Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

Gamma transition intensity determination using multidetector coincidence data

This work describes two similar methods for calculating gamma transition intensities from multidetector coincidence measurements. In the first one, applicable to experiments where the angular correlation function is explicitly fitted, the normalization parameter from this fit is used to determine the gamma transition intensities. In the second, that can be used both in angular correlation or DCO measurements, the spectra obtained for all the detector pairs are summed up, in order to get the best detection statistics possible, and the analysis of the resulting bidimensional spectrum is used to calculate the transition intensities; in this method, the summation of data corresponding to different angles minimizes the influence of the angular correlation coefficient. Both methods are then tested in the calculation of intensities for well-known transitions from a (152)Eu standard source, as well as in the calculation of intensities obtained in beta-decay experiments with (193)Os and (155)Sm sources, yielding excellent results in all these cases. (C) 2009 Elsevier B.V. All rights reserved.

Observational constraints on the dark energy and dark matter mutual coupling

We examine different phenomenological interaction models for Dark Energy and Dark Matter by performing statistical joint analysis with observational data arising from the 182 Gold type la supernova samples, the shift parameter of the Cosmic Microwave Background given by the three-year Wilkinson Microwave Anisotropy Probe observations, the baryon acoustic oscillation measurement from the Sloan Digital Sky Survey and age estimates of 35 galaxies. Including the time-dependent observable, we add sensitivity of measurement and give complementary results for the fitting. The compatibility among three different data sets seem to imply that the coupling between dark energy and dark matter is a small positive value, which satisfies the requirement to solve the coincidence problem and the second law of thermodynamics, being compatible with previous estimates. (c) 2008 Elsevier B.V. All rights reserved.

Deviance residuals in generalised log-gamma regression models with censored observations

In this article, we compare three residuals based on the deviance component in generalised log-gamma regression models with censored observations. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and the empirical distribution of each residual is displayed and compared with the standard normal distribution. For all cases studied, the empirical distributions of the proposed residuals are in general symmetric around zero, but only a martingale-type residual presented negligible kurtosis for the majority of the cases studied. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended for the martingale-type residual in generalised log-gamma regression models with censored data. A lifetime data set is analysed under log-gamma regression models and a model checking based on the martingale-type residual is performed.

Local influence in estimating equations

Local influence diagnostics based on estimating equations as the role of a gradient vector derived from any fit function are developed for repeated measures regression analysis. Our proposal generalizes tools used in other studies (Cook, 1986: Cadigan and Farrell, 2002), considering herein local influence diagnostics for a statistical model where estimation involves an estimating equation in which all observations are not necessarily independent of each other. Moreover, the measures of local influence are illustrated with some simulated data sets to assess influential observations. Applications using real data are presented. (C) 2010 Elsevier B.V. All rights reserved.

Bayesian inference for a skew-normal IRT model under the centred parameterization

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is interest in studying latent variables. These latent variables are directly considered in the Item Response Models (IRM) and they are usually called latent traits. A usual assumption for parameter estimation of the IRM, considering one group of examinees, is to assume that the latent traits are random variables which follow a standard normal distribution. However, many works suggest that this assumption does not apply in many cases. Furthermore, when this assumption does not hold, the parameter estimates tend to be biased and misleading inference can be obtained. Therefore, it is important to model the distribution of the latent traits properly. In this paper we present an alternative latent traits modeling based on the so-called skew-normal distribution; see Genton (2004). We used the centred parameterization, which was proposed by Azzalini (1985). This approach ensures the model identifiability as pointed out by Azevedo et al. (2009b). Also, a Metropolis Hastings within Gibbs sampling (MHWGS) algorithm was built for parameter estimation by using an augmented data approach. A simulation study was performed in order to assess the parameter recovery in the proposed model and the estimation method, and the effect of the asymmetry level of the latent traits distribution on the parameter estimation. Also, a comparison of our approach with other estimation methods (which consider the assumption of symmetric normality for the latent traits distribution) was considered. The results indicated that our proposed algorithm recovers properly all parameters. Specifically, the greater the asymmetry level, the better the performance of our approach compared with other approaches, mainly in the presence of small sample sizes (number of examinees). Furthermore, we analyzed a real data set which presents indication of asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of strong negative asymmetry of the latent traits distribution. (C) 2010 Elsevier B.V. All rights reserved.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

An R implementation for generalized Birnbaum-Saunders distributions

The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. in this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples

The two-parameter Birnbaum-Saunders distribution has been used successfully to model fatigue failure times. Although censoring is typical in reliability and survival studies, little work has been published on the analysis of censored data for this distribution. In this paper, we address the issue of performing testing inference on the two parameters of the Birnbaum-Saunders distribution under type-II right censored samples. The likelihood ratio statistic and a recently proposed statistic, the gradient statistic, provide a convenient framework for statistical inference in such a case, since they do not require to obtain, estimate or invert an information matrix, which is an advantage in problems involving censored data. An extensive Monte Carlo simulation study is carried out in order to investigate and compare the finite sample performance of the likelihood ratio and the gradient tests. Our numerical results show evidence that the gradient test should be preferred. Further, we also consider the generalized Birnbaum-Saunders distribution under type-II right censored samples and present some Monte Carlo simulations for testing the parameters in this class of models using the likelihood ratio and gradient tests. Three empirical applications are presented. (C) 2011 Elsevier B.V. All rights reserved.

An extension of the generalized Birnbaum-Saunders distribution

In this paper we present an extension of the generalized Birnbaum-Saunders distribution family introduced in [Diaz-Garcia, J.A., Leiva-Sanchez, V., 2005. A new family of life distributions based on the contoured elliptically distributions. Journal of Statistical Planning and Inference 128 (2), 445-457] with a view to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied for some special members of this family such as the slash Birnbaum-Saunders and slash-t Birnbaum-Saunders. Simulation studies for some particular cases and a real data analysis are also reported, illustrating the usefulness of the extension considered. (C) 2008 Elsevier B.V. All rights reserved.

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.

A robust Bayesian approach to null intercept measurement error model with application to dental data

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the Skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial. (C) 2008 Elsevier B.V. All rights reserved.

Thermal analysis of biodegradable microparticles containing ciprofloxacin hydrochloride obtained by spray drying technique

Thermal analysis has been extensively used to obtain information about drug-polymer interactions and to perform pre-formulation studies of pharmaceutical dosage forms. In this work, biodegradable microparticles of poly(D,L-lactide-co-glycolide) (PLGA) containing ciprofloxacin hydrochloride (CP) in various drug:polymer ratios were obtained by spray drying. The main purpose of this study was to investigate the effect of the spray drying process on the drug-polymer interactions and on the stability of microparticles using differential scanning calorimetry (DSC), thermogravimetry (TG) and derivative thermogravimetry (DTG) and infrared spectroscopy (IR). The results showed that the high levels of encapsulation efficiency were dependant on drug:polymer ratio. DSC and TG/DTG analyses showed that for physical mixtures of the microparticles components the thermal profiles were different from those signals obtained with the pure substances. Thermal analysis data disclosed that physical interaction between CP and PLGA in high temperatures had occurred. The DSC and TG profiles for drug-loaded microparticles were very similar to the physical mixtures of components and it was possible to characterize the thermal properties of microparticles according to drug content. These data indicated that the spray dryer technique does not affect the physicochemical properties of the microparticles. In addition, the results are in agreement with IR data analysis demonstrating that no significant chemical interaction occurs between CP and PLGA in both physical mixtures and microparticles. In conclusion, we have found that the spray drying procedure used in this work can be a secure methodology to produce CP-loaded microparticles. (C) 2007 Elsevier B.V. All rights reserved.

A quantum chemical study on a set of non-imidazole H(3) antihistamine molecules

Molecular orbital calculations were carried out on a set of 28 non-imidazole H(3) antihistamine compounds using the Hartree-Fock method in order to investigate the possible relationships between electronic structural properties and binding affinity for H3 receptors (pK(i)). It was observed that the frontier effective-for-reaction molecular orbital (FERMO) energies were better correlated with pK(i) values than highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energy values. Exploratory data analysis through hierarchical cluster (HCA) and principal component analysis (PCA) showed a separation of the compounds in two sets, one grouping the molecules with high pK(i) values, the other gathering low pK(i) value compounds. This separation was obtained with the use of the following descriptors: FERMO energies (epsilon(FERMO)), charges derived from the electrostatic potential on the nitrogen atom (N(1)), electronic density indexes for FERMO on the N(1) atom (Sigma((FERMO))c(i)(2)). and electrophilicity (omega`). These electronic descriptors were used to construct a quantitative structure-activity relationship (QSAR) model through the partial least-squares (PLS) method with three principal components. This model generated Q(2) = 0.88 and R(2) = 0.927 values obtained from a training set and external validation of 23 and 5 molecules, respectively. After the analysis of the PLS regression equation and the values for the selected electronic descriptors, it is suggested that high values of FERMO energies and of Sigma((FERMO))c(i)(2), together with low values of electrophilicity and pronounced negative charges on N(1) appear as desirable properties for the conception of new molecules which might have high binding affinity. 2010 Elsevier Inc. All rights reserved.