Showing papers in "Applied statistics in 1987"

On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture

Abstract: An important but difficult problem in practice is assessing the number of components g in a mixture. An obvious way of proceeding is to use the likelihood ratio test statistic λ to test for the smallest value of g consistent with the data. Unfortunately with mixture models, regularity conditions do not hold for –2 log λ to have it usual asymptotic null distribution of chi‐squared. In this paper the role of the bootstrap is highlighted for the assessment of the null distribution of –2 log λ for the test of a single normal density versus a mixture of two normal densities in the univariate case.

A Method for Comparing Profiles of Repeated Measurements

Abstract: On propose une methode de comparaison des profils de mesures repetees, basee sur la structure de covariance d'ante-dependance de Gabriel (1961-1962). Cette methode est appropriee pour des experiences dans lesquelles aucun point specifique des profils n'est connu pour etre interessant a priori

Modelling variance heterogeneity in normal regression using GLIM

Abstract: On montre que le modele considere peut etre ajuste par le maximum de vraisemblance et que le parametre moyen peut etre estime simultanement

Selection of Variables to Preserve Multivariate Data Structure, Using Principal Components

Abstract: On propose une nouvelle methode basee sur l'analyse Procrustes et on montre qu'elle fournit un meilleur sous-ensemble pour les donnees analysees en premier

Regression Analysis of Relative Survival Rates

Abstract: Survival from cancer or other chronic diseases is often measured using the relative survival rate. This, in turn, is defined as the ratio of the observed survival rate in the patient group under consideration to the expected survival rate in a group taken from the general population. At the beginning of the follow-up period, apart from the disease under study, factors affecting survival (e.g. age and sex) should be similar in the two groups. This paper outlines how a proportional hazards regression model may be adapted to the relative survival rates using GLIM. The method is illustrated by data on lung cancer patients diagnosed in Finland in 1 968-1 970.

Generalized Linear Model Diagnostics Using the Deviance and Single Case Deletions

Abstract: SUMMARY This paper exploits the one step approximation, derived by Pregibon (1981), for the changes in the deviance of a generalized linear model when a single case is deleted from the data This approximation suggests a particular set of residuals which can be used, not only to identify outliers and examine distributional assumptions, but also to calculate measures of the influence of single cases on various inferences that can be drawn from the fitted model using likelihood ratio statistics Regression diagnostics for the Normal linear model are now well established in the literature They are comprehensively surveyed by Cook and Weisberg (1982) Many of these diagnostics use statistics which measure the effects of deleting single cases from the data These statistics exploit the exact algebraic relationship between the least squares fit of the linear model to a complete set of n cases, and the fit to the n - 1 cases remaining after the deletion of a single case The maximum likelihood (ML) estimation of most generalized linear models (GLMs) requires iterative methods The ML estimates from n - 1 cases cannot then be obtained as explicit functions of the results of the fit to all n cases In an important paper Pregibon (1981) derives useful one step approximations for the changes in the ML estimate and the deviance of the model when a single case is deleted, and he discusses some diagnostic methods which use these approximations Cook and Weisberg (1982) discuss GLM diagnostics briefly in Section 54 and they make use of Pregibon's results McCullagh and Nelder (1983) discuss diagnostics in their chapter on model checking (chapter 11) but Pregibon's approximations are not mentioned In this paper I describe some GLM diagnostics which all make use of Pregibon's one step approximations for the change in the components of the deviance when a single case is deleted Section 2 establishes the notation of the paper, Section 3 states the one step approximations, and Section 4 shows how these approximations can be used to define residuals and to measure the influence of individual cases on different aspects of the fitted model Throughout these three sections the computations will be exemplified using quantal assay data taken from Table V of Irwin (1937) These data were chosen for two reasons Firstly they have been reanalysed by Copenhaver and Mielke (1977) and Morgan (1985) and they are known to contain some features of interest Secondly, as they comprise only five cases, a variety of single case diagnostics can be completely tabulated and compared without taking up much space These data are

Fitting Smooth Paths to Spherical Data

Abstract: On propose une approche unifiee qui est invariante sous des modifications du systeme de coordonnees et qui tient compte de la geometrie de la sphere de facon naturelle

Modelling the extraneous variance in the presence of extra-binomial variation

Abstract: On considere deux methodes usuelles pour l'ajustement des proportions: le maximum de vraisemblance sous un modele beta-binomial et une methode des moments basee sur la structure de la moyenne et de la variance. Ces methodes sont etendues pour permettre la modelisation de la composante extra-binomiale de la variance comme fonction de la moyenne

Applications of ranking methods to multiple comparison procedures and factorial experiments

Abstract: Non parametric tests based on Kruskal Wallis ranks are discussed. Problems that arise in their application to multiple comparison procedures and multifactorial analyses when the null hypothesis is false are investigated. Solutions of the former are proposed which involve re‐ranking the observations within subsets of the data. A solution to the latter is proposed based on combinations of Friedman rank sums.

Non-Parametric Logistic and Proportional Odds Regression

Abstract: SUMMARY We describe the additive non-parametric logistic regression model of the form logit[P(x)] ==a+ -fj(xj), where P(x) = P(y = 1 1 x) for a 0-1 variable y, x is a vector of p covariates, and the f; are general real-valued functions. Each of the f; can be chosen to be either linear, general non-linear (estimated by a scatterplot smoother) or step functions for discrete covariates. The functions are estimated simultaneously using the "local scoring algorithm". The model can be used as an exploratory tool for uncovering the form of covariate effects or it can be used in a more formal manner in model building. We also describe the additive proportional odds model logit[yk(x)] = Ik)-fj(X1) for ordinal response data. Here Yk is the probability of the response being at most k: yk(X) = P( Y ? k I x). Both these models are motivated and described in detail, and several examples are given.

A Log-Linear Model for Binary Cross-Over Data

Abstract: On propose une methode de construction de modeles pour des donnees binaires qui fait le parallele avec les methodes existantes pour des donnees continues

Randomly Choosing Parameters from the Stationarity and Invertibility Region of Autoregressive–Moving Average Models

Abstract: SUMMARY Choice of appropriate parameter configurations for time series simulations is not always easy. One possible approach when simulating from autoregressive-moving average models is to choose parameter values from a uniform distribution on the stationarity and invertibility region associated with such models. In this paper, well-known time series results are applied to this problem to give a neat method which comprises generating partial autocorrelations independently distributed as appropriate beta variates and applying a standard transformation to obtain the parameters from these.

A New Graphical Method for Detecting Single and Multiple Outliers in Univariate and Multivariate Data

Abstract: A new graphical approach based on Wilks's (1963) statistic is proposed. The method is found to be useful in the detection of outliers in univariate and multivariate data. Masking and swamping effects in the sample are easily revealed. The method is illustrated with examples and simulations.

Ranked set sampling with non-random selection of sets and errors in ranking

Abstract: On integre un travail precedent sur le classement imparfait avec un modele simple de selection non aleatoire d'echantillons dans un ensemble et on examine l'effet de ces sources d'erreur sur la precision de l'estimateur

Screening vs prevalence estimation

Abstract: SUMMARY Screening and estimation of disease prevalence both often involve the use of an imperfect instrument for identifying those likely to be suffering from the disease. Sometimes an instrument designed with one of these aims in mind is used for the other. However, the aims are different, and what might be good for one need not be so for the other. The mathematics of the difference is explored and examples are given.

Asymptotic expansions for the Bingham distribution

Abstract: On developpe des series asymptotiques qui permettent a la constante de normalisation d'etre facilement et precisement evaluee quand une ou plusieurs valeurs du parametre est grande

Fitting Smooth Paths to Rotation Data

Abstract: In the study of plate tectonics in geophysics, estimates are available of the cumulative motion of continental plates relative to each other between various geological epochs. For a given pair of plates this relative movement may be summarized at each time by a 3 × 3 proper rotation matrix describing the orientation of a plate relative to its initial position. The general problem of point and interval rotation estimation at other times is addressed by using a spline method for fitting smooth paths to such sequences of cumulative rotations. The parameterization of 3 × 3 rotations as unsigned four‐dimensional directions is particularly convenient. The preferred tangent space projection also makes easy the construction of point and interval estimates of the instantaneous angular velocity vector of the relative motion.

Bootstrap comparison of non-nested generalized linear models: applications in survival analysis and epidemiology

Abstract: Bootstrapping the differences of deviances of non‐nested generalized linear models is proposed for comparing the goodness‐of‐fit of such models. Two examples are used for illustration. Different parametrizations of a dose‐response model are compared in a carcinogenicity study as are multiplicative and additive models in an epidemiological example.

Estimating Carcinogenic Potency from a Rodent Tumorigenicity Experiment

Abstract: Rodent tumorigenicity experiments are conducted to determine whether a particular substance accelerates tumour development. The association between exposure to this substance and the risk of tumour development can be characterized by a measure of carcinogenic potency. The most commonly used potency measure, the dose effect on the lifetime risk of tumour, may be seriously biased, especially when control and exposed groups differ with respect to longevity. However, more appropriate measures, which account for age at death, are largely unavailable except in the special cases of instantly lethal or nonlethal tumours or tumours with observable onset. In this paper, we propose an estimate of carcinogenic potency based on a proportonal prevalence odds model which applies regardless of tumour lethality and can be calculated using standard statistical methodologies. Furthermore, we show how our estimator can be used to generalize available potency estimators to tumours of any lethality.

Measuring Marathon Courses: An Application of Statistical Calibration Theory

Abstract: Marathon and other road-running courses are frequently measured by means of a calibrated bicycle wheel. The process involves an initial calibration over a standard distance, followed by the course measurement itself. We would like to know how accurate this procedure is. We develop both maximum-likelihood and Bayesian methods of analysis, and apply them to data collected for the 1984 Olympic Games. An innovation is the use of dynamic models to cope with changes in the calibration constants.

The rating of players in racquetball tournaments

Abstract: On developpe des estimations du maximum de vraisemblance et de la methode des moments pour les probabilites de gains de rallyes pour certains sports dans lesquels les points ne peuvent etre comptabilises que par le serveur

An application of the truncated 2-piece normal-distribution to the measurement of depths of arsenic implants in silicon

Abstract: The truncated two-piece normal distribution is applied to data obtained from backscattering experiments in order to investigate the depth of arsenic implants in silicon.

A note on the variance of the Box-Cox regression transformation estimate

Abstract: On donne une expression justifiee asymptotiquement pour la variance estimee de l'estimation du parametre de transformation dans une transformation de regression Box-Cox standard