Using auxiliary data for parameter estimation with non-ignorably missing outcomes

We propose a method for estimating parameters in generalized linear models when the outcome variable is missing for some subjects and the missing data mechanism is non-ignorable. We assume throughout that the covariates are fully observed. One possible method for estimating the parameters is maximum likelihood with a non-ignorable missing data model. However, caution must be used when fitting non-ignorable missing data models because certain parameters may be inestimable for some models. Instead of fitting a non-ignorable model, we propose the use of auxiliary information in a likelihood approach to reduce the bias, without having to specify a non-ignorable model. The method is applied to a mental health study.     

A simple method for estimating a regression model for κ between a pair of raters

Agreement studies commonly occur in medical research, for example, in the review of X-rays by radiologists, blood tests by a panel of pathologists and the evaluation of psychopathology by a panel of raters. In these studies, often two observers rate the same subject for some characteristic with a discrete number of levels. The κ-coefficient is a popular measure of agreement between the two raters. The κ-coefficient may depend on covariates, i.e. characteristics of the raters and/or the subjects being rated. Our research was motivated by two agreement problems. The first is a study of agreement between a pastor and a co-ordinator of Christian education on whether they feel that the congregation puts enough emphasis on encouraging members to work for social justice (yes versus no). We wish to model the κ-coefficient as a function of covariates such as political orientation (liberal versus conservative) of the pastor and co-ordinator. The second example is a spousal education study, in which we wish to model the κ-coefficient as a function of covariates such as the highest degree of the father of the wife and the father of the husband. We propose a simple method to estimate the regression model for the κ-coefficient, which consists of two logistic (or multinomial logistic) regressions and one linear regression for binary data. The estimates can be easily obtained in any generalized linear model software program.     

Stochastic relaxation,Gibbs distributions and the Bayesian restoration of images*

We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, non-linear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low-energy states (‘annealing’), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ‘relaxation’ algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.     

Changes in occupational mix in engineering 1964–1972

Changes in the occupational structure could arise from different rates of output, and hence employment, growth in sectors of engineering or from changes in the occupational mix of the sectors. Almost all the change arises from the latter and, more importantly, the rate of change is not constant. Changes in the sector occupational mix will follow from investment and an understanding of this relationship is crucial to progress in manpower demand forecasting.     

Bayesian Methods for Missing Covariates in Cure Rate Models

We propose methods for Bayesian inference for missing covariate data with a novel class of semi-parametric survival models with a cure fraction. We allow the missing covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one dimensional conditional distributions. We assume that the missing covariates are missing at random (MAR) throughout. We propose an informative class of joint prior distributions for the regression coefficients and the parameters arising from the covariate distributions. The proposed class of priors are shown to be useful in recovering information on the missing covariates especially in situations where the missing data fraction is large. Properties of the proposed prior and resulting posterior distributions are examined. Also, model checking techniques are proposed for sensitivity analyses and for checking the goodness of fit of a particular model. Specifically, we extend the Conditional Predictive Ordinate (CPO) statistic to assess goodness of fit in the presence of missing covariate data. Computational techniques using the Gibbs sampler are implemented. A real data set involving a melanoma cancer clinical trial is examined to demonstrate the methodology.     

The human ecology of tornadoes

This paper offers an empirical test of the impact of human ecological patterns and other known correlates on tornado occurrence. It uses the National Severe Storms Forecast Center’s information on tornadoes from 1950 through 1990 and employs ecological data from the U.S. Bureau of the Census and the Environmental Protection Agency. The results show that metropolitan and other urban counties have higher odds of tornado occurrence than rural counties, and that the probability of occurrence of tornadoes increases with increases in the number of previous tornadoes. The paper assesses the meaning of this finding for demographers, atmospheric scientists, engineers, and disaster managers.     

A social indicator based on time allocation

The authors have developed a social indicator, called Lambda, that has as its base the manner in which individuals allocate their time among various life activities. This indicator does not suffer from the usual demand characteristics and experimenter bias associated with most subjective social indicators, i.e., those based on question-naires. It is not a single rate indicator in the sense of suicide rate. Lambda is a weighted sum social indicator with both subjective and objective aspects. The weights are decided by the population under consideration and not by the investigators or some other outside agents. The elements to be summed are the frequency functions for the discrepancies that arise when individuals state the amount of time they would like to spend in an activitiy versus the amount of time they actually spend at the activity. There are frequency functions for each activity. The properties of this indicator are discussed in detail. A pilot study comparing Lambda to another social indicator and some demographic variables was conducted with 1012 undergraduate students. The results of the pilot study show a high correlation between Lambda and the other social indicator. The results are presented. Lambda is currently being used by the Gallup organization.