A class of bivariate regression models for discrete and/or continuous responses

ABSTRACT

A general class of models for discrete and/or continuous responses is proposed in which joint distributions are constructed via the conditional approach. It is assumed that the distributions of one response and of the other response given the first one belong to exponential family of distributions. Furthermore, the marginal means are related to the covariates by link functions and a dependency structure between the responses is inserted into the model. Estimation methods, diagnostic analysis and a simulation study considering a Bernoulli-exponential model, a particular case of the class, are presented. Finally, this model is used in a real data set.     

Geometry in Canonical Correlations

In this article, a useful proposition relating the canonical correlations in multi-way layout to the singular values of a specific matrix is proved and also a geometrical explanation of canonical correlations as an angle between subspaces is given.     

Measuring Kurtosis by Right and Left Inequality Orders

The question of how to measure kurtosis in both symmetric and asymmetric distributions is addressed using the kurtosis diagram of Zenga (2006 Zenga , M. ( 2006 ). Kurtosis . In : Kotz , S. , Read , C. B. , Balakrishnan , N. , Vidakovic , B. , eds. Encyclopedia of Statistical Sciences. 2nd ed . New York : John Wiley and Sons . [Google Scholar]). Kurtosis is related to inequality at either side of the median, and we establish a hierarchy of kurtosis orderings in which the kurtosis diagram stands at the weakest level. A sufficient condition for constructing kurtosis measures compatible with such ordering is provided. The merits of the proposed approach in both clarifying and formalizing the idea of kurtosis are evaluated and examples are discussed throughout.     

On cumulative entropies

In analogy with the cumulative residual entropy recently proposed by Wang et al. [2003a. A new and robust information theoretic measure and its application to image alignment. In: Information Processing in Medical Imaging. Lecture Notes in Computer Science, vol. 2732, Springer, Heidelberg, pp. 388–400; 2003b. Cumulative residual entropy, a new measure of information and its application to image alignment. In: Proceedings on the Ninth IEEE International Conference on Computer Vision (ICCV’03), vol. 1, IEEE Computer Society Press, Silver Spring, MD, pp. 548–553], we introduce and study the cumulative entropy, which is a new measure of information alternative to the classical differential entropy. We show that the cumulative entropy of a random lifetime X can be expressed as the expectation of its mean inactivity time evaluated at X. Hence, our measure is particularly suitable to describe the information in problems related to ageing properties of reliability theory based on the past and on the inactivity times. Our results include various bounds to the cumulative entropy, its connection to the proportional reversed hazards model, and the study of its dynamic version that is shown to be increasing if the mean inactivity time is increasing. The empirical cumulative entropy is finally proposed to estimate the new information measure.     

20 years of Bologna - a story of success,a story of failure

The Bologna Process is a unique harmonisation process taking place outside the policy-making framework of the European Union. It aims at enhancing the comparability and compatibility of higher education structures and degrees across Europe, as well as to institutionalise quality assurance mechanisms. The aim of this article is to provide a condensed, up-to-date overview of the Bologna Process with regard to structural characteristics, before embedding it into a discussion on processes on voluntary policy convergence and to which extent we should be able to find this kind of policy harmonisation in the realm of the Bologna Process. Related to this are questions why this, in principle, completely voluntary process of policy harmonisation, has appealed to so many countries and why they might or might not feel committed to the implementation of its policies and tools.     

Testing Overdispersion in CUBE Models

A practical problem with large-scale survey data is the possible presence of overdispersion. It occurs when the data display more variability than is predicted by the variance–mean relationship. This article describes a probability distribution generated by a mixture of discrete random variables to capture uncertainty, feeling, and overdispersion. Specifically, several tests for detecting overdispersion will be implemented on the basis of the asymptotic theory for maximum likelihood estimators. We discuss the results of a simulation experiment concerning log-likelihood ratio, Wald, Score, and Profile tests. Finally, some real datasets are analyzed to illustrate the previous results.     

Influence diagnostics for the Weibull-Negative-Binomial regression model with cure rate under latent failure causes

In this paper, we propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest follows the Negative Binomial distribution and the time to event follows a Weibull distribution. Indeed, we introduce the Weibull-Negative-Binomial (WNB) distribution, which can be used in order to model survival data when the hazard rate function is increasing, decreasing and some non-monotonous shaped. Another advantage of the proposed model is that it has some distributions commonly used in lifetime analysis as particular cases. Moreover, the proposed model includes as special cases some of the well-know cure rate models discussed in the literature. We consider a frequentist analysis for parameter estimation of a WNB model with cure rate. Then, we derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, the methodology is illustrated on a medical data.     

Investigating impacts of complex sampling on latent growth curve modelling

We investigate the impacts of complex sampling on point and standard error estimates in latent growth curve modelling of survey data. Methodological issues are illustrated with empirical evidence from the analysis of longitudinal data on life satisfaction trajectories using data from the British Household Panel Survey, a national representative survey in Great Britain. A multi-process second-order latent growth curve model with conditional linear growth is used to study variation in the two perceived life satisfaction latent factors considered. The benefits of accounting for the complex survey design are considered, including obtaining unbiased both point and standard error estimates, and therefore correctly specified confidence intervals and statistical tests. We conclude that, even for the rather elaborated longitudinal data models that were considered, estimation procedures are affected by variance-inflating impacts of complex sampling.     

Barrios and burbs: residential context and health-risk behaviors among Angeleno adolescents

The increasing size of the Latino immigrant population in the United States underscores the need for a more complete understanding of the role that social context plays in influencing the health of immigrants and their children. This analysis explores the possibility that residential location influences the health-risk behaviors of Latino youth in Los Angeles County, California. The data come from the Los Angeles Family and Neighborhood Survey. We apply multivariate, multilevel Rasch models to two scales of adolescent health-risk behaviors (substance use and delinquency). The findings suggest that residence in Census tracts characterized by above-county-average levels of Latinos and above-county-average levels of poverty is associated with increased odds of health-risk behaviors for Latino adolescents, particularly for those born in the United States. The findings lend support to the contention, put forth in the segmented assimilation literature, that disadvantaged urban contexts increase the risk that U.S.-born children of immigrants will experience downward assimilation.     

SIMPCA: a framework for rotating and sparsifying principal components

We propose an algorithmic framework for computing sparse components from rotated principal components. This methodology, called SIMPCA, is useful to replace the unreliable practice of ignoring small coefficients of rotated components when interpreting them. The algorithm computes genuinely sparse components by projecting rotated principal components onto subsets of variables. The so simplified components are highly correlated with the corresponding components. By choosing different simplification strategies different sparse solutions can be obtained which can be used to compare alternative interpretations of the principal components. We give some examples of how effective simplified solutions can be achieved with SIMPCA using some publicly available data sets.