What is natural fertility? The modelling of a concept

The value and importance of the concept of natural fertility have been widely debated since Henry's work in the late 1950s. Whereas Henry regarded natural fertility largely as a useful concept for model building, Coale-Trussell demonstrated that this concept could also be used to analyze patterns of age-specific fertility. The set of age-specific marital fertility schedules assembled by Henry and then used by Coale and Trussell involved largely small populations drawn from disparate sources. Nonetheless, from this diverse and fragmentary data, Henry was able to construct a standard of natural fertility which, in the operational form developed by Coale-Trussell, has proved remarkably general in its application and utility. This in turn suggests that the physiological forces shaping fertility are exceedingly strong, especially the incidence of physiological sterility. There appears to be no single universal pattern of natural fertility. Rather, there is a set of closely related age profiles, the exact shape of which is determined by specific behavioral and social factors that influence childbearing. The increase in physiological sterility with age serves to give an upper limit to fertility at each age, while other factors determine how close a given population comes to that maximum. Although no society has ever demonstrated Henry's ideal notion of a purely physiological fertility pattern, the effect of the intervening factors is often weak. In terms of the Coale-Trussell model, maximum likelihood estimation offers the most informative method of implementation and a time series for 1 population is more readily interpretable than a cross-section comparing several populations.     

AVERAGE PREDICTIVE COMPARISONS FOR MODELS WITH NONLINEARITY, INTERACTIONS, AND VARIANCE COMPONENTS

In a predictive model, what is the expected difference in the outcome associated with a unit difference in one of the inputs? In a linear regression model without interactions, this average predictive comparison is simply a regression coefficient (with associated uncertainty). In a model with nonlinearity or interactions, however, the average predictive comparison in general depends on the values of the predictors. We consider various definitions based on averages over a population distribution of the predictors, and we compute standard errors based on uncertainty in model parameters. We illustrate with a study of criminal justice data for urban counties in the United States. The outcome of interest measures whether a convicted felon received a prison sentence rather than a jail or non-custodial sentence, with predictors available at both individual and county levels. We fit three models: (1) a hierarchical logistic regression with varying coefficients for the within-county intercepts as well as for each individual predictor; (2) a hierarchical model with varying intercepts only; and (3) a nonhierarchical model that ignores the multilevel nature of the data. The regression coefficients have different interpretations for the different models; in contrast, the models can be compared directly using predictive comparisons. Furthermore, predictive comparisons clarify the interplay between the individual and county predictors for the hierarchical models and also illustrate the relative size of varying county effects.     

Predicting Oscar winners

Each year, hundreds of millions of people worldwide watch the televised Oscars ceremony. Can one predict which films and which directors, actors and actresses will win the Oscars? Iain Pardoe believes that he can.     

Applying discrete choice models to predict Academy Award winners

Summary.  Every year since 1928, the Academy of Motion Picture Arts and Sciences has recognized outstanding achievement in film with their prestigious Academy Award, or Oscar. Before the winners in various categories are announced, there is intense media and public interest in predicting who will come away from the awards ceremony with an Oscar statuette. There are no end of theories about which nominees are most likely to win, yet despite this there continue to be major surprises when the winners are announced. The paper frames the question of predicting the four major awards—picture, director, actor in a leading role and actress in a leading role—as a discrete choice problem. It is then possible to predict the winners in these four categories with a reasonable degree of success. The analysis also reveals which past results might be considered truly surprising—nominees with low estimated probability of winning who have overcome nominees who were strongly favoured to win.     

A GRAPHICAL DIAGNOSTIC FOR VARIANCE FUNCTIONS

This paper proposes diagnostic plots for regression variance functions. It shows how to extend graphical methodology that uses Bayesian sampling for checking the regression mean function to also check the variance function. Plots can be constructed quickly and easily for any model of interest. These plots help to identify model weaknesses and can suggest ways to make improvements. The proposed methodology is illustrated with two examples: a simple linear regression model to fix ideas, and a more complex study involving count data to demonstrate the potential for wide application.