Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

Influence diagnostics for linear models with first-order autoregressive elliptical errors

We introduce in this paper the class of linear models with first-order autoregressive elliptical errors. The score functions and the Fisher information matrices are derived for the parameters of interest and an iterative process is proposed for the parameter estimation. Some robustness aspects of the maximum likelihood estimates are discussed. The normal curvatures of local influence are also derived for some usual perturbation schemes whereas diagnostic graphics to assess the sensitivity of the maximum likelihood estimates are proposed. The methodology is applied to analyse the daily log excess return on the Microsoft whose empirical distributions appear to have AR(1) and heavy-tailed errors. (C) 2008 Elsevier B.V. All rights reserved.

Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Network genealogy of 195-bp satellite DNA supports the superimposed hybridization hypothesis of Trypanosoma cruzi evolutionary pattern

Trypanosoma cruzi is highly diverse genetically and has been partitioned into six discrete typing units (DTUs), recently re-named T. cruzi I-VI. Although T. cruzi reproduces predominantly by binary division, accumulating evidence indicates that particular DTUs are the result of hybridization events. Two major scenarios for the origin of the hybrid lineages have been proposed. It is accepted widely that the most heterozygous TcV and TcVI DTUs are the result of genetic exchange between TcII and TcIII strains. On the other hand, the participation of a TcI parental in the current genome structure of these hybrid strains is a matter of debate. Here, sequences of the T. cruzi-specific 195-bp satellite DNA of TcI, TcII, Tat, TcV, and TcVI strains have been used for inferring network genealogies. The resulting genealogy showed a high degree of reticulation, which is consistent with more than one event of hybridization between the Tc DTUs. The data also strongly suggest that Tat is a hybrid with two distinct sets of satellite sequences, and that genetic exchange between TcI and TcII parentals occurred within the pedigree of the TcV and TcVI DTUs. Although satellite DNAs belong to the fast-evolving portion of eukaryotic genomes, in >100 satellite units of nine T. cruzi strains we found regions that display 100% identity. No DTU-specific consensus motifs were identified, inferring species-wide conservation. (C) 2010 Elsevier B.V. All rights reserved.

Analytical Assessment of a Home Made Capillary Electrophoresis Equipment with Linear Charge Coupled Device for Visible Light Absorption Detection in the Determination of Food Dyes

The performance of modular home made capillary electrophoresis equipment with spectrophotometric detection, at a visible region by means of a miniaturized linear charge coupled device, was evaluated for the determination of four food dyes. This system presents a simple but efficient home made cell detection scheme. A computer program that converts the spectral data after each run into the electropherograms was developed to evaluate the analytical parameters. The dyes selected for analytical evaluation of the system were Brilliant Blue FCF, Fast Green FCF, Sunset Yellow FCF, and Amaranth. Separation was carried out in a 29cm length and 75 mu m I.D fused silica capillary, using 10mmolL-1 borate buffer at pH 9, with separation voltage of 7.5kV. The detection limits for the dyes were between 0.3 and 1.5mgL-1 and the method presented adequate linearity over the ranges studied, with correlation coefficients greater than 0.99. The method was applied for determination and quantification of these dyes in fruit juices and candies.