Bayesian composite Tobit quantile regression

Composite quantile regression models have been shown to be effective techniques in improving the prediction accuracy [H. Zou and M. Yuan, Composite quantile regression and the oracle model selection theory, Ann. Statist. 36 (2008), pp. 1108–1126; J. Bradic, J. Fan, and W. Wang, Penalized composite quasi-likelihood for ultrahighdimensional variable selection, J. R. Stat. Soc. Ser. B 73 (2011), pp. 325–349; Z. Zhao and Z. Xiao, Efficient regressions via optimally combining quantile information, Econometric Theory 30(06) (2014), pp. 1272–1314]. This paper studies composite Tobit quantile regression (TQReg) from a Bayesian perspective. A simple and efficient MCMC-based computation method is derived for posterior inference using a mixture of an exponential and a scaled normal distribution of the skewed Laplace distribution. The approach is illustrated via simulation studies and a real data set. Results show that combine information across different quantiles can provide a useful method in efficient statistical estimation. This is the first work to discuss composite TQReg from a Bayesian perspective.     

Arrow’s Axiom and Full Rationality for Fuzzy Choice Functions

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function satisfies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that these conditions are also equivalent with weak and strong fuzzy congruence axioms WFCA and SFCA. It is studied the Arrow index, a new concept that indicates the degree to which a fuzzy choice function satisfies the Fuzzy Arrow Axiom. The author wishes to express her gratitude to the two anonymous reviewers for their valuable comments and discussions that contributed to a higher quality of the paper. Some of their comments can be found in the final version of the paper. An abstract of this paper was presented at the First Spain Italy Netherlands Meeting on Game Theory SING, Maastricht, The Netherlands, June 2005.     

Congruence indicators for fuzzy choice functions

We introduce the congruence indicators WFCA(·) and SFCA(·) corresponding to fuzzy congruence axioms WFCA and SFCA. These indicators measure the degree to which a fuzzy choice function verifies the axioms WFCA and SFCA, respectively. The main result of the paper establishes for a given choice function the relationship between its congruence indicators and some rationality conditions. One obtains a fuzzy counterpart of the well-known Arrow–Sen theorem in crisp choice functions theory.     

Trajectories of interethnic contact and prejudice in a four-waves study of Romanian teenager–parent pairs

This article investigated negatively valenced contact and the relationship between parental and teenagers’ outgroup negativity in a context of interethnic conflict based on the latent trajectory analysis of a four-wave study of teenager–parent pairs (N?=?234). The analyses revealed that negative outgroup information prevailed both intra- and inter-generationally. On one hand, ascending trends of negative contact correlated positively and significantly with ascending trends of outgroup negativity and this relationship was stronger than the opposite association between change in positive contact and change in outgroup negativity. On the other hand, parental increases in outgroup negativity were associated with similar increases among teenagers, but there were no significant relationships between parental change in positive contact and teenagers’ positive contact and prejudice. The discussion focuses on the implications of the results for the positive–negative contact asymmetry and on the importance of social communication in conflicting contexts.     

An Automated MCEM Algorithm for Hierarchical Models with Multivariate and Multitype Response Variables

In this article, we consider a model allowing the analysis of multivariate data, which can contain data attributes of different types (e.g., continuous, discrete, binary). This model is a two-level hierarchical model which supports a wide range of correlation structures and can accommodate overdispersed data. Maximum likelihood estimation of the model parameters is achieved with an automated Monte Carlo expectation maximization algorithm. Our method is tested in a simulation study in the bivariate case and applied to a data set dealing with beehive activity.