Penalized likelihood and Bayesian function selection in regression models

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive predictors has been considered only more recently. Several competing suggestions have been developed at about the same time and often do not refer to each other. This article provides a state-of-the-art review on function selection, focusing on penalized likelihood and Bayesian concepts, relating various approaches to each other in a unified framework. In an empirical comparison, also including boosting, we evaluate several methods through applications to simulated and real data, thereby providing some guidance on their performance in practice.     

On a generalization to Marshall–Olkin scheme and its application to Burr type XII distribution

Marshall–Olkin semi-Burr and Marshall–Olkin Burr distributions are introduced and studied. Their various characteristics in reliability analysis are derived. Applications in time series analysis are discussed.     

Career Development in Middle Childhood: A Qualitative Inquiry

The purpose of this investigation was to explore childhood career development by examining 4th‐ and 5th‐grade students' career and self‐awareness, exploration, and career planning. Responses to written assignments provided qualitative data for analysis. Written narrative data were analyzed using consensual qualitative research methods as described by C. E. Hill, B. J. Thompson, and E. N. Williams (1997). Consistent with theory (D. Super, 1990), children's reflections on prominent career tasks and influences revealed 8 of the 9 (all but curiosity) dimensions of childhood career development as outlined by Super. In addition, participants described their conceptions of work, a domain not explicitly articulated by Super and worthy of further inquiry.     

Social Well-Being in Northern Ireland: A Longitudinal Study 1958–1998

This paper examines the question of how social well-being, or quality of life, in Northern Ireland has changed through time from 1958 to 1998. After reviewing major economic trends and governmental policy affecting the region, we develop an overall measure of quality of life based on previous research into social well-being in Northern Ireland. We find that the ‘Troubles’ clearly impact the quality of life in Northern Ireland but not necessarily as broadly as one might suspect. The majority of the sixteen underlying indicators used for creating a measure of social well-being remain largely unaffected by the conflict and closely track increases in overall United Kingdom Gross Domestic Product. The remaining five measures of social well-being are significantly impacted by the conflict. The resulting measures of social well-being and some suggested uses for future research are then presented.     

A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution

Summary.  A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway–Maxwell–Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway–Maxwell–Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway–Maxwell–Poisson distribution in fitting count data which do not seem to follow the Poisson distribution.