Ronald Christensen

Log-linear models

This book examines log-linear models for contingency tables. It uses previous knowledge of analysis of variance and regression to motivate and explicate the use of log-linear models. It is a textbook primarily directed at advanced Masters degree students in statistics but can be used at both higher and lower levels. Outlines for introductory, intermediate and advanced courses are given in the preface. All the fundamental statistics for analyzing data using log-linear models are given.

A New Perspective on Priors for Generalized Linear Models

Abstract This article deals with specifications of informative prior distributions for generalized linear models. Our emphasis is on specifying distributions for selected points on the regression surface; the prior distribution on regression coefficients is induced from this specification. We believe that it is inherently easier to think about conditional means of observables given the regression variables than it is to think about model-dependent regression coefficients. Previous use of conditional means priors seems to be restricted to logistic regression with one predictor variable and to normal theory regression. We expand on the idea of conditional means priors and extend these to arbitrary generalized linear models. We also consider data augmentation priors where the prior is of the same form as the likelihood. We show that data augmentation priors are special cases of conditional means priors. With current Monte Carlo methodology, such as importance sampling and Gibbs sampling, our priors result in...

Linear models for multivariate, time series, and spatial data

Multivariate linear models discrimination and allocation frequency analysis of time series time domain analysis linear models for spatial data.

Case-deletion diagnostics for mixed models

Mixed linear models arise in many areas of application. Standard estimation methods for mixed models are sensitive to bizarre observations. Such influential observations can completely distort an analysis and lead to inappropriate actions and conclusions. We develop case-deletion diagnostics for detecting influential observations in mixed linear models. Diagnostics for both fixed effects and variance components are proposed. Computational formulas are given that make the procedures feasible. The methods are illustrated using examples.

Plane Answers to Complex Questions

Plane answers to complex questions , Plane answers to complex questions , کتابخانه دیجیتال جندی شاپور اهواز

Bayesian Binomial Regression: Predicting Survival at a Trauma Center

Abstract Standard methods for analyzing binomial regression data rely on asymptotic inferences. Bayesian methods can be performed using simple computations, and they apply for any sample size. We provide a relatively complete discussion of Bayesian inferences for binomial regression with emphasis on inferences for the probability of “success.” Furthermore, we illustrate diagnostic tools, perform model selection among nonnested models, and examine the sensitivity of the Bayesian methods.

Identifiability of Models for Multiple Diagnostic Testing in the Absence of a Gold Standard

We discuss the issue of identifiability of models for multiple dichotomous diagnostic tests in the absence of a gold standard (GS) test. Data arise as multinomial or product-multinomial counts depending upon the number of populations sampled. Models are generally posited in terms of population prevalences, test sensitivities and specificities, and test dependence terms. It is commonly believed that if the degrees of freedom in the data meet or exceed the number of parameters in a fitted model then the model is identifiable. Goodman (1974, Biometrika 61, 215-231) established that this was not the case a long time ago. We discuss currently available models for multiple tests and argue in favor of an extension of a model that was developed by Dendukuri and Joseph (2001, Biometrics 57, 158-167). Subsequently, we further develop Goodmans technique, and make geometric arguments to give further insight into the nature of models that lack identifiability. We present illustrations using simulated and real data.

Bayesian accelerated failure time analysis with application to veterinary epidemiology

Standard methods for analysing survival data with covariates rely on asymptotic inferences. Bayesian methods can be performed using simple computations and are applicable for any sample size. We propose a practical method for making prior specifications and discuss a complete Bayesian analysis for parametric accelerated failure time regression models. We emphasize inferences for the survival curve rather than regression coefficients. A key feature of the Bayesian framework is that model comparisons for various choices of baseline distribution are easily handled by the calculation of Bayes factors. Such comparisons between non-nested models are difficult in the frequentist setting. We illustrate diagnostic tools and examine the sensitivity of the Bayesian methods.

Bayesian Resolution of the “Exchange Paradox”

Abstract In this article we present a paradox that can be used to illustrate Bayesian principles in the classroom. The paradox is also resolved using a frequentist argument and illustrates how the misapplication of a symmetry argument causes problems.

The equivalence of predictions from universal kriging and intrinsic random-function kriging

A proof is provided that the predictions obtained from kriging based on intrinsic random functions of orderk are identical to those obtained from anappropriate universal kriging model. This is a theoretical result based on known variability measures. It does not imply that people performing traditional universal kriging will get the same predictions as those using intrinsic random functions, because traditionally these methods differ in how variability is modeled. For intrinsic random functions, the same proof shows that predictions do not depend on the specific choice of the generalized covariance function. It is argued that the choice between these methods is really one of modeling and estimating the variability in the data.