ON THE OPTIMAL ASYMPTOTIC TESTS FOR THE EFFECTS OF CLOUD SEEDING ON RAINFALL (1) THE CASE OF FIXED EFFECTS

In this paper we consider a sequence of experimental units {u_n} which are t o be treated according to some random scheme. A general randomized design is suggested for the purpose. Asymptotic tests, optimal in some sense, are derived for testing the absence of the effects of the treatment. These tests are applicable in various situations, for example, when the treatment effects are additive or when they are multiplicative. Based on the asymptotic power of the tests obtained, optimality of various designs is discussed. The randomized designs discussed here have a wide range of applicability, e.g. in weather modification experiments and bio-assay.     

The effect of individual variability on the life table

A general formulation of the life table in the presence of individual jeterogeneity is presented. The possible effects of heterogeneity on the various life table functions are outlined. For the case of ordinary life tables, a method is presented for the evaluation of these effects. The proposed method id illustrated by a numerical example.     

Robust regression estimators compared via monte carlo

This paper presents results of a Monte Carlo simulation of eight families of robust regression estimators in various situations. The effects studied include long-tailed error terms, measurement error in the independent variables, various spacings of the independent variables, different sample sizes and correlation between the independent variables. An estimator that combines the best features of several of the estimators is recommended for further study.     

Circular balanced repeated measurements designs

The concept of a circular design is defined and when proper balance for various effects is assumed, its universal optimality is proved over the class of all designs with the same set of parameters, Such designs are shown to minimize the variance of the best linear unbiased estimators of contrasts of residual and direct effects over the class of equireplicated designs. All models assume first order residual effects and are of a circular nature. The proofs are presented in a unified manner for several models at a time. They are based on certain matrix domination which occurs when parameters are eliminated from a linear modelj this latter fact is proved for a general linear model.     

Analysis of error-prone survival data under additive hazards models: measurement error effects and adjustments

Covariate measurement error occurs commonly in survival analysis. Under the proportional hazards model, measurement error effects have been well studied, and various inference methods have been developed to correct for error effects under such a model. In contrast, error-contaminated survival data under the additive hazards model have received relatively less attention. In this paper, we investigate this problem by exploring measurement error effects on parameter estimation and the change of the hazard function. New insights of measurement error effects are revealed, as opposed to well-documented results for the Cox proportional hazards model. We propose a class of bias correction estimators that embraces certain existing estimators as special cases. In addition, we exploit the regression calibration method to reduce measurement error effects. Theoretical results for the developed methods are established, and numerical assessments are conducted to illustrate the finite sample performance of our methods.     

Seasonality in U.S. Consumer Demand

This study uses a new body of quarterly, not seasonally adjusted, data to test various hypotheses regarding consumer demand. The almost complete demand system (ACS) was used to test for the various restrictions of economic theory and for the presence of seasonality. Zero-degree homogeneity, Cournot aggregation, and negativity were, for the most part, accepted. Tests showed that seasonal effects can be modeled by quarterly intercepts and that slope coefficients are homogeneous over seasons. Also, it was demonstrated that although habit plays a significant role, it is not as prominent as past studies have shown.     

Fast EM-type implementations for mixed effects models

The mixed effects model, in its various forms, is a common model in applied statistics. A useful strategy for fitting this model implements EM-type algorithms by treating the random effects as missing data. Such implementations, however, can be painfully slow when the variances of the random effects are small relative to the residual variance. In this paper, we apply the 'working parameter' approach to derive alternative EM-type implementations for fitting mixed effects models, which we show empirically can be hundreds of times faster than the common EM-type implementations. In our limited simulations, they also compare well with the routines in S-PLUS® and Stata® in terms of both speed and reliability. The central idea of the working parameter approach is to search for efficient data augmentation schemes for implementing the EM algorithm by minimizing the augmented information over the working parameter, and in the mixed effects setting this leads to a transfer of the mixed effects variances into the regression slope parameters. We also describe a variation for computing the restricted maximum likelihood estimate and an adaptive algorithm that takes advantage of both the standard and the alternative EM-type implementations.     

On testing random effects in the nested-error regression model

We derive an exact F-test for random effects in the nested-error regression model. The derivation utilizes a matrix decomposition that offers a transformation of the response vector into two independent subvectors. When the random effects are absent, the test statistic reduces to a ratio of two independent residual sums of squares that are computed by fitting a regression model using each subvector. A small simulation study compares the power of the F-test with various recent tests and shows that the proposed test has a competitive performance under small as well as large number of clusters.     

Third order point process intensity estimation for reaction time experiment data

The authors consider a simple parametric model for data from a point process version of a reaction time experiment to test the nature of thinning mechanisms in the presence of nonlinear inhibition in the eye‐brain‐hand system. In particular, they study the effects of two such mechanisms on the third order intensity estimate. An alternative nonparametric estimate is also considered in this context. These various approaches are applied on twelve runs of real data, but the analysis turns out to be inconclusive: neither mechanism can be ruled out, nor the possibility that their effects could be combined.     

A model of toxoplasmosis incidence in the UK: evidence synthesis and consistency of evidence

Summary.  We present a Bayesian evidence synthesis model combining data on seroprevalence, seroconversion and tests of recent infection, to produce estimates of current incidence of toxoplasmosis in the UK. The motivation for the study was the need for an estimate of current average incidence in the UK, with a realistic assessment of its uncertainty, to inform a decision model for a national screening programme to prevent congenital toxoplasmosis. The model has a hierarchical structure over geographic region, a random-walk model for temporal effects and a fixed age effect, with one or more types of data informing the regional estimates of incidence. Inference is obtained by using Markov chain Monte Carlo simulations. A key issue in the synthesis of evidence from multiple sources is model selection and the consistency of different types of evidence. Alternative models of incidence are compared by using the deviance information criterion, and we find that temporal effects are region specific. We assess the consistency of the various forms of evidence by using cross-validation where practical, and posterior and mixed prediction otherwise, and we discuss how these measures can be used to assess different aspects of consistency in a complex evidence structure. We discuss the contribution of the various forms of evidence to estimated current average incidence.     

Bayesian analysis of longitudinal ordered data with flexible random effects using McMC: application to diabetic macular Edema data

In the analysis of correlated ordered data, mixed-effect models are frequently used to control the subject heterogeneity effects. A common assumption in fitting these models is the normality of random effects. In many cases, this is unrealistic, making the estimation results unreliable. This paper considers several flexible models for random effects and investigates their properties in the model fitting. We adopt a proportional odds logistic regression model and incorporate the skewed version of the normal, Student's t and slash distributions for the effects. Stochastic representations for various flexible distributions are proposed afterwards based on the mixing strategy approach. This reduces the computational burden being performed by the McMC technique. Furthermore, this paper addresses the identifiability restrictions and suggests a procedure to handle this issue. We analyze a real data set taken from an ophthalmic clinical trial. Model selection is performed by suitable Bayesian model selection criteria.     

Posterior consistency in frailty models and simulation studies to test the presence of random effects

The estimation of random effects in frailty models is an important problem in survival analysis. Testing for the presence of random effects can be essential to improving model efficiency. Posterior consistency in dispersion parameters and coefficients of the frailty model was demonstrated in theory and simulations using the posterior induced by Cox’s partial likelihood and simple priors. We also conducted simulation studies to test for the presence of random effects; the proposed method performed well in several simulations. Data analysis was also conducted. The proposed method is easily tractable and can be used to develop various methods for Bayesian inference in frailty models.     

A Case Study for Modelling Cancer Incidence Using Bayesian Spatio‐Temporal Models

Researchers familiar with spatial models are aware of the challenge of choosing the level of spatial aggregation. Few studies have been published on the investigation of temporal aggregation and its impact on inferences regarding disease outcome in space–time analyses. We perform a case study for modelling individual disease outcomes using several Bayesian hierarchical spatio‐temporal models, while taking into account the possible impact of spatial and temporal aggregation. Using longitudinal breast cancer data from South East Queensland, Australia, we consider both parametric and non‐parametric formulations for temporal effects at various levels of aggregation. Two temporal smoothness priors are considered separately; each is modelled with fixed effects for the covariates and an intrinsic conditional autoregressive prior for the spatial random effects. Our case study reveals that different model formulations produce considerably different model performances. For this particular dataset, a classical parametric formulation that assumes a linear time trend produces the best fit among the five models considered. Different aggregation levels of temporal random effects were found to have little impact on model goodness‐of‐fit and estimation of fixed effects.     

The survival of newly founded firms: a case-study into varying-coefficient models

Summary.  The success of a newly founded firm depends on various initial risk factors or start-up conditions such as the market that the business is aiming for, the experience and the age of the founder, the preparation before the launch, the financial frame and the legal form of the firm. These risk factors determine the chance of survival for the venture. However, the effects of these risk factors may change with time. Some effects may vanish whereas others remain constant. We analyse the survival of 1123 newly founded firms in the state of Bavaria, Germany. Our focus is on the investigation of time variation in the effects of risk factors. Time variation is tackled within the framework of varying-coefficient models, where time smoothly modifies the effects of risk factors. An important issue in our analysis is the separation of risk factors which have time-varying effects from those which have time constant effects. We make use of the Akaike criterion to separate these two types of risk factor.     

Random effects regression mixtures for analyzing infant habituation

Random effects regression mixture models are a way to classify longitudinal data (or trajectories) having possibly varying lengths. The mixture structure of the traditional random effects regression mixture model arises through the distribution of the random regression coefficients, which is assumed to be a mixture of multivariate normals. An extension of this standard model is presented that accounts for various levels of heterogeneity among the trajectories, depending on their assumed error structure. A standard likelihood ratio test is presented for testing this error structure assumption. Full details of an expectation-conditional maximization algorithm for maximum likelihood estimation are also presented. This model is used to analyze data from an infant habituation experiment, where it is desirable to assess whether infants comprise different populations in terms of their habituation time.     

An investigation of the impact of various geographical scales for the specification of spatial dependence

Ecological studies are based on characteristics of groups of individuals, which are common in various disciplines including epidemiology. It is of great interest for epidemiologists to study the geographical variation of a disease by accounting for the positive spatial dependence between neighbouring areas. However, the choice of scale of the spatial correlation requires much attention. In view of a lack of studies in this area, this study aims to investigate the impact of differing definitions of geographical scales using a multilevel model. We propose a new approach – the grid-based partitions and compare it with the popular census region approach. Unexplained geographical variation is accounted for via area-specific unstructured random effects and spatially structured random effects specified as an intrinsic conditional autoregressive process. Using grid-based modelling of random effects in contrast to the census region approach, we illustrate conditions where improvements are observed in the estimation of the linear predictor, random effects, parameters, and the identification of the distribution of residual risk and the aggregate risk in a study region. The study has found that grid-based modelling is a valuable approach for spatially sparse data while the statistical local area-based and grid-based approaches perform equally well for spatially dense data.     

A hierarchical modelling approach for measuring reliability of and agreement between two types of magnetic field dosimeter

Summary.  The paper describes how to use hierarchical models to assess the reliability of and agreement between two or more types of measurement device. The idea is illustrated by fitting a linear model with nested random effects to a set of data that was obtained from the calibration of two samples of extremely low frequency magnetic field meters. The paper focuses on the formulation of a suitable model that accounts for the various aspects of the calibration protocol and the subsequent interpretation of the parameter estimates. The approach is very flexible and can easily be tuned to the various needs arising in the measurement agreement framework. It can be seen as an extension of the common practice of using a one-way random-effects model to retrieve a measure of agreement.     

Mixed two- and four-level fractional factorial split-plot designs with clear effects

Mixed-level designs have become widely used in the practical experiments. When the levels of some factors are difficult to be changed or controlled, fractional factorial split-plot (FFSP) designs are often used. It is highly to know when a mixed-level FFSP design with resolution III or IV has clear effects. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and four-level factors to have various clear factorial effects, including two types of main effects and three types of two-factor interaction components. The structures of such designs are shown and illustrated with examples.     

Visualising interaction effects

In drug discovery, statisticians often work with biologists and chemists to uncover relationships between the various chemical properties and the biological effects of compounds. The aim is to "design" drugs that have exactly the desired pharmaceutical effects. Phil Woodward and Mark Whitlock of Pfizer Global R&D show how a graph can uncover deeply hidden relationships and guide chemists in their efforts to find the next blockbuster drug.     

Purchase timing models in marketing: a review

In this work we review various approaches to modeling the purchase behavior of consumers in marketing. Special emphasis is given to the timing of purchases. We also discuss in detail a new approach which models the hazard function in a flexible dynamic way thus yielding self-exciting phenomena. In particular our approach is able to incorporate seasonal and advertising effects and past purchase decisions. The method is applied to panel data for fast moving consumer goods.