Likelihood analysis for a class of beta mixed models

Beta regression is a suitable choice for modelling continuous response variables taking values on the unit interval. Data structures such as hierarchical, repeated measures and longitudinal typically induce extra variability and/or dependence and can be accounted for by the inclusion of random effects. In this sense, Statistical inference typically requires numerical methods, possibly combined with sampling algorithms. A class of Beta mixed models is adopted for the analysis of two real problems with grouped data structures. We focus on likelihood inference and describe the implemented algorithms. The first is a study on the life quality index of industry workers with data collected according to an hierarchical sampling scheme. The second is a study assessing the impact of hydroelectric power plants upon measures of water quality indexes up, downstream and at the reservoirs of the dammed rivers, with a nested and longitudinal data structure. Results from different algorithms are reported for comparison including from data-cloning, an alternative to numerical approximations which also allows assessing identifiability. Confidence intervals based on profiled likelihoods are compared with those obtained by asymptotic quadratic approximations, showing relevant differences for parameters related to the random effects. In both cases, the scientific hypothesis of interest was investigated by comparing alternative models, leading to relevant interpretations of the results within each context.     

Determinants of voluntary executive stock option disclosure in Brazil

This study investigates whether the governance attributes of Brazilian companies are associated with voluntary executive stock option (ESO) disclosure. Results show that Brazilian companies voluntarily disclose very little about their ESO plans, and that board size, presence of a compensation committee, and auditing by a Big 4 firm are significantly related to the degree of voluntary ESO disclosure. We also show that family-controlled companies in Brazil are associated with low voluntary ESO disclosure. Results are robust to a number of specification tests, dependent and explanatory variable measurements, and sample composition. This study has professional and regulatory implications for Brazil and other emerging capital markets. The results underscore the need for stricter rules for executive compensation reporting in Brazil, and they invite policy makers and regulators in emerging markets to consider the effects of company-level governance factors on disclosure incentives.     

Games With Discontinuous Payoffs: A Strengthening of Reny's Existence Theorem

We provide a pure Nash equilibrium existence theorem for games with discontinuous payoffs whose hypotheses are in a number of ways weaker than those of the theorem of Reny (1999). In comparison with Reny's argument, our proof is brief. Our result subsumes a prior existence result of Reny (1999) that is not covered by his theorem. We use the main result to prove the existence of pure Nash equilibrium in a class of finite games in which agents' pure strategies are subsets of a given set, and in turn use this to prove the existence of stable configurations for games, similar to those used by Schelling (1971, 1972) to study residential segregation, in which agents choose locations.     

On a tobit–Birnbaum–Saunders model with an application to medical data

The tobit model allows a censored response variable to be described by covariates. Its applications cover different areas such as economics, engineering, environment and medicine. A strong assumption of the standard tobit model is that its errors follow a normal distribution. However, not all applications are well modeled by this distribution. Some efforts have relaxed the normality assumption by considering more flexible distributions. Nevertheless, the presence of asymmetry could not be well described by these flexible distributions. A real-world data application of measles vaccine in Haiti is explored, which confirms this asymmetry. We propose a tobit model with errors following a Birnbaum–Saunders (BS) distribution, which is asymmetrical and has shown to be a good alternative for describing medical data. Inference based on the maximum likelihood method and a type of residual are derived for the tobit–BS model. We perform global and local influence diagnostics to assess the sensitivity of the maximum likelihood estimators to atypical cases. A Monte Carlo simulation study is carried out to empirically evaluate the performance of these estimators. We conduct a data analysis for the mentioned application of measles vaccine based on the proposed model with the help of the R software. The results show the good performance of the tobit–BS model.     

Weighted sums of associated variables

We study the convergence of weighted sums of associated random variables. The convergence for the typical $n^{1/p}$ normalization is proved assuming finiteness of moments somewhat larger than $p$, but still smaller than 2, together with suitable control on the covariance structure described by a truncation that generates covariances that do not grow too quickly. We also consider normalizations of the form $n^{1/q}{log}^{1/\gamma }n$, where $q$ is now linked with the properties of the weighting sequence. We prove the convergence under a moment assumption than is weaker that the usual existence of the moment-generating function. Our results extend analogous characterizations known for sums of independent or negatively dependent random variables.     

Parent–Child Communicational Characteristics: A Comparison Study between Subjects from Post-Divorce and Intact Nuclear Families

ABSTRACT

The occurrence of divorce seems to have impact on parent–child communication, with subsequent implications on the children well-being and development. The present study aims to analyze the influence that divorce has on parent–child communication comparing 102 participants from post-divorced families and 100 participants from intact nuclear families. Measures consisted of a sociodemographic questionnaire and Perception Scale of Parenting Communication. Despite literature indicators, the main findings reveal the absence of significant statistical differences between both family structures, concerning to parent–child communication. Overall, it was registered some statistically significant differences concerning to specific divorce variables. These findings demystifying the idea that post-divorce families establish less positive communication patterns when compared with intact nuclear families.     

Random Choice as Behavioral Optimization

We develop an extension of Luce's random choice model to study violations of the weak axiom of revealed preference. We introduce the notion of a stochastic preference and show that it implies the Luce model. Then, to address well‐known difficulties of the Luce model, we define the attribute rule and establish that the existence of a well‐defined stochastic preference over attributes characterizes it. We prove that the set of attribute rules and random utility maximizers are essentially the same. Finally, we show that both the Luce and attribute rules have a unique consistent extension to dynamic problems.