Modified likelihood ratio tests for unit gamma regressions.

Regression analyses are commonly performed with doubly limited continuous dependent variables; for instance, when modeling the behavior of rates, proportions and income concentration indices. Several models are available in the literature for use with such variables, one of them being the unit gamma regression model. In all such models, parameter estimation is typically performed using the maximum likelihood method and testing inferences on the model's parameters are usually based on the likelihood ratio test. Such a test can, however, deliver quite imprecise inferences when the sample size is small. In this paper, we propose two modified likelihood ratio test statistics for use with the unit gamma regressions that deliver much more accurate inferences when the number of data points in small. Numerical (i.e. simulation) evidence is presented for both fixed dispersion and varying dispersion models, and also for tests that involve nonnested models. We also present and discuss two empirical applications.

Inference and diagnostics for heteroscedastic nonlinear regression models under skew scale mixtures of normal distributions.

The heteroscedastic nonlinear regression model (HNLM) is an important tool in data modeling. In this paper we propose a HNLM considering skew scale mixtures of normal (SSMN) distributions, which allows fitting asymmetric and heavy-tailed data simultaneously. Maximum likelihood (ML) estimation is performed via the expectation-maximization (EM) algorithm. The observed information matrix is derived analytically to account for standard errors. In addition, diagnostic analysis is developed using case-deletion measures and the local influence approach. A simulation study is developed to verify the empirical distribution of the likelihood ratio statistic, the power of the homogeneity of variances test and a study for misspecification of the structure function. The method proposed is also illustrated by analyzing a real dataset.

Bayesian Analysis of Evolutionary Divergence with Genomic Data under Diverse Demographic Models.

We present a new Bayesian method for estimating demographic and phylogenetic history using population genomic data. Several key innovations are introduced that allow the study of diverse models within an Isolation-with-Migration framework. The new method implements a 2-step analysis, with an initial Markov chain Monte Carlo (MCMC) phase that samples simple coalescent trees, followed by the calculation of the joint posterior density for the parameters of a demographic model. In step 1, the MCMC sampling phase, the method uses a reduced state space, consisting of coalescent trees without migration paths, and a simple importance sampling distribution without the demography of interest. Once obtained, a single sample of trees can be used in step 2 to calculate the joint posterior density for model parameters under multiple diverse demographic models, without having to repeat MCMC runs. Because migration paths are not included in the state space of the MCMC phase, but rather are handled by analytic integration in step 2 of the analysis, the method is scalable to a large number of loci with excellent MCMC mixing properties. With an implementation of the new method in the computer program MIST, we demonstrate the method's accuracy, scalability, and other advantages using simulated data and DNA sequences of two common chimpanzee subspecies: Pan troglodytes (P. t.) troglodytes and P. t. verus.

Examining associations between dietary patterns and metabolic CVD risk factors: a novel use of structural equation modelling.

The association between dietary patterns and metabolic cardiovascular risk factors has long been addressed but there is a lack of evidence towards the effects of the overall diet on the complex net of biological inter-relationships between risk factors. This study aimed to derive dietary patterns and examine their associations with metabolic cardiovascular risk factors following a theoretic model for the relationship between them. Participants included 417 adults of both sexes, enrolled to the cross-sectional population-based study performed in Brazil. Body weight, waist circumference, high-sensitivity C-reactive protein, blood pressure, total cholesterol:HDL-cholesterol ratio, TAG:HDL-cholesterol ratio, fasting plasma glucose and serum leptin were evaluated. Food consumption was assessed by two non-consecutive 24-h dietary recalls adjusted for the within-person variation of intake. A total of three dietary patterns were derived by exploratory structural equation modelling: 'Traditional', 'Prudent' and 'Modern'. The 'Traditional' pattern had a negative and direct effect on obesity indicators (serum LEP, body weight and waist circumference) and negative indirect effects on total cholesterol:HDL-cholesterol ratio, TAG:HDL-cholesterol ratio and fasting plasma glucose. The 'Prudent' pattern had a negative and direct effect on systolic blood pressure. No association was observed for the 'Modern' pattern and metabolic risk factors. In conclusion, the 'Traditional' and 'Prudent' dietary patterns were negatively associated with metabolic cardiovascular risk factors among Brazilian adults. Their apparent protective effects against obesity and high blood pressure may be important non-pharmacological strategies for the prevention and control of obesity-related metabolic disorders and CVD.

Extracting Spurious Latent Classes in Growth Mixture Modeling With Nonnormal Errors.

Growth mixture modeling is generally used for two purposes: (1) to identify mixtures of normal subgroups and (2) to approximate oddly shaped distributions by a mixture of normal components. Often in applied research this methodology is applied to both of these situations indistinctly: using the same fit statistics and likelihood ratio tests. This can lead to the overextraction of latent classes and the attribution of substantive meaning to these spurious classes. The goals of this study are (1) to explore the performance of the Bayesian information criterion, sample-adjusted BIC, and bootstrap likelihood ratio test in growth mixture modeling analysis with nonnormal distributed outcome variables and (2) to examine the effects of nonnormal time invariant covariates in the estimation of the number of latent classes when outcome variables are normally distributed. For both of these goals, we will include nonnormal conditions not considered previously in the literature. Two simulation studies were conducted. Results show that spurious classes may be selected and optimal solutions obtained in the data analysis when the population departs from normality even when the nonnormality is only present in time invariant covariates.