influence analysis of ranking data this paper develops diagnostic measures to identify those observations in thurstonian models for ranking data which unduly influence parameter estimates that are obtained by the partition maximum likelihood approach of chan and bentler 1998 diagnostic measures are constructed by employing the local influence approach that uses geometric techniques to assess the effect of small perturbations on a postulated statistical model very little additional effort is required to compute the proposed diagnostic measures because all of the necessary building blocks are readily available after a usual fit of the model

diagnostics for a cumulative multinomial generalized linear model with applications to grouped toxicological mortality data abstract toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment in this article we develop and extend a number of diagnostic tools for the detection of mean misspecification or systematic departures of the mean link specification in cumulative multinomial generalized linear models fit to such data several real data sets are used to illustrate these diagnostics these tools help the analyst to differentiate between two sources of lack of fit in such models mean misspecification and extra multinomial variation or overdispersion

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

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

the standardized influence matrix and its applications abstract in this article we introduce the standardized influence matrix sim of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions sifs evaluated at the data points we propose principal component analysis for the sim and its complement sim analysis as a diagnostic tool for regression or other statistical inference and provide theoretical insight to the local influence defined by cook we show that sim analysis reveals the multivariate structure of outlying and or influential points specifically sim analysis uncovers hidden structures of influence such as clustering that cannot be identified by the lengths of the standardized influences finally examples in linear regression show that a diagnostic method using sim is more effective if robust parameter estimates are used in calculating the sample sim

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

influence measures for logistic regression another point of view summary several measures of influence for logistic regression have been suggested these measures have been developed for the purpose of identifying observations which are influential relative to the estimation of the regression coefficients vector and the deviance we propose measures for detecting influence relative to the determination of probabilities and the classification of future observations the relationships among measures are indicated

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

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

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

on the estimation of the structural index from low pass filtered magnetic data abstractthe estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data such as euler deconvolution however these estimates are unstable even in the presence of a weak amount of noise and euler deconvolution of noisy data leads to an underestimation of structural index and depth we have studied how the structural index and depth estimates are affected by applying low pass filtering to the data physically based low pass filters such as upward continuation and integration have been shown to be the best choice over a range of altitudes upward continuation or orders integration filters mainly because their outputs have a well defined physical meaning in contrast mathematical low pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields the c norm criterion is a reliable strategy to produce a stabilized vertical derivative and we disc

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

regularity of einstein manifolds and the codimension 4 conjecture in this paper we are concerned with the regularity of noncollapsed riemannian manifolds m n g with bounded ricci curvature as well as their gromov hausdor limit spaces m n dj dgh x d where dj denotes the riemannian distance our main result is a solution to the codimension 4 conjecture namely thatx is smooth away from a closed subset of codimension 4 we combine this result with the ideas of quantitative stratication to prove a priori l q estimates on the full curvaturejrmj for all q v 0 and diam m d contains at most a nite number of dieomorphism classes a local version is used to show that noncollapsed 4 manifolds with bounded ricci curvature have a priori l 2 riemannian curvature estimates

double exponential families and their use in generalized linear regression abstract in one parameter exponential families such as the binomial and poisson the variance is a function of the mean double exponential families allow the introduction of a second parameter that controls variance independently of the mean double families are used as constituent distributions in generalized linear regressions in which both means and variances are allowed to depend on observed covariates the theory is applied to two examples a logistic regression and a large two way contingency table in such cases the binomial model of variance is often untrustworthy for example because genuine random sampling was infeasible the subjects may have been obtained in clumps so that the statistician should really be using smaller sample sizes clumped sampling is just one of many possible causes of overdispersion a habitual source of concern to users of binomial and poisson models this article concerns a class of regression families that allow the statistician to model overdispersion while carrying

local influence to detect influential data structures for generalized linear mixed models biometrics 2001 dec 57 4 1166 72 related articles books linkout local influence to detect influential data structures for generalized linear mixed models ouwens mj tan fe berger mp department of methodology and statistics maastricht university the netherlands mario ouwens stat unimaas nl this article discusses the generalization of the local influence measures for normally distributed responses to local influence measures for generalized linear models with random effects for these models it is shown that the subject oriented influence measure is a special case of the proposed observation oriented influence measure a two step diagnostic procedure is proposed the first step is to search for influential subjects a search for influential observations is proposed as the second step an illustration of a two treatment multiple period crossover trial demonstrates the practical importance of the detection of influential observations in addition to the detection of influential subjects

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

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

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

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

assessing influence on predictions from generalized linear models influence diagnostics for predictions from a normal linear model examine the effect of deleting a single case on either the point prediction or the predictive density function instead of deleting cases we apply the local influence method of cook 1986 to assess the effect of small perturbations of continuous data on a specified point prediction from a generalized linear model based on local perturbations of the vector of responses case weights explanatory variables or the components of one case the diagnostics can detect different kinds of influence some of the diagnostics are illustrated with an example and compared to standard diagnostic methods

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

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