Unconstrained parametrizations for variance-covariance matrices

The estimation of variance-covariance matrices through optimization of an objective function, such as a log-likelihood function, is usually a difficult numerical problem. Since the estimates should be positive semi-definite matrices, we must use constrained optimization, or employ a parametrization that enforces this condition. We describe here five different parametrizations for variance-covariance matrices that ensure positive definiteness, thus leaving the estimation problem unconstrained. We compare the parametrizations based on their computational efficiency and statistical interpretability. The results described here are particularly useful in maximum likelihood and restricted maximum likelihood estimation in linear and non-linear mixed-effects models, but are also applicable to other areas of statistics.     

Slack-variable models versus Scheffé's mixture models

Slack-variable models are compared against Scheffé's polynomial model for mixture experiments. The notion of model equivalence and the use of various diagnostic measures provide effective tools in making such comparisons, particularly when the experimental region is highly constrained. It is demonstrated that the choice of the best fitting model, through variable selection, depends on which mixture component is selected as a slack variable, and on the size of the fitted model. In addition, the equivalence of two well-known representations of a complete mixture model is shown to be valid. Two numerical examples are presented.     

Remaining childless in affluent economies: a comparison of France, West Germany, Italy and Spain, 1994–2001 Rester sans enfant dans des sociétés d'abondances: une comparaison de la France, l'Allemagne de l'Ouest et l'Espagne, 19994–2001

This article explores why women delay childbearing and increase their likelihood to remain childless in Spain, Italy, West Germany and France. We take a macro–micro perspective and show that national institutions influence women’s life transitions, in particular partnership and motherhood. For coupled women, we find two alternative modes out of childlessness. In countries with high direct and indirect child costs, like Spain and Italy, entering a male-breadwinner couple or occupying a stable and high-income position facilitates motherhood, while in the French context motherhood is most likely in a dual-earner partnership.      

Work-related factors contributing to chronic disability in low back pain

Low back pain is a costly and incapacitating musculoskeletal disorder. Prospective studies documenting the capacity of work-related factors to predict chronicity are few in number, the methodology used is very diversified, and the results obtained diverge. The aim of the present study is to investigate the capacity of work-related objective (non-psychosocial) and psychosocial factors to predict chronic disability related to low back pain. A longitudinal prospective study with two measurement times was carried out. The sample (N = 258) consisted of workers with subacute low back pain who were on sick leave and receiving compensation from the CSST (Quebec Workers' Compensation Board). Of all the work-related variables measured, perceived stress and fears and beliefs about work were associated with return to work status at the six-month follow-up. The results obtained show the importance of considering fears and beliefs about work when identifying people in the subacute phase of low back pain who are at risk of developing chronic disability.     

Collective and Unitary Models: A Clarification

In this note we identify and clarify a confusion that has arisen in the literature about the exact relationship between unitary and collective models and what enters the Pareto weight and the sharing function. We suggest that we should denote as ‘unitary’ any model that leads to outcomes that satisfy the Slutsky conditions whether or not these outcomes depend on distribution factors. In particular, income pooling is neither necessary nor sufficient for a unitary model. We also show that the presence of prices or total expenditure in the sharing rule cannot be used as a test for a unitary model.

The exponential Poisson logarithmic distribution

Abstract

In this article, we proposed a new three parameter lifetime distribution motivated mainly by lifetime issues, which generalizes the Exponential Poisson distribution proposed by Cancho et al. (2011) Cancho, V.G., Louzada-Neto, F., Barriga, G.D. (2011). The poisson-exponential lifetime distribution. Computat. Statist. Data Anal. 55:677–686.[Crossref], [Web of Science ®] , [Google Scholar]. We derive various standard mathematical properties of the proposed model including a formal proof of its probability density function and hazard rate function. The inference via the maximum likelihood approach is discussed. The performance of the maximum likelihood estimators, the likelihood ratio test and its power are studied by simulation. Finally, the proposed model is fitted to two real data sets and it is compared with several models.     

Waiting time to exhaust lottery numbers

Questions related to lotteries are usually of interest to the public since people think there is a magic formula which will help them to win lottery draws. This note shows how to compute the expected waiting time to observe specific numbers in a sequence of lottery draws and show that surprising facts are expected to occur.