diagnostic measures for the cox regression model with missing covariates this paper investigates diagnostic measures for assessing the influence of observations and model misspecification in the presence of missing covariate data for the cox regression model our diagnostics include case deletion measures conditional martingale residuals and score residuals the q distance is proposed to examine the effects of deleting individual observations on the estimates of finite dimensional and infinite dimensional parameters conditional martingale residuals are used to construct goodness of fit statistics for testing possible misspecification of the model assumptions a resampling method is developed to approximate the p values of the goodness of fit statistics simulation studies are conducted to evaluate our methods and a real data set is analyzed to illustrate their use

approximating the noninferior set in multiobjective linear programming problems abstract the aim of this paper is to develop algorithms for approximating the noninferior set in the objective space for multiobjective linear programming problems with three oor more objectives a geometrical measure of error is used in controlling the number of extreme points needed in generating an approximation of desired accuracy in more specific terms the error in the approximation is estimated by computing the deviation of a polytope containing the entire noninferior set the upper bounding polytope from a lower bounding polytope whose interior is known to be inferior extreme points are added to the approximation in an attempt to reduce the deviation between the two polytopes in as few computations as possible the facets in the approximation of the noninferior set are obtained by computing the convex hull of the extreme points generated by the algorithm suitable tests are developed to determine those facets of the convex hull that belong to the approximation

transformations in regression a robust analysis we consider two approaches to robust estimation for the box cox power transformation model one approach maximizes weighted modified likelihoods a second approach bounds a measure of gross error sensitivity among our primary concerns is the performance of these estimators on actual data in examples that we study there seem to be only minor differences between these two robust estimators but they behave rather differently than the maximum likelihood estimator or estimators that bound only the influence of the residuals these examples show that model selection determination of the transformation parameter and outlier identification are fundamentally interconnected

on measuring sensitivity to parametric model misspecification summary in settings where parametric inference is inconsistent under model misspecification the discrepancy between correct and misspecified inferences is compared with the discrepancy between correct and misspecified models to make the comparison tractable large sample and small misspecification approximations are employed the ratio of the approximate discrepancy between inferences to the approximate discrepancy between models is regarded as a relative measure of sensitivity to model misspecification the maximum ratio over a family of correct distributions is determined as a measure of worst case sensitivity as well the distribution producing this maximum can be examined to see how a particular combination of a parametric family and estimand is susceptible to model misspecifications statisticians recognize that in reality no models are really correct in many parametric situations model misspecifications give rise to asymptotically inconsistent estimators of parameters the goal of this work is to quantify how bad an estimator can be relative to the degree of model misspecification the rationale for such an investigation is that misleading inferences arise when a bad answer is produced from an only mildly misspecified model we are less concerned about bad inferences arising from grossly misspecified models as such models are likely to be screened out by diagnostic checks we quantify the sensitivity of a parametric family and estimand to model misspecifications by comparing the kullback leibler kl divergence between correct and misspecified inferences with the kl divergence between correct and misspecified models more specifically the divergence between inferences can be based on either sampling distributions of maximum likelihood estimators or posterior distributions for tractability local approx imations to the kl divergence are employed in a somewhat similar spirit to cook 1986 the maximum ratio of approximate divergences over a class of correct models can be com puted as a worst case measure of sensitivity to misspecifications as well the correct model achieving the maximum can be examined to gain insight into the kind of departures from the model which are damaging this methodology is described fully in the next section then section 3 details an application to some common parametric models for survival data the paper concludes with a discussion in section 4 some technical comments are relegated to appendix a and appendix b

a new statistic for influence in linear regression since the seminal article by cook the usual way to measure the influence of an observation in a statistical model is to delete the observation from the sample and compute a convenient norm of the change in the parameters or in the vector of forecasts in this article we define a new way to measure the influence of an observation based on how this observation is being influenced by the rest of the data more precisely the new statistic we propose is defined as the squared norm of the vector of changes of the forecast of one observation when each of the sample points are deleted one by one we prove that this new statistic has asymptotically a normal distribution and is able to detect a group of high leverage similar outliers that will be undetected by cook s statistic we show in several examples that the proposed statistic is useful for detecting heterogeneity in regression models in large high dimensional datasets

fourier pseudospectral method with kepler mapping for travelling waves with discontinuous slope application to corner waves of the ostrovsky hunter equation and equatorial kelvin waves in the four mode approximation many species of travelling waves have a single branch of solutions which ends at finite amplitude with a singular wave whose slope is discontinuous a so called corner wave fourier pseudospectral methods converge exponentially fast with n the truncation of the series for the smooth waves but the error falls only as o 1 n for a wave with a slope discontinuity we show that the error rate can be accelerated to o 1 n3 by making the change of coordinate kepler map x z sin z unfortunately there is a subtlety the end in a singular solution bifurcation is possible only for infinite dimensional systems we show that the truncated fourier pseudospectral approximation has roots on both sides of the corner wave the bifurcation can be detected by i a step function like jump in the residual of the differential equation at the corner wave and ii by observing the slope of u x which becomes discontinuous only at the corner wave itself these concepts are illustrated for the equatorially trapped ocean kelvin wave in the so called four latitudinal mode approximation however corner waves arise in many species of waves and the concepts explained here are applicable to all

an interactive reference point approach for multiobjective mixed integer programming using branch and bound abstract we propose an interactive reference point approach for multiple objective mixed integer linear programming problems that exploits the use of branch and bound techniques for solving the scalarizing programs at each dialogue phase the decision maker must specify a criterion reference point or just choose an objective function he she wants to improve in respect to the previous efficient nondominated solution in the latter case a directional search is performed adjusting automatically the reference point used at each stage tchebycheff mixed integer scalarizing programs are successively solved by branch and bound postoptimality techniques have been developed enabling the algorithm to profit from previous computations to solve the next scalarizing programs the previous branch and bound tree is used as a starting point and operations of simplification and branching are then performed to obtain a new efficient solution computational results have shown that this approach is effective for carrying out directional or local searches for efficient solutions

local influence diagnostics for quasi likelihood and lognormal estimates of a biological reference point from some fish stock and recruitment models we present local influence diagnostics to measure the sensitivity of a biological limit reference point lrp estimated from fitting a model to stock and recruitment data lrps are low levels of stock size that the management of commercial fisheries should avoid with high probability the lrp we examine is the stock size at which recruitment is 50 of the maximum s 50 we derive analytic equations to describe the effects on s 50 of changing the weight that observations are given in estimation we derive equations for the ricker beverton holt and hockey stick stock recruit models and four estimation methods including the error sums of squares method on log responses and three quasi likelihood methods we conclude from case studies that the hockey stick model produces the most robust estimates

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

regression diagnostics for general linear regression models abstract for the linear regression model y x e the local sensitivities of estimates for are investigated with respect to a general error structure for the residuals e in particular we define local sensitivity analysis as matrix derivatives of the general least squares gls estimator with respect to changes in the weight matrix 1 where var e the results are extensions of derivative formulas given in belsley kuh and welsch 1980 for ordinary least squares ols regressions an example is given showing how the new derivatives can be used for regression diagnostics in regression models with autocorrelated errors

an analytic approximation to the cardinal functions of gaussian radial basis functions on an infinite lattice gaussian radial basis functions rbfs have been very useful in computer graphics and for numerical solutions of partial differential equations where these rbfs are defined on a grid with uniform spacing h as translates of the master function f x a h exp a 2 h 2 x 2 where a is a user choosable constant unfortunately computing the coefficients of f x jh a h requires solving a linear system with a dense matrix it would be much more efficient to rearrange the basis functions into the equivalent lagrangian or cardinal basis because the interpolation matrix in the new basis is the identity matrix the cardinal basis c j x a h is defined by the set of linear combinations of the gaussians such that c j kh 1 when k j and c j kh 0 for all integers k j we show that the cardinal functions for the uniform grid are c j x h a c x h j a where c x a a 2 p sin px sinh a 2x the relative error is only about 4exp email protected 2 a 2 as demonstrated by the explicit second order approximation it has long been known that the error in a series of gaussian rbfs does not converge to zero for fixed a as h 0 but only to an error saturation proportional to exp email protected 2 a 2 because the error in our approximation to the master cardinal function c x a is the square of the error saturation there is no penalty for using our new approximations to obtain matrix free interpolating rbf approximations to an arbitrary function f x the master cardinal function on a uniform grid in d dimensions is just the direct product of the one dimensional cardinal functions thus in two dimensions c x y a a 4 p 2 sin px sin py sinh a 2x sinh a 2y we show that the matrix free interpolation can be extended to non uniform grids by a smooth change of coordinates

perturbation selection and influence measures in local influence analysis cook s j roy statist soc ser b 48 1986 133 169 local influence approach based on normal curvature is an important diagnostic tool for assessing local influence of minor perturbations to a statistical model however no rigorous approach has been developed to address two fundamental issues the selection of an appropriate perturbation and the development of influence measures for objective functions at a point with a nonzero first derivative the aim of this paper is to develop a differential geometrical framework of a perturbation model called the perturbation manifold and utilize associated metric tensor and affine curvatures to resolve these issues we will show that the metric tensor of the perturbation manifold provides important information about selecting an appropriate perturbation of a model moreover we will introduce new influence measures that are applicable to objective functions at any point examples including linear regression models and linear mixed models are examined to demonstrate the effectiveness of using new influence measures for the identification of influential observations

bayesian case influence diagnostics for survival models we propose bayesian case influence diagnostics for complex survival models we develop case deletion influence diagnostics for both the joint and marginal posterior distributions based on the kullback leibler divergence k l divergence we present a simplified expression for computing the k l divergence between the posterior with the full data and the posterior based on single case deletion as well as investigate its relationships to the conditional predictive ordinate all the computations for the proposed diagnostic measures can be easily done using markov chain monte carlo samples from the full data posterior distribution we consider the cox model with a gamma process prior on the cumulative baseline hazard we also present a theoretical relationship between our case deletion diagnostics and diagnostics based on cox s partial likelihood a simulated data example and two real data examples are given to demonstrate the methodology

assessing local influence for specific restricted likelihood application to factor analysis in restricted statistical models since the first derivatives of the likelihood displacement are often nonzero the commonly adopted formulation for local influence analysis is not appropriate however there are two kinds of model restrictions in which the first derivatives of the likelihood displacement are still zero general formulas for assessing local influence under these restrictions are derived and applied to factor analysis as the usually used restriction in factor analysis satisfies the conditions various influence schemes are introduced and a comparison to the influence function approach is discussed it is also shown that local influence for factor analysis is invariant to the scale of the data and is independent of the rotation of the factor loadings

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

local influence analysis of nonlinear structural equation models by regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete data log likelihood function in the em algorithm we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model the basic building blocks of local influence analysis are computed via observations of the latent variables generated by the metropolis hastings algorithm while the diagnostic measures are obtained via the conformal normal curvature seven perturbation schemes including some perturbation schemes on latent vectors are investigated the proposed procedure is illustrated by a simulation study and a real example

analysis of multi type recurrent events in longitudinal studies application to a skin cancer prevention trial we consider the statistical modeling and analysis of replicated multi type point process data with covariates such data arise when heterogeneous subjects experience repeated events or failures which may be of several distinct types the underlying processes are modeled as nonhomogeneous mixed poisson processes with random subject and fixed covariate effects the method of maximum likelihood is used to obtain estimates and standard errors of the failure rate parameters and regression coefficients score tests and likelihood ratio statistics are used for covariate selection a graphical test of goodness of fit of the selected model is based on generalized residuals measures for determining the influence of an individual observation on the estimated regression coefficients and on the score test statistic are developed an application is described to a large ongoing randomized controlled clinical trial for the efficacy of nutritional supplements of selenium for the prevention of two types of skin cancer

local model influence abstract this article develops a general method for assessing the influence of model assumptions in a bayesian analysis we assume that model choices are indexed by a hyperparameter with some given initial choice we use the term model to encompass both the sampling model and the prior distribution we wish to assess the effect of changing the hyperparameter away from the initial choice we are performing a sensitivity analysis with the hyperparameter defining our perturbations we use the kullback leibler divergence to measure the difference between posteriors corresponding to different choices of the hyperparameter we also measure the change in priors if small changes in the priors lead to large changes in posteriors the choice of hyperparameter is influential the second order difference in the kullback leibler divergence is expressed by fisher information matrices the relative change in posteriors compared with priors may be summarized by the relative eigenvalue of the posterior and prior fishe

diagnostics for mixed model analysis of variance we describe a new method for assessment of model inadequacy in maximum likelihood mixed model analysis of variance in particular we discuss its use in diagnosing perturbations from the usual assumption of constant error variance and from the assumption that each realization of a given random factor has been drawn from the same normal population computer implementation of the procedure is described and an example is presented involving the analysis of filter cartridges used with commercial respirators

general classes of influence measures for multivariate regression abstract many of the existing measures for influential subsets in univariate ordinary least squares ols regression analysis have natural extensions to the multivariate regression setting such measures may be characterized by functions of the submatrices h i of the hat matrix h where i is an index set of deleted cases and q i the submatrix of q e e t e 1 e t where e is the matrix of ordinary residuals two classes of measures are considered f tr h i q i i h i q i a i h i b and f det i h i q i a i h i b where f is a scalar function of the dimensions of matrices and a and b are integers these characterizations motivate us to consider separable leverage and residual components for multiple case influence and are shown to have advantages in computing influence measures for subsets in the recent statistical literature on regression analysis much attention has been given to problems of detecting observations that individually or jointly exert a disproportionate

on local influence analysis of full information item factor models the full information item factor fiif model is very useful for analyzing relations of dichotomous variables in this article we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the fiif model the development is based on a q displacement function which is closely related with the monte carlo em algorithm in the ml estimation in the e step of this algorithm the conditional expectations are approximated by sample means of observations simulated by the gibbs sampler from the appropriate conditional distributions it turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures the diagnoses are based on the conformal normal curvature that can be computed easily a number of interesting perturbation schemes are considered the methodology is illustrated with two real examples

influence diagnostics for the cross validated smoothing parameter in spline smoothing abstract this article addresses the problem of influence in estimating the smoothing parameter when fitting a univariate smoothing spline diagnostics are presented that can identify observations that locally influence the choice of smoothing parameter by generalized cross validation either through their case weights or observed responses generalized cross validation and the diagnostic methods are given a frequency interpretation and illustrated with examples

influence analysis for skew normal semiparametric joint models of multivariate longitudinal and multivariate survival data the normality assumption of measurement error is a widely used distribution in joint models of longitudinal and survival data but it may lead to unreasonable or even misleading results when longitudinal data reveal skewness feature this paper proposes a new joint model for multivariate longitudinal and multivariate survival data by incorporating a nonparametric function into the trajectory function and hazard function and assuming that measurement errors in longitudinal measurement models follow a skew normal distribution a monte carlo expectation maximization em algorithm together with the penalized splines technique and the metropolis hastings algorithm within the gibbs sampler is developed to estimate parameters and nonparametric functions in the considered joint models case deletion diagnostic measures are proposed to identify the potential influential observations and an extended local influence method is presented to assess local influence of minor perturbations simulation studies and a real example from a clinical trial are presented to illustrate the proposed methodologies copyright 2017 john wiley sons ltd

a note on local influence based on normal curvature summary object functions other than the likelihood displacement such as a parameter estimate or a test statistic can also be used in local influence analysis the normal curvatures of these object functions have been studied in situations where the slopes were non zero in these situations we show that the normal curvature is not scale invariant and thus ambiguous conclusions will be drawn comments on the application of the general normal curvature formula are presented

sensitivity analysis of structural equation models the main purpose of this paper is to investigate the sensitivity analysis of structural equation model when minor perturbation is introduced some influence measure that based on the general case weight perturbation is derived for the generalized least squares estimation an influence measure that related to the cook s distance is also developed for the special case deletion perturbation scheme using the proposed methodology the influential observation in a data set can be detected moreover the general theory can be applied to detect the influential parameters in a model finally some illustrative artificial and real examples are presented

zero one programming with multiple criteria abstract the study of multiple criteria problems is not new but during the last seventeen years more and more study has been done in this area the study of 0 1 multiple criteria problems started much later than the study of continuous multiple criteria problems some of the earliest works on 0 1 problems with multiple criteria was first presented in 1973 quite a few solution methods have been developed since then especially during the last seven years in this paper most of these methods and some applications will be treated

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

influence on confidence regions for regression coefficients in generalized linear models abstract influence on confidence regions has received less attention than the problem of influence on regression coefficients in generalized linear models diagnostics are given for examining influence on confidence intervals or the confidence region for all of the regression coefficients these diagnostics permit one to check whether the standard errors of the coefficients are sensitive to the exact specification of case weights or the observed values of the explanatory variables or the response the diagnostics are illustrated with an example and compared to standard diagnostic methods

a diagnostic for cox regression and general conditional likelihoods abstract diagnostics for changes in the maximum likelihood estimate of due to deletion of single observations in linear and logistic regression models are equivalent to diagnostics obtained from fitting augmented regression models for the cox proportional hazards model and in conditional models for arbitrarily matched or stratified data diagnostics derived from augmented regression models are again useful and easy to compute these diagnostics are applicable to different formulations for the multiplicative covariable effects over time or over strata an exact or approximate treatment of tied failure times or multiple case matching and time dependent covariates

conformal normal curvature and assessment of local influence in 1986 r d cook proposed differential geometry to assess local influence of minor perturbations of statistical models we construct a conformally invariant curvature the conformal normal curvature for the same purpose this curvature provides a measure of local influence ranging from 0 to 1 with objective bench marks to judge largeness we study various approaches to using the conformal normal curvature and the relationships between these approaches

combining linear regression models when and how model combining i e mixing methods have been proposed in recent years to deal with uncertainty in model selection even though advantages of model combining over model selection have been demonstrated in simulations and data examples it is still unclear to a large extent when model combining should be preferred in this work first we propose an instability measure to capture the uncertainty of model selection in estimation called perturbation instability in estimation pie based on perturbation of the sample we demonstrate that estimators from model selection can have large pie values and that model combining substantially reduces the instability for such cases second we propose a model combining method adaptive regression by mixing with model screening arms and derive a theoretical property in arms a screening step is taken to narrow down the list of candidate models before combining which not only saves computing time but also can improve estimation accuracy third we compare arms w

bayesian influence analysis a geometric approach in this paper we develop a general framework of bayesian influence analysis for assessing various perturbation schemes to the data the prior and the sampling distribution for a class of statistical models we introduce a perturbation model to characterize these various perturbation schemes we develop a geometric framework called the bayesian perturbation manifold and use its associated geometric quantities including the metric tensor and geodesic to characterize the intrinsic structure of the perturbation model we develop intrinsic influence measures and local influence measures based on the bayesian perturbation manifold to quantify the effect of various perturbations to statistical models theoretical and numerical examples are examined to highlight the broad spectrum of applications of this local influence method in a formal bayesian analysis

diagnostics for heteroscedasticity in regression summary for the usual regression model without replication we provide a diagnostic test for heteroscedasticity based on the score statistic a graphical procedure to complement the score test is also presented some key u ords influence linear model residual score test diagnostic methods in linear regression are used to examine the appropriateness of assumptions underlying the modelling process and to locate unusual characteristics of the data that may influence conclusions the recent literature on diagnostics is dominated by studies of methods for the detection of influential observations cook weisberg 1982 provide a review diagnostics for the relevance of specific assumptions however have not received the same degree of attention even though these may be of equal importance our purpose here is to provide appropriate diagnostic techniques to aid in an assessment of the validity of the usual assumption of homoscedasticity when little or no replication is present available methods for studying this assumption include both graphical and nongraphical procedures the usual graphical procedure consists of plotting the ordinary least squares residuals against fitted values or an explanatory variable a megaphone shaped pattern is taken as evidence that the variance depends on the quantity plotted on tlle abscissa weisberg 1980 chapter 6 in 3 we suggest several ways in which this

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

influence analysis based on the case sensitivity function the case sensitivity function approach to influence analysis is introduced as a natural smooth extension of influence curve methodology in which both the insights of geometry and the power of convex analysis are available in it perturbation is defined as movement between probability vectors defining weighted empirical distributions a euclidean geometry is proposed giving such perturbations both size and direction the notion of the salience of a perturbation is emphasized this approach has several benefits a general probability case weight analysis results answers to a number of outstanding questions follow directly rescaled versions of the three usual finite sample influence curve measures seen now to be required for comparability across different sized subsets of cases are readily available these new diagnostics directly measure the salience of the infinitesimal perturbations involved their essential unity both within and between subsets is evident geometrically finally it is shown how a relaxation strategy in which a high dimensional 0 ncm discrete problem is replaced by a low dimensional o n continuous problem can combine with convex optimization results to deliver better performance in challenging multiple case influence problems further developments are briefly indicated

sensitivity of score tests for zero inflation in count data in many biomedical applications count data have a large proportion of zeros and the zero inflated poisson regression zip model may be appropriate a popular score test for zero inflation comparing the zip model to a standard poisson regression model was given by van den broek similarly for count data that exhibit extra zeros and are simultaneously overdispersed a score test for testing the zip model against a zero inflated negative binomial alternative was proposed by ridout hinde and demetrio however these test statistics are sensitive to anomalous cases in the data and incorrect inferences concerning the choice of model may be drawn in this paper diagnostic measures are derived to assess the influence of observations on the score statistics two examples that motivated the application of zero inflated regression models are considered to illustrate the importance of sensitivity analysis of the zero inflation tests

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

the multicriteria p facility median location problem on networks abstract in this paper we discuss the multicriteria p facility median location problem on networks with positive and negative weights we assume that the demand is located at the nodes and can be different for each criterion under consideration the goal is to obtain the set of pareto optimal locations in the graph and the corresponding set of non dominated objective values to that end we first characterize the linearity domains of the distance functions on the graph and compute the image of each linearity domain in the objective space the lower envelope of a transformation of all these images then gives us the set of all non dominated points in the objective space and its preimage corresponds to the set of all pareto optimal solutions on the graph for the bicriteria 2 facility case we present a low order polynomial time algorithm also for the general case we propose an efficient algorithm which is polynomial if the number of facilities and criteria is fixed

an algorithm for multiobjective zero one linear programming a branch and bound algorithm is presented which is based on the extension of implicit enumeration techniques to multiobjective zero one linear programming and which appears to be computationally quite efficient domination tests aiming at identifying paths of the enumeration tree that lead to dominated solutions as high up the tree as possible are developed some computational results are also given

transformations and influential cases in regression we describe a diagnostic method for assessing the degree to which individual cases and groups of cases influence the box cox likelihood estimate of the transformation parameter for the response variable in linear regression models we compare the method to a method proposed by atkinson 1982 and sketch the extension to explanatory variables we present two examples

influence diagnostics for linear longitudinal models abstract influence diagnostics are important for analyzing cross sectional regression studies because they allow the analyst to understand the impact of individual observations on the estimated regression model in this article we consider the role of influence diagnostics in subject specific longitudinal models diagnostics are proposed under both fixed and random subject effects our approach is based on subject deletion which in this setting involves deleting a group of correlated observations we develop partial influence statistics to understand the combined impact of observations from a subject on population parameters simple computational formulas make the procedures feasible finally we illustrate the use of our new influence statistics by examining a dataset to model a taxpayer s charitable givings

a spatial statistical analysis of tumor growth abstract growth models for tumors commonly are developed for a one dimensional summary e g number of cells volume at the supracellular level however ignoring tumor shape leads to oversimplification of the growth mechanism for example an oncologist would view the discovery of a compact tumor of volume v differently from the discovery of two osculatory compact tumors each of volume v 2 this article presents a growth model that uses shape information at a previous time to describe the tumor at the present time an analysis is given of three successive two dimensional images of cell islands which are obtained from in vitro growth of human breast cancer cells

regression transformation diagnostics using local influence abstract following box and cox 1964 the use of transformations in regression analysis is now common recently there has been emphasis on diagnostic methods for transformation much of which has involved deletion of data cases summaries were given by cook and weisberg 1982 and atkinson 1985 this article obtains diagnostics for the estimated regression parameter of the box cox transformation of the response variable in the linear model instead of deleting cases the more general notions of perturbing assumptions of the model or components of the data are employed as in the local influence approach of cook 1986 the diagnostics then arise from local changes to the transformation parameter estimate caused by small perturbations the case direction in which small perturbations have the greatest effect is the main diagnostic quantity an appeal of the approach is that it allows simultaneous perturbations affecting all data cases not just one at a time deletions it can thus point to groups of in

transformation model diagnostics we apply the local influence method of lawrance to assess the effect of the case weights perturbation on the transformation power estimator in the box cox regression model we show that this method is the same as the local influence method proposed by cook furthermore the difference in local influence diagnostics between the case weights perturbation and the constant variances perturbation is examined and the relationship between the localinfluence diagnostic and the deletion diagnostic is studied an example is presented to illustrate local influence diagnostics

deleted residuals the qr factored newton iteration and other methods for formally overdetermined determinate discretizations of nonlinear eigenproblems for solitary cnoidal and shock waves abstract solitary waves cnoidal waves and shock waves can be computed by solving a nonlinear eigenvalue problem which in discretized form is a system of nonlinear algebraic equations unfortunately many such systems are singular because the solution is not unique until one or more additional constraints are imposed for example if the waves are translationally invariant and u x is a solution then so also is u x for arbitrary to obtain a unique solution one must impose an additional condition to reduce the one parameter family of solutions by constraining we describe five methods for coping with such singular systems i reformulation of the problem ii deleting residuals iii keller s bordered matrix scheme iv qr factored overdetermined newton iteration and v pseudoinverse newton iteration we illustrate these ideas using the cnoidal waves of the korteweg de vries equation the traveling shocks of the korteweg de vries burgers equation and the weakly nonlocal solitary waves of the nonlinear equatorial beta plane equations finite difference fourier and rational chebyshev pseudospectral methods and spectrally upgraded finite differences are applied reformulation and deleting residuals are the cheapest strategies but the qr factored newton iteration is needed for the shock waves which lack the symmetry of the other two wave species

an interactive weighted tchebycheff procedure for multiple objective programming the procedure samples the efficient set by computing the nondominated criterion vector that is closest to an ideal criterion vector according to a randomly weighted tchebycheff metric using filtering techniques maximally dispersed representatives of smaller and smaller subsets of the set of nondominated criterion vectors are presented at each iteration the procedure has the advantage that it can converge to non extreme final solutions especially suitable for multiple objective linear programming the procedure is also applicable to integer and nonlinear multiple objective programs

local influence of predictors in multiple linear regression local influence diagnostics can be used to assess the influence of predictor values in multiple linear regression for n observations and k regressors an eigenanalysis of an nk nk matrix is required to assess the influence on the estimated coefficients we provide the analytic expressions for the eigenvectors and show that they are easily computed describe influence on the parameter estimates of a principal components regression and are related to leverage outliers and added variables plots the results indicate that multicollinearity and overfitting contribute to a fitted model s sensitivity leading to strategies for model assessment and selection

two graphical displays for outlying and influential observations in regression summary the paper describes two procedures for detecting observations with outlying values either in the response variable or in the explanatory variables in multiple regression these procedures are presented as half normal plots with envelopes derived from simulation in order to avoid overinterpretation of the data analysis of a well known data set leads to the use of a data transformation a simple test for which is commended and to some comments on the relationship with robust regression the widespread availability of sophisticated computer software has made the fitting of multiple regression equations painless but the very ease of these procedures may cause insufficient care to be given to checking and scrutiny of the data transcription punching and data manipulation errors may lead to bad values both of the observations y and of the independent or explanatory variables x it is the purpose of the present paper to describe and exemplify two plots which provide checks against such bad values it is argued that these plots and a test for transformations should accompany any thorough regression analysis bad values of the response or outliers have long been detected by a variety of plots of residuals bad values of the explanatory variables are less easily detected even when they lead to an extreme point in the design space since the fitted equation will pass close to such an influential observation the residual may not be especially large even after allowance has been made for the small variance of the fitted value at such a point to detect such behaviour a quantity is needed which exhibits the dependence of the fitted model on each point or group of points discussions of such quantities are given by hoaglin welsch 1978 and more recently by belsley kuh welsch 1980 2 1 by cook weisberg 1980 and by pregibon 1981 the quantity used here is a modification of a statistic proposed by cook 1977 which is derived in 2 two half normal plots are presented in 3 as an aid to interpretation envelopes to the plots are generated by simulation examples of the plots are given in 4 both for simulated data and for the stack loss data given by brownlee 1965 p 454 transformations of this data set are discussed in 5 the paper concludes with some comments on the relationship with robust

aspects of the predictive and estimative approaches in the determination of probabilities summary an exposition of the predictive observabilistic and estimative approaches for determining probabilities within a bayesian framework is presented it is demonstrated that the usual measurement error model can be subsumed under either the estimative or observabilistic modes and that a much more frequently occurring model should be treated in the latter mode because of mathematical tractability the simple exponential distribution is used to exhibit these concepts and a particular data set used to exemplify the type of calculations that are necessary and the inferences that can be made in a previous paper geisser 1971 i argued that the predictive approach in statistics which had long been neglected or entirely disregarded was a more appropriate vehicle for the transtnission of a statistical inference practically speaking than the classical estimative approach the predictive approach couches inferences and decisions in terms of observables or potential observables or interesting functions thereof while the estimative approach is involved with parameters in this paper i shall attempt to present compelling arguments that predictivism or observabilism is also a generally superior conceptual framework for inference which can subsume the estimative approach when valid as a limiting case particularly in the determination of probabilities predictive or observabilistic inference is directed towards statements about a finite number of observables that conceptually have or had the potential of being generated clearly this includes sample surveys or any kind of sampling from a finite population since estimation here involves statements about some function of the finite totality of observations from the population which is often misdesignated as a parameter 7 passage to the limit will then include estimation since parameters will be entities that arise from the prediction of a function of an infinite number of potential observables another situation where some difficulty in drawing a distinction between parameters and observables frequently arises is in the measuring of some physical constant speed of light length of a table etc with an imperfect instrument here the model is that the observed value is the parameter or true value plus measurement error say

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

parameter orthogonality and approximate conditional inference on propose une statistique du rapport de vraisemblance construite a partir de la distribution conditionnelle des observations etant donne les estimateurs du maximum de vraisemblance pour les parametres de nuisance

using cutting planes in an interactive reference point approach for multiobjective integer linear programming problems we propose an interactive approach for multiple objective integer linear programming moilp problems that combines the use of the tchebycheff metric with cutting plane techniques at each interaction the method computes the nondominated solution for the moilp problem that is closest to a reference point according to the tchebycheff metric the information provided by the decision maker in each dialogue phase is used to adjust the next reference point through a sensitivity analysis stage cutting plane techniques enable the method to take advantage of computations performed at previous iterations to solve the next scalarizing integer program we address both theoretical issues and the computational implementation

a diagnostic procedure based on local influence cook s 1986 normal curvature measure is useful for sensitivity analysis of model assumptions in statistical models however there is no rigorous approach based on the normal curvature for addressing two fundamental issues to assess the extent of discrepancy between an assumed model and the underlying model from which the data are generated and to identify suspicious data points for which the discrepancy is most evident our purpose is to establish a theoretically sound procedure for resolving these issues for case weight perturbation under the framework of independent distributions we show that the local influence measure cook s distance and likelihood distance are asymptotically equivalent a diagnostic procedure based on local influence is proposed for evaluating model misspecification and for detecting influential points simultaneously we analyse two real datasets

location of several outliers in multiple regression data using elemental sets the outlying tendency of any case in a multiple regression of p predictors may be estimated by drawing all subsets of size p from the remaining cases and fitting the model each such subset yields an elemental residual for the case in question and a suitable summary statistic of them can be used as an estimate of the case s outlying tendency we propose two such summary statistics an unweighted median which is of bounded influence and a weighted median which is more efficient but less robust the computational load of the procedure is reduced by using random samples in place of the full set of subsets of size p as a byproduct the method yields useful information on the influence or leverage of cases and the mutual masking of high leverage points

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

a predictive view of the detection and characterization of influential observations in regression analysis abstract assuming a set of observations is available from the general linear model and assuming prior information about parameters we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations

a diagnostic statistic for the score test abstract this article provides exact and approximate expressions for the change in the score test on deletion of observations deletions of individuals and of entire risk sets from matched case control and survival studies are discussed in detail a simple formula is derived which measures the contribution of individual strata to score tests based on combining several contingency tables the diagnostic is illustrated by application to the stanford heart transplant data

sensitivity analysis for nonrandom dropout a local influence approach diggle and kenward 1994 applied statistics 43 49 93 proposed a selection model for continuous longitudinal data subject to nonrandom dropout it has provoked a large debate about the role for such models the original enthusiasm was followed by skepticism about the strong but untestable assumptions on which this type of model invariably rests since then the view has emerged that these models should ideally be made part of a sensitivity analysis this paper presents a formal and flexible approach to such a sensitivity assessment based on local influence cook 1986 journal of the royal statistical society series b 48 133 169 the influence of perturbing a missing at random dropout model in the direction of nonrandom dropout is explored the method is applied to data from a randomized experiment on the inhibition of testosterone production in rats

bicriteria network location bnl problems with criteria dependent lengths and minisum objectives abstract we present a new location model which is a generalization of the bicritera median problem we introduce two sum objectives and criteria dependent edge lengths for this np complete problem a solution method finding all the efficient solutions is presented the method is a two phases approach which can easily be applied as an interactive method in phase 1 the supported solutions are found and in phase 2 the unsupported solutions are found this method can be thought of as a general approach to bi objective combinatorial optimization boco problems

bayesian and frequentist predictive inference for the patterns of care studies abstract the patterns of care studies were conducted to determine the quality of care received by cancer patients whose primary treatment modality is radiation therapy in this article we propose and evaluate models which if acceptable permit bayesian and frequentist model based predictive inference for the desired finite population parameters using both hierarchical bayesian and frequentist mixed linear models we describe methodology for making the desired inferences emphasizing the use of transformed random variables finally we compare the frequentist bayes and empirical bayes approaches using data from one of the surveys all three methods produce essentially the same value for the finite population mean the standard empirical bayes and frequentist measures of variability are very much smaller than those derived from the bayesian approach the latter reflecting uncertainty about the values of the scale parameters in the model

global sensitivity results for generalized least squares estimates abstract the covariance matrix for the residuals of a regression process is written as the identity matrix plus a matrix v the matrix v is bounded from above and the corresponding set of generalized least squares estimates is identified the extreme estimates in this set are functions of the usual t statistics in particular the number t k 8 1 2 t measures the influence of reweighting extreme observations where t k gives the degrees of freedom t is the t statistic and the weights on observations are allowed to vary by a factor of at most 2

applications of a parametric model for informative censoring in this article we explore the use of a parametric model for analyzing survival data which is defined to allow sensitivity analysis for the presence of informative censoring the dependence between the failure and the censoring processes is expressed through a parameter delta and a general bias function b t theta we calculate the expectation of the potential bias due to informative censoring which is an overall measure of how misleading our results might be if censoring is actually nonignorable bounds are also calculated for quantities of interest e g parameter of the distribution of the failure process which do not depend on the choice of the bias function for fixed delta an application that relates to systematic lupus erythematosus data illustrates how additional information can result in reducing the uncertainty on estimates of the location parameter sensitivity analysis on a relative risk parameter is also explored

solving zero one multiple objective programs through implicit enumeration abstract research on algorithms designed to solve zero one multiple objective linear programs has been rather limited this paper presents a solution procedure for these problems based on the concept of implicit enumeration computational experience is reported and analyzed advantages disadvantages and extensions of the algorithm are discussed

solitons from sine waves analytical and numerical methods for non integrable solitary and cnoidal waves abstract the fkdv equation u t uu x u xxxxx 0 is used as a testbed for a variety of analytical and numerical methods that can be applied to solitary waves and cnoidal waves of non integrable differential equations that is to say to equations which cannot be solved by the inverse scattering transform the basic tools are i pade approximants formed from power series in the amplitude ii a newton kantorovich pseudospectral fourier continuation numerical method iii singular perturbation theory for two interacting solitons of almost identical phase speed iv bifurcation and branch switching methods v the imbricate soliton series a number of new results for the fkdv equation are obtained including extensive numerical calculations of the spatially periodic solutions with one peak cnoidal wave and two peaks bicnoidal wave per period an analytical expression for the double peaked soliton bion calculation of both the limit and bifurcation points for the bicnoidal wave and finally the computation of accurate analytical approximations to the cnoidal wave for all amplitudes more important all of these analytical and numerical tools are highly effective for this equation in spite of the fact that it cannot be solved by the inverse scattering transform work now in progress will apply these methods to non integrable equations in two space dimensions

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

the detection of influential subsets in linear regression by using an influence matrix this paper presents a new method to identify influential subsets in linear regression problems the procedure uses the eigenstructure of an influence matrix which is defined as the matrix of uncentred covariances of the effect on the whole data set of deleting each observation normalized to include the univariate cook statistics on the diagonal it is shown that the eigenstructure of the influence matrix is useful to identify influential subsets and a procedure for detecting influential sets is proposed the method is illustrated with two examples

local influence for generalized linear models with missing covariates in the analysis of missing data sensitivity analyses are commonly used to check the sensitivity of the parameters of interest with respect to the missing data mechanism and other distributional and modeling assumptions in this article we formally develop a general local influence method to carry out sensitivity analyses of minor perturbations to generalized linear models in the presence of missing covariate data we examine two types of perturbation schemes the single case and global perturbation schemes for perturbing various assumptions in this setting we show that the metric tensor of a perturbation manifold provides useful information for selecting an appropriate perturbation we also develop several local influence measures to identify influential points and test model misspecification simulation studies are conducted to evaluate our methods and real datasets are analyzed to illustrate the use of our local influence measures

assessing influence for pharmaceutical data in zero inflated generalized poisson mixed models for clustered count data with excess zeros where the observations are either over dispersed or under dispersed the zero inflated generalized poisson mixed zigpm regression model may be appropriate in which the baseline discrete distribution is a generalized poisson distribution which is a natural extension of standard poisson distribution motivated by one data set drawn from a pharmaceutical study influence diagnostics for zigpm models based on case deletion and local influence analysis are developed in this work the one step approximations of the estimates under case deletion model and some case deletion measures are given meanwhile local influence measures are obtained under various perturbations of the observed data or model assumptions results from a pharmaceutical study illustrate the usefulness of the diagnostic statistics

a general method for local sensitivity analysis with application to regression models and other optimization problems this article introduces a method for sensitivity analysis of general applicability the method is based on the well known duality property of mathematical programming which states that the partial derivatives of the primal objective function with respect to the constraints on the right side parameters are the negative of the optimal values of the dual problem variables for the parameters or data for which sensitivities are sought to appear on the right side they are converted into artificial variables and set to their actual values thus obtaining the desired constraints the method is applicable to linear and nonlinear models to normal and nonnormal models and to least squares and other methods of estimation in addition to its general applicability the method is also computationally inexpensive because the necessary information becomes available without extra calculations the theoretical basis for the method is given and illustrated by its application to least squares least absolute value an

influential variables in linear regression based on a statistic proposed by cook 1977 for the detection of influential observations we propose a measure for the influence of variables in linear regression models and we introduce the leverage of a variable the new diagnostic can be used to identify important collinearities and in the checking of a fitted model to assess the effect of additional variables on the parameter estimates

a legendre pseudospectral method for computing travelling waves with corners slope discontinuities in one space dimension with application to whitham s equation family if the dispersion in a nonlinear hyperbolic wave equation is weak in the sense that the frequency k of cos kx is bounded as k it is common that i travelling waves exist up to a limiting amplitude with wave breaking for higher amplitudes and ii the limiting wave has a corner that is a discontinuity in slope because corner waves are not smooth standard numerical methods converge poorly as the number of grid points is increased however the corner wave is important because at least in some systems it is the attractor for all large amplitude initial conditions here we devise a legendre pseudospectral method which is uncorrupted by the singularity the symmetric u x u x wave can be computed on an interval spanning only half the spatial period since u is smooth on this domain which does not include the corner except as an endpoint all numerical difficulties are avoided a key step is to derive an extra boundary condition which uniquely identifies the corner wave with both the grid point values of u x and phase speed c as unknowns the discretized equations imposing three boundary conditions on a second order differential equation are solved by a newton raphson iteration although our method is illustrated by the so called whitham s equation ut uux du dx where d is a very general linear operator the ideas are widely applicable

augmented mixed beta regression models for periodontal proportion data continuous clustered proportion data often arise in various domains of medicine and public health where the response variable of interest is a proportion or percentage quantifying disease status for the cluster units ranging between zero and one however because of the presence of relatively disease free as well as heavily diseased subjects in any study the proportion values can lie in the interval 0 1 while beta regression can be adapted to assess covariate effects in these situations its versatility is often challenged because of the presence excess of zeros and ones because the beta support lies in the interval 0 1 to circumvent this we augment the probabilities of zero and one with the beta density controlling for the clustering effect our approach is bayesian with the ability to borrow information across various stages of the complex model hierarchy and produces a computationally convenient framework amenable to available freeware the marginal likelihood is tractable and can be used to develop bayesian case deletion influence diagnostics based on q divergence measures both simulation studies and application to a real dataset from a clinical periodontology study quantify the gain in model fit and parameter estimation over other ad hoc alternatives and provide quantitative insight into assessing the true covariate effects on the proportion responses

leverage in least squares additive plus multiplicative fits for two way tables abstract an additive plus multiplicative model can describe both main effects and row x column interactions in two way tables of data when each cell contains exactly one observation a least squares fit for this nonlinear model calculates the main effects using means of rows and columns and then fits a multiplicative term to the additive residuals using the singular value decomposition a natural extension of the hat matrix for a linear model yields a definition of leverage that provides insights about the impact of erroneous data values on the fit theoretical and numerical investigations reveal the complex nature of leverage for this nonlinear model

analyzing residuals in calibration problems the analysis of residuals in the calibration or inverse regression problem is considered a statistic is proposed that is appropriate to the specific use of the regression equation in this context namely estimating x from y the statistic similar in spirit to cook s distance may be used to measure the influence a particular observation may have on future estimates of x from the calibration curve it may also be used to measure the differences between estimates of x obtained using calibration curves based on different models an example is given