Designs for generalized linear models with several variables and model uncertainty

Standard factorial designs sometimes may be inadequate for experiments that aim to estimate a generalized linear model, for example, for describing a binary response in terms of several variables. A method is proposed for finding exact designs for such experiments that uses a criterion allowing for uncertainty in the link function, the linear predictor, or the model parameters, together with a design search. Designs are assessed and compared by simulation of the distribution of efficiencies relative to locally optimal designs over a space of possible models. Exact designs are investigated for two applications, and their advantages over factorial and central composite designs are demonstrated.

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

Fitting genetic models to twin data with binary and ordered categorical responses: A comparison of structural equation modelling and Bayesian hierarchical models

We compare Bayesian methodology utilizing free-ware BUGS (Bayesian Inference Using Gibbs Sampling) with the traditional structural equation modelling approach based on another free-ware package, Mx. Dichotomous and ordinal (three category) twin data were simulated according to different additive genetic and common environment models for phenotypic variation. Practical issues are discussed in using Gibbs sampling as implemented by BUGS to fit subject-specific Bayesian generalized linear models, where the components of variation may be estimated directly. The simulation study (based on 2000 twin pairs) indicated that there is a consistent advantage in using the Bayesian method to detect a correct model under certain specifications of additive genetics and common environmental effects. For binary data, both methods had difficulty in detecting the correct model when the additive genetic effect was low (between 10 and 20%) or of moderate range (between 20 and 40%). Furthermore, neither method could adequately detect a correct model that included a modest common environmental effect (20%) even when the additive genetic effect was large (50%). Power was significantly improved with ordinal data for most scenarios, except for the case of low heritability under a true ACE model. We illustrate and compare both methods using data from 1239 twin pairs over the age of 50 years, who were registered with the Australian National Health and Medical Research Council Twin Registry (ATR) and presented symptoms associated with osteoarthritis occurring in joints of the hand.

A zero-augmented gamma mixed model for longitudinal data with many zeros

In many occupational safety interventions, the objective is to reduce the injury incidence as well as the mean claims cost once injury has occurred. The claims cost data within a period typically contain a large proportion of zero observations (no claim). The distribution thus comprises a point mass at 0 mixed with a non-degenerate parametric component. Essentially, the likelihood function can be factorized into two orthogonal components. These two components relate respectively to the effect of covariates on the incidence of claims and the magnitude of claims, given that claims are made. Furthermore, the longitudinal nature of the intervention inherently imposes some correlation among the observations. This paper introduces a zero-augmented gamma random effects model for analysing longitudinal data with many zeros. Adopting the generalized linear mixed model (GLMM) approach reduces the original problem to the fitting of two independent GLMMs. The method is applied to evaluate the effectiveness of a workplace risk assessment teams program, trialled within the cleaning services of a Western Australian public hospital.

Integrable generalized spin ladder models based on the SU(1|3) and SU(3|1) algebras

We present two integrable spin ladder models which possess a general free parameter besides the rung coupling J. The models are exactly solvable by means of the Bethe ansatz method and we present the Bethe ansatz equations. We analyze the elementary excitations of the models which reveal the existence of a gap for both models that depends on the free parameter. (C) 2003 American Institute of Physics.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

Generalized Perk-Schultz models: solutions of the Yang-Baxter equation associated with quantized orthosymplectic superalgebras

The Perk-Schultz model may be expressed in terms of the solution of the Yang-Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra U-q (gl(m/n)], with a multiparametric coproduct action as given by Reshetikhin. Here, we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras U-q[osp(m/n)]. In this manner, we obtain generalizations of the Perk-Schultz model.

Redefining functional models of basal ganglia organisation: Role for the posteroventral pallidum in linguistic processing?

Traditionally the basal ganglia have been implicated in motor behavior, as they are involved in both the execution of automatic actions and the modification of ongoing actions in novel contexts. Corresponding to cognition, the role of the basal ganglia has not been defined as explicitly. Relative to linguistic processes, contemporary theories of subcortical participation in language have endorsed a role for the globus pallidus internus (GPi) in the control of lexical-semantic operations. However, attempts to empirically validate these postulates have been largely limited to neuropsychological investigations of verbal fluency abilities subsequent to pallidotomy. We evaluated the impact of bilateral posteroventral pallidotomy (BPVP) on language function across a range of general and high-level linguistic abilities, and validated/extended working theories of pallidal participation in language. Comprehensive linguistic profiles were compiled up to 1 month before and 3 months after BPVP in 6 subjects with Parkinson's disease (PD). Commensurate linguistic profiles were also gathered over a 3-month period for a nonsurgical control cohort of 16 subjects with PD and a group of 16 non-neurologically impaired controls (NC). Nonparametric between-groups comparisons were conducted and reliable change indices calculated, relative to baseline/3-month follow-up difference scores. Group-wise statistical comparisons between the three groups failed to reveal significant postoperative changes in language performance. Case-by-case data analysis relative to clinically consequential change indices revealed reliable alterations in performance across several language variables as a consequence of BPVP. These findings lend support to models of subcortical participation in language, which promote a role for the GPi in lexical-semantic manipulation mechanisms. Concomitant improvements and decrements in postoperative performance were interpreted within the context of additive and subtractive postlesional effects. Relative to parkinsonian cohorts, clinically reliable versus statistically significant changes on a case by case basis may provide the most accurate method of characterizing the way in which pathophysiologically divergent basal ganglia linguistic circuits respond to BPVP.

Polytomous item response theory models

Polytomous Item Response Theory Models provides a unified, comprehensive introduction to the range of polytomous models available within item response theory (IRT). It begins by outlining the primary structural distinction between the two major types of polytomous IRT models. This focuses on the two types of response probability that are unique to polytomous models and their associated response functions, which are modeled differently by the different types of IRT model. It describes, both conceptually and mathematically, the major specific polytomous models, including the Nominal Response Model, the Partial Credit Model, the Rating Scale model, and the Graded Response Model. Important variations, such as the Generalized Partial Credit Model are also described as are less common variations, such as the Rating Scale version of the Graded Response Model. Relationships among the models are also investigated and the operation of measurement information is described for each major model. Practical examples of major models using real data are provided, as is a chapter on choosing an appropriate model. Figures are used throughout to illustrate important elements as they are described.

Role of generalized and episode specific memories in the word frequency effect in recognition

Frequency, recency, and type of prior exposure to very low-and high-frequency words were manipulated in a 3-phase (i.e., familiarization training, study, and test) design. Increasing the frequency with which a definition for a very low-frequency word was provided during familiarization facilitated the word's recognition in both yes-no (Experiment 1) and forced-choice paradigms (Experiment 2). Recognition of very low-frequency words not accompanied by a definition during familiarization first increased, then decreased as familiarization frequency increased (Experiment I). Reasons for these differences were investigated in Experiment 3 using judgments of recency and frequency. Results suggested that prior familiarization of a very low-frequency word with its definition may allow a more adequate episodic representation of the word to be formed during a subsequent study trial. Theoretical implications of these results for current models of memory are discussed.

Production under uncertainty and choice under uncertainty in the emergence of generalized expected utility theory

This paper presents a personal view of the interaction between the analysis of choice under uncertainty and the analysis of production under uncertainty. Interest in the foundations of the theory of choice under uncertainty was stimulated by applications of expected utility theory such as the Sandmo model of production under uncertainty. This interest led to the development of generalized models including rank-dependent expected utility theory. In turn, the development of generalized expected utility models raised the question of whether such models could be used in the analysis of applied problems such as those involving production under uncertainty. Finally, the revival of the state-contingent approach led to the recognition of a fundamental duality between choice problems and production problems.

A generalized Markov sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis-Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.

Forecasting with serially correlated regression models

In this article we investigate the asymptotic and finite-sample properties of predictors of regression models with autocorrelated errors. We prove new theorems associated with the predictive efficiency of generalized least squares (GLS) and incorrectly structured GLS predictors. We also establish the form associated with their predictive mean squared errors as well as the magnitude of these errors relative to each other and to those generated from the ordinary least squares (OLS) predictor. A large simulation study is used to evaluate the finite-sample performance of forecasts generated from models using different corrections for the serial correlation.

The specification of vector autoregressive moving average models

In this paper we propose a new identification method based on the residual white noise autoregressive criterion (Pukkila et al. , 1990) to select the order of VARMA structures. Results from extensive simulation experiments based on different model structures with varying number of observations and number of component series are used to demonstrate the performance of this new procedure. We also use economic and business data to compare the model structures selected by this order selection method with those identified in other published studies.