Likelihood Factorizations for Mixed Discrete and Continuous Variables

Some general remarks are made about likelihood factorizations, distinguishing parameter-based factorizations and concentration-graph factorizations. Two parametric families of distributions for mixed discrete and continuous variables are discussed. Conditions on graphs are given for the circumstances under which their joint analysis can be split into separate analyses, each involving a reduced set of component variables and parameters. The result shows marked differences between the two families although both involve the same necessary condition on prime graphs. This condition is both necessary and sufficient for simplified estimation in Gaussian and for discrete log linear models.     

Semiparametric Additive Accelerated Life Models

In this paper we investigate the asymptotic properties of estimators obtained for the semiparametric additive accelerated life model proposed by Bagdonavicius & Nikulin (1995). This model generalizes the well known additive hazards model of survival analysis and is close to the general transformation model (see Dabrowska & Doksum, 1988). Asymptotic properties of the estimator of the regression parameter and the estimator of the reliability function are given in the case of right censoring for discretized data and a numerical example illustrates these results.     

Efficacy of programmes for the unemployed: discrete time modelling of duration data from a matched-comparison study

An evaluation is described of two UK Government programmes for the long-term unemployed in Great Britain, Employment Training and Employment Action, using discrete time hazard modelling of event histories. The study design employed a closely matched comparison group and carefully chosen control variables to minimize the effect of selection bias on conclusions. The effect of unobserved heterogeneity is investigated by using some standard random effect model formulations.     

The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology

For frequency counts, the situation of extra zeros often arises in biomedical applications. This is demonstrated with count data from a dental epidemiological study in Belo Horizonte (the Belo Horizonte caries prevention study) which evaluated various programmes for reducing caries. Extra zeros, however, violate the variance–mean relationship of the Poisson error structure. This extra-Poisson variation can easily be explained by a special mixture model, the zero-inflated Poisson (ZIP) model. On the basis of the ZIP model, a graphical device is presented which not only summarizes the mixing distribution but also provides visual information about the overall mean. This device can be exploited to evaluate and compare various groups. Ways are discussed to include covariates and to develop an extension of the conventional Poisson regression. Finally, a method to evaluate intervention effects on the basis of the ZIP regression model is described and applied to the data of the Belo Horizonte caries prevention study.     

Gibbs sampling for Bayesian non-conjugate and hierarchical models by using auxiliary variables

We demonstrate the use of auxiliary (or latent) variables for sampling non-standard densities which arise in the context of the Bayesian analysis of non-conjugate and hierarchical models by using a Gibbs sampler. Their strategic use can result in a Gibbs sampler having easily sampled full conditionals. We propose such a procedure to simplify or speed up the Markov chain Monte Carlo algorithm. The strength of this approach lies in its generality and its ease of implementation. The aim of the paper, therefore, is to provide an alternative sampling algorithm to rejection-based methods and other sampling approaches such as the Metropolis–Hastings algorithm.     

Extensions of Fill's algorithm for perfect simulation

Fill's algorithm for perfect simulation for attractive finite state space models, unbiased for user impatience, is presented in terms of stochastic recursive sequences and extended in two ways. Repulsive discrete Markov random fields with two coding sets like the auto-Poisson distribution on a lattice with 4-neighbourhood can be treated as monotone systems if a particular partial ordering and quasi-maximal and quasi-minimal states are used. Fill's algorithm then applies directly. Combining Fill's rejection sampling with sandwiching leads to a version of the algorithm which works for general discrete conditionally specified repulsive models. Extensions to other types of models are briefly discussed.     

The robustness of the quasilikelihood estimator

The quasilikelihood estimator is widely used in data analysis where a likelihood is not available. We illustrate that with a given variance function it is not only conservative, in minimizing a maximum risk, but also robust against a possible misspecification of either the likelihood or cumulants of the model. In examples it is compared with estimators based on maximum likelihood and quadratic estimating functions.     

Between stability and higher-order asymptotics

We discuss the effects of model misspecifications on higher-order asymptotic approximations of the distribution of estimators and test statistics. In particular we show that small deviations from the model can wipe out the nominal improvements of the accuracy obtained at the model by second-order approximations of the distribution of classical statistics. Although there is no guarantee that the first-order robustness properties of robust estimators and tests will carry over to second-order in a neighbourhood of the model, the behaviour of robust procedures in terms of second-order accuracy is generally more stable and reliable than that of their classical counterparts. Finally, we discuss some related work on robust adjustments of the profile likelihood and outline the role of computer algebra in this type of research.     

A Multiple Imputation Approach to Linear Regression with Clustered Censored Data

Weextend Wei and Tanner's (1991) multiple imputation approach insemi-parametric linear regression for univariate censored datato clustered censored data. The main idea is to iterate the followingtwo steps: 1) using the data augmentation to impute for censoredfailure times; 2) fitting a linear model with imputed completedata, which takes into consideration of clustering among failuretimes. In particular, we propose using the generalized estimatingequations (GEE) or a linear mixed-effects model to implementthe second step. Through simulation studies our proposal comparesfavorably to the independence approach (Lee et al., 1993), whichignores the within-cluster correlation in estimating the regressioncoefficient. Our proposal is easy to implement by using existingsoftwares.     

The Analysis of Crop Variety Evaluation Data in Australia

The major aim of crop variety evaluation is to predict the future performance of varieties. This paper presents the routine statistical analysis of data from late-stage testing of crop varieties in Australia. It uses a two-stage approach for analysis. The data from individual trials from the current year are analysed using spatial techniques. The resultant table of variety-by-trial means is combined with tables from previous years to form the data for an overall mixed model analysis. Weights allow for the data being estimates with varying accuracy. In view of the predictive aim of the analysis, variety effects and interactions are regarded as random effects. Appropriate inferential tools have been developed to assist with interpretation of the results. Analyses must be conducted in a timely manner so that variety predictions can be published and disseminated to growers immediately after harvest each year. Factors which facilitate this include easy access to historic data and the use of specialist mixed model software.