating function mean deviations density function of the order statistics and their moments are derived We discuss maximum likelihood estimation of the model s parameters The superiority of the new model is illustrated by means of three failure real data sets (C) 2010 Elsevier B V All rights reserved

The beta Laplace distribution

The Laplace distribution is one of the earliest distributions in probability theory. For the first time, based on this distribution, we propose the so-called beta Laplace distribution, which extends the Laplace distribution. Various structural properties of the new distribution are derived, including expansions for its moments, moment generating function, moments of the order statistics, and so forth. We discuss maximum likelihood estimation of the model parameters and derive the observed information matrix. The usefulness of the new model is illustrated by means of a real data set. (C) 2011 Elsevier B.V. All rights reserved.