hierarchical generalised linear models a synthesis of generalised linear models random effect models and structured dispersions summary hierarchical generalised linear models are developed as a synthesis of generalised linear models mixed linear models and structured dispersions we generalise the restricted maximum likelihood method for the estimation of dispersion to the wider class and show how the joint fitting of models for mean and dispersion can be expressed by two interconnected generalised linear models the method allows models with i any combination of a generalised linear model distribution for the response with any conjugate distribution for the random effects ii structured dispersion components iii different link and variance functions for the fixed and random effects and iv the use of quasilikelihoods in place of likelihoods for either or both of the mean and dispersion models inferences can be made by applying standard procedures in particular those for model checking to components of either generalised linear model we also show by numerical studies that the new method gives an efficient estimation procedure for substantial class of models of practical importance likelihood type inference is extended to this wide class of models in a unified way

generic singularities of nilpotent orbit closures according to a theorem of brieskorn and slodowy the intersection of the nilpotent cone of a simple lie algebra with a transverse slice to the subregular nilpotent orbit is a simple surface singularity at the opposite extremity of the poset of nilpotent orbits the closure of the minimal nilpotent orbit is also an isolated symplectic singularity called a minimal singularity for classical lie algebras kraft and procesi showed that these two types of singularities suffice to describe all generic singularities of nilpotent orbit closures specifically any such singularity is either a simple surface singularity a minimal singularity or a union of two simple surface singularities of type a 2k 1 in the present paper we complete the picture by determining the generic singularities of all nilpotent orbit closures in exceptional lie algebras up to normalization in a few cases we summarize the results in some graphs at the end of the paper in most cases we also obtain simple surface singularities or minimal singularities though often with more complicated branching than occurs in the classical types there are however six singularities that do not occur in the classical types three of these are unibranch non normal singularities an sl 2 c variety whose normalization is a 2 an sp 4 c variety whose normalization is a 4 and a two dimensional variety whose normalization is the simple surface singularity a 3 in addition there are three 4 dimensional isolated singularities each appearing once we also study an intrinsic symmetry action on the singularities extending slodowy s work for the singularity of the nilpotent cone at a point in the subregular orbit

generalized linear models for enzyme kinetic data ruppert cressie and carroll 1989 discuss various models for fitting the michaelismenten equations to data on enzyme kinetics i find it surprising that they do not include among the models they consider generalized linear models glms with an inverse link mccullagh and nelder 1989 chap 8 the advantages of glms over data transformation have often been rehearsed see e g nelder and pregibon 1987 the assumption of normality of errors is extended in glms to include any exponential family and is separated from the transformation required to produce additive effects of the systematic factors the data are analysed on the original scale which often makes more sense than the transformed scale in this paper i analyse the enzyme kinetic data quoted by ruppert et al as their table 8 the data are given here in table 1 the postulated relation their equation 3 1 is

quantum reduction for affine superalgebras we extend the homological method of quantization of generalized drinfeld sokolov reductions to affine superalgebras this leads in particular to a unified representation theory of superconformal algebras

hierarchical poisson regression modeling abstract the poisson model and analyses here feature nonexchangeable gamma distributions although exchangeable following a scale transformation for individual parameters with standard deviations proportional to means a relatively uninformative prior distribution for the shrinkage values eliminates the ill behavior of maximum likelihood estimators of the variance components when tested in simulation studies the resulting procedure provides better coverage probabilities and smaller risk than several other published rules and thus works well from bayesian and frequentist perspectives alike the computations provide fast accurate density approximations to individual parameters and to structural regression coefficients the computer program is publicly available through statlib

normality of nilpotent varieties in e6 abstract we determine which nilpotent orbits in e6 have closures which are normal varieties and which do not at the same time we are able to verify a conjecture in e sommers comm math univ sancti pauli 49 1 2000 101 104 concerning functions on non special nilpotent orbits for e6

using the overdispersed exponential family to estimate the distribution of usual daily intakes of people aged between 18 and 28 in taiwan assessment of usual dietary intake of a population is essential to understand the nutrition status of the population methods like 24 hour dietary recall and food records are commonly used for this task however within individual variation exists in the food record data methods considering measurement errors have been used to evaluate the association between nutrient intakes and diseases few have been devoted to estimating the distribution of usual daily intakes this paper proposes applying the formulation of the overdispersed exponential family to estimate the distribution of usual nutrient intake and applies the adjustments developed by liu to reduce the variance of the distribution the proposed method has the advantages of working on the original scale of data and implementation convenience the adjustment of the variance is carried out by dividing the variance into within individual variance and among individual variance the adjusted variance then is used to estimate the distribution of the usual daily intake sampling weights are considered in all the steps except the estimation of the ratio of within to among variance the data for this study are from the nutritional and health survey in taiwan conducted between 1993 and 1996 nahsit 1993 1996 an independent external set of data for people aged between 18 and 28 years 49 males and 20 females is used to estimate the ratio of within to among individual variance due to the availability of data in estimating the ratio of within to among individual variance 430 males and 422 females in the nahsit sample are used to estimate the distribution of usual daily intakes for people aged between 18 and 28 in taiwan the distribution also allows us to estimate the proportion of people who do not meet the recommended daily nutrient allowance rdna the results show that the intakes of calcium and vitamin e of this group of people fall far below rdna

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

iterated smoothed bootstrap confidence intervals for population quantiles this paper investigates the effects of smoothed bootstrap iterations on coverage probabilities of smoothed bootstrap and bootstrap t confidence intervals for population quantiles and establishes the optimal kernel bandwidths at various stages of the smoothing procedures the conventional smoothed bootstrap and bootstrap t methods have been known to yield one sided coverage errors of orders o n 1 2 and o n 2 3 respectively for intervals based on the sample quantile of a random sample of size n we sharpen the latter result to o n 5 6 with proper choices of bandwidths at the bootstrapping and studentization steps we show further that calibration of the nominal coverage level by means of the iterated bootstrap succeeds in reducing the coverage error of the smoothed bootstrap percentile interval to the order o n 2 3 and that of the smoothed bootstrap t interval to o n 58 57 provided that bandwidths are selected of appropriate orders simulation results confirm our asymptotic findings suggesting that the iterated smoothed bootstrap t method yields the most accurate coverage on the other hand the iterated smoothed bootstrap percentile method interval has the advantage of being shorter and more stable than the bootstrap t intervals

fractional order statistic approximation for nonparametric conditional quantile inference abstract using and extending fractional order statistic theory we characterize the o n 1 coverage probability error of the previously proposed hutson 1999 confidence intervals for population quantiles using l statistics as endpoints we derive an analytic expression for the n 1 term which may be used to calibrate the nominal coverage level to get o n 3 2 log n 3 coverage error asymptotic power is shown to be optimal using kernel smoothing we propose a related method for nonparametric inference on conditional quantiles this new method compares favorably with asymptotic normality and bootstrap methods in theory and in simulations code is provided for both unconditional and conditional inference

diagnostic measures for model criticism abstract we discuss the problem of model criticism with emphasis on developing summary diagnostic measures we approach model criticism by identifying possible troublesome features of the currently entertained model embedding the model in an elaborated model and measuring the value of elaborating this requires three elements a model elaboration a prior distribution and a utility function each triplet generates a different diagnostic measure we focus primarily on the measure given by a kullback leibler divergence between the marginal prior and posterior distributions on the elaboration parameter we also develop a linearized version of this diagnostic and use it to show that our procedure is related to other tools commonly used for model diagnostics such as bayes factors and the score function one attraction of this approach is that it allows model criticism to be performed jointly with parameter inference and prediction also this diagnostic approach aims at maintaining an exploratory nature t

analyzing dispersion effects from replicated factorial experiments recent developments in quality engineering methods have led to considerable interest in the analysis of dispersion effects from designed experiments a commonly used method for identifying important dispersion effects from replicated experiments is based on least squares analysis of the logarithm of the within replication variance bartlett and kendall 1946 box and meyer 1986 introduced a pooling technique for unreplicated two level experiments we extend this to replicated two level experiments and compare its performance with the least squares analysis we show that both of these methods can be obtained as special cases of maximum likelihood estimation under normal theory the pooling technique is generally biased and is not recommended for model identification the least squares analysis performs well as a model identification tool but the estimators can be inefficient in such cases we recommend that the parameters of the identified submodel be estimated by maximum likelihood we derive some prop

a finite mixture distribution for modelling multinomial extra variation summary we propose a new distribution to model categorical data exhibiting overdispersion when the overdispersion is believed to be caused by clumped sampling the proposed distribution is a finite mixture of multinomial random variables the finite mixture representation facilitates computation of the maximum likelihood estimator for large cluster sizes we derive an approximation for the fisher information matrix of the model and an explicit expression for the joint asymptotic efficiency of the maximum likelihood estimator relative to a quasi likelihood estimator

generalizing logistic regression by nonparametric mixing abstract logistic regression is a common technique for analyzing the effect of a covariate vector x on the number of successes y in m trials when y has a binomial distribution but at times either the logistic curve does not describe the probability of success p x adequately or m is larger than 1 and y is more variable than the binomial distribution allows overdispersion relative to the binomial distribution is possible if the m trials in a set or litter are positively correlated an important covariate is omitted or x is measured with error a simple way to accommodate departures from the logit link and overdispersion is to introduce a random intercept and thus permit a random propensity toward success when varies between individual binary trials according to a discrete or multimodal distribution p x has smooth steps and y has a binomial m p x distribution when the random is constant for a set of m binary trials and varies between sets of m trials according to a discrete or multimodal

generalized linear models with varying dispersion summary generalized linear models are further generalized to include a linear predictor for the dispersion as well as for the mean it is shown how the convenient structure of generalized linear models can be carried over to this more general setting by considering the mean and dispersion structure separately mean and dispersion submodels are formulated for this the dependent variable for the dispersion submodel being the deviance components of the mean submodel the fact that both submodels are essentially generalized linear models themselves is used to derive simple expressions for the likelihood equations and for asymptotic tests estimation algorithms are proposed which have good convergence properties the results apply mainly to the normal inverse gaussian and gamma distributions but can be extended to discrete distributions by using quasi likelihoods the methods developed are applied to a well known data set

generalized linear models a new program for depression is instituted in the hopes of reducing the number of visits each patient makes to the emergency room in the year following treatment predictors include among many others treatment yes no race and drug and alcohol usage indices a common and minimally invasive treatment for jaundice in newborns is exposure to light yet the cost of this is high mainly because of longer hospital stays which are expensive predictors of the cost include race gestational age and birthweight

modeling overdispersed or underdispersed count data with generalized poisson integer valued garch models abstract overdispersion in time series of counts is very common and has been well studied by many authors but the opposite phenomenon of underdispersion may also be encountered in real applications and receives little attention based on popularity of the generalized poisson distribution in regression count models and of poisson ingarch models in time series analysis we introduce a generalized poisson ingarch model which can account for both overdispersion and underdispersion compared with the double poisson ingarch model conditions for the existence and ergodicity of such a process are easily given we analyze the autocorrelation structure and also derive expressions for moments of order 1 and 2 we consider the maximum likelihood estimators for the parameters and establish their consistency and asymptotic normality we apply the proposed model to one overdispersed real example and one underdispersed real example respectively which indicates that the proposed methodology performs better than other conventional model based methods in the literature

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

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

miscellanea an extension of morel nagaraj s finite mixture distribution for modelling multinomial clustered data morel nagaraj 1993 proposed a finite mixture distribution for modelling multinomial extra variation when the extra variation is believed to be caused by clumped multinomial sampling with one clumping we propose an extension of the model to incorporate possible multiple clumping we show that the extended finite mixture distribution is a multinomial mixing distribution with different mixing coefficients we derive maximum likelihood estimating equations and an asymptotic approximation to the fisher information matrix for the parameters of the model a real life dataset is analysed

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

poisson overdispersion estimates based on the method of asymmetric maximum likelihood abstract a common difficulty in regression problems with poisson or binomial or other exponential family response variables is over dispersion the scatter around the fitted regression is too large by the standards of poisson variability this article concerns the description estimation and testing of various patterns of overdispersion with particular emphasis on the poisson case asymmetric maximum likelihood aml is a method of fitting regressions for the conditional percentiles of the response variable as a function of the predictors e g the conditional 90th percentile of y given x distances between the various regression percentiles give a direct assessment of overdispersion the discussion is carried through in terms of an archaeological data set where we see that the counts are overdispersed by a factor of 1 35 in one part of the covariate space but not at all in another moreover the overdispersion is about 40 larger in the positive response direction than in the negative the aml es

a note on extended quasi likelihood abstract we study the method of extended quasi likelihood estimation and inference of a variance function recently proposed by nelder pregibon 1987 the estimates are inconsistent in general and the test levels can be biased but in many cases such as the exponential family the inconsistency and bias will not be a major concern extended quasi likelihood is compared with carroll ruppert s 1982 pseudo likelihood method which gives consistent estimates and when slightly modified asymptotically unbiased tests we quantify the showing in this instance that the two estimates are closely related and may be asymptotically equivalent in many important cases however in some cases outside the exponential family an asymptotic bias can persist heteroscedastic regression model

on the reliability of n mixture models for count data n mixture models describe count data replicated in time and across sites in terms of abundance n and detectability p they are popular because they allow inference about n while controlling for factors that influence p without the need for marking animals using a capture recapture perspective we show that the loss of information that results from not marking animals is critical making reliable statistical modeling of n and p problematic using just count data one cannot reliably fit a model in which the detection probabilities are distinct among repeat visits as this model is overspecified this makes uncontrolled variation in p problematic by counter example we show that even if p is constant after adjusting for covariate effects the constant p assumption scientifically plausible alternative models in which n or its expectation is non identifiable or does not even exist as a parameter lead to data that are practically indistinguishable from data generated under an n mixture model this is particularly the case for sparse data as is commonly seen in applications we conclude that under the constant p assumption reliable inference is only possible for relative abundance in the absence of questionable and or untestable assumptions or with better quality data than seen in typical applications relative abundance models for counts can be readily fitted using poisson regression in standard software such as r and are sufficiently flexible to allow controlling for p through the use covariates while simultaneously modeling variation in relative abundance if users require estimates of absolute abundance they should collect auxiliary data that help with estimation of p

infinite chiral symmetry in four dimensions we describe a new correspondence between four dimensional conformal field theories with extended supersymmetry and two dimensional chiral algebras the meromorphic correlators of the chiral algebra compute correlators in a protected sector of the four dimensional theory infinite chiral symmetry has far reaching consequences for the spectral data correlation functions and central charges of any four dimensional theory with mathcal n 2 superconformal symmetry

modeling the dependence between number of trials and success probability in beta binomial poisson mixture distributions des modeles beta binomiaux sont frequemment utilises pour des donnees binomiales avec sur dispersion avec une probabilite binomiale de succes suivant une distribution beta on suppose que le nombre d essais binomiaux dans chaque binomiale est non aleatoire et non liee a la probabilite de succes dans de nombreuses etudes sur le comportement neanmoins les observations binomiales ont des structures plus complexes dans cet article nous developpons un modele de melange beta binomial poisson pour autoriser une relation entre le nombre d essais et la probabilite de succes pour des donnees binomiales avec sur dispersion nous mettons en oeuvre un algorithme em pour calculer simultanement des estimations du maximum de vraisemblance des parametres du modele et de leur ecart type correspondant a titre d illustration nous appliquons cette methodologie a l etude du comportement alimentaire de herons a dos vert dans deux ruisseaux du sud ouest du missouri

testing for independence in a two way table new interpretations of the chi square statistic the classical chi square test for independence in a two way contingency table often rejects the independence hypothesis at an extremely small significance level particularly when the sample size is large this paper proposes some alternative distributions to independence to help interpret the chi 2 statistic in such situations the uniform alternative in which every possible contingency table of the given dimension and sample size receives equal probability leads to the volume test as originally suggested in a regression context by h hotelling exponential family theory is used to generate a class of intermediate alternatives between independence and uniformity leading to a random effects model for contingency tables

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

exponential dispersion models on etudie les proprietes generales de la classe des modeles de dispersion exponentiels qui est la generalisation multivariable des modeles de distribution d erreur de nelder et wedderburn 1972

dirichlet process mixed generalized linear models abstract although generalized linear models glm s are an attractive and widely used class of models they are limited in the range of density shapes that they can provide for instance they are unimodal exponential families of densities in the response variable with tail behavior determined by the implicit mean variance relationship dirichlet process dp mixing adds considerable flexibility to these models using such mixing we develop models that we call dpmglm s which still retain the glm character with regard to the mean overdispersed glm s oglm s provide an alternative class of models to cope with extra variability in samples we show that how oglm s may be dp mixed leading to what we call dpmoglm s these models are extremely rich moreover recent computational advances enable them to be fitted straightforwardly we illustrate this with both simulated and real datasets we also address the question of choosing between the glm oglm dpmglm and dpmoglm finally we consider extensions by

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

on the irreducibility of associated varieties of w algebras abstract we investigate the irreducibility of the nilpotent slodowy slices that appear as the associated variety of w algebras furthermore we provide new examples of vertex algebras whose associated variety has finitely many symplectic leaves

prepivoting to reduce level error of confidence sets summary approximate confidence sets for a parameter 0 may be obtained by referring a function of 0 and of the sample to an estimated quantile of that function s sampling distribution we call this function the root of the confidence set either asymptotic theory or bootstrap methods can be used to estimate the desired quantile when the root is not a pivot in the sense of classical statistics the actual level of the approximate confidence set may differ substantially from the intended level prepivoting is the transformation of a confidence set root by its estimated bootstrap cumulative distribution function prepivoting can be iterated bootstrap confidence sets generated from a root prepivoted one or more times have smaller error in level than do confidence sets based on the original root the first prepivoting is nearly equivalent to studentizing when that operation is appropriate further iterations of prepivoting make higher order corrections automatically

bartlett adjustments to the likelihood ratio statistic and the distribution of the maximum likelihood estimator for rather general parametric models a simple connection is established between the bartlett adjustment factor of the log likelihood ratio statistic and the normalizing constant c of the formula c i i 1 2l for the conditional distribution of a maximum likelihood estimator as applied to the full model and the model of the hypothesis tested this leads to a relatively simple demonstration that division of the likelihood ratio statistic by a suitable constant or estimated factor improves the chi squared approximation to its distribution various expressions for these quantities are discussed in particular for the case of a one dimensional parameter an approximation to the constants involved is derived which does not require integration over the sample space

semiparametric analysis of heterogeneous data using varying scale generalized linear models this article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically and develops efficient semiparametric inferences for the parametric components of the models such models provide a means to adapt for heterogeneity in the data due to varying exposures varying levels of aggregation and so on the class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases we present an algorithm to estimate the scale function nonparametrically and obtain asymptotic distribution theory for regression parameter estimates in particular we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound we also describe bootstrap based goodness of scale test we illustrate the methodology with simulations published data and data from collaborative research on ultrasound safety

overdispersion diagnostics for generalized linear models abstract generalized linear models glm s are simple convenient models for count data but they assume that the variance is a specified function of the mean although overdispersed glm s allow more flexible mean variance relationships they are often not as simple to interpret nor as easy to fit as standard glm s this article introduces a convexity plot or c plot for short that detects overdispersion and relative variance curves and relative variance tests that help to understand the nature of the overdispersion convexity plots sometimes detect overdispersion better than score tests and relative variance curves and tests sometimes distinguish the source of the overdispersion better than score tests

approximate bayesian inference in conditionally independent hierarchical models parametric empirical bayes models abstract we consider two stage models of the kind used in parametric empirical bayes peb methodology calling them conditionally independent hierarchical models we suppose that there are k units which may be experimental subjects cities study centers etcetera at the first stage the observation vectors yi for units i 1 k are independently distributed with densities p yi i or more generally p yi i at the second stage the unit specific parameter vectors i are iid with densities p i the peb approach proceeds by regarding the second stage distribution as a prior and noting that if were known inference about could be based on its posterior since is not known the simplest peb methods estimate the parameter by maximum likelihood or some variant and then treat as if it were known to be equal to this estimate although this procedure is sometimes satisfactory a well known defect is that it neglects the uncertainty due to the estimation of in this article w

a review of some extensions to generalized linear models although generalized linear models are reasonably well known they are not as widely used in medical statistics as might be appropriate with the exception of logistic log linear and some survival models at the same time the generalized linear modelling methodology is decidedly outdated in that more powerful methods involving wider classes of distributions non linear regression censoring and dependence among responses are required limitations of the generalized linear modelling approach include the need for the iterated weighted least squares iwls procedure for estimation and deviances for inferences these restrict the class of models that can be used and do not allow direct comparisons among models from different distributions powerful non linear optimization routines are now available and comparisons can more fruitfully be made using the complete likelihood function the link function is an artefact necessary for iwls to function with linear models but that disappears once the class is extended to truly non linear models restricting comparisons of responses under different treatments to differences in means can be extremely misleading if the shape of the distribution is changing this may involve changes in dispersion or of other shape related parameters such as the skewness in a stable distribution with the treatments or covariates any exact likelihood function defined as the probability of the observed data takes into account the fact that all observable data are interval censored thus directly encompassing the various types of censoring possible with duration type data in most situations this can now be as easily used as the traditional approximate likelihood based on densities finally methods are required for incorporating dependencies among responses in models including conditioning on previous history and on random effects one important procedure for constructing such likelihoods is based on kalman filtering

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

mixtures of g priors in generalized linear models abstractmixtures of zellner s g priors have been studied extensively in linear models and have been shown to have numerous desirable properties for bayesian variable selection and model averaging

asymptotic behavior of linear permutation tests under general alternatives with application to test selection and study design abstract tests based on the permutation of observations are a common and attractive method of comparing two groups of outcomes in part because they retain proper test size with minimal assumptions and can have high efficiency toward specific alternatives of interest in addition permutation tests may be used with discrete or categorical outcomes for which linear rank tests are not designed permutation tests are now increasingly used to analyze discrete or continuous responses that themselves are functions of several statistics examples of such summary statistics include the area under the curve generated by repeated measures of a laboratory marker or an overall composite score from a quality of life study here even simple structures for the joint distribution of the component statistics can lead to complex differences between the distributions of summary statistics of the comparison groups despite their attractive features surprisingly little is known about the behavior of linear permutation tests

empirical bayes methods for combining likelihoods abstract suppose that several independent experiments are observed each one yielding a likelihood l k k for a real valued parameter of interest k for example k might be the log odds ratio for a 2 2 table relating to the kth population in a series of medical experiments this article concerns the following empirical bayes question how can we combine all of the likelihoods l k to get an interval estimate for any one of the k s say 1 the results are presented in the form of a realistic computational scheme that allows model building and model checking in the spirit of a regression analysis no special mathematical forms are required for the priors or the likelihoods this scheme is designed to take advantage of recent methods that produce approximate numerical likelihoods l k k even in very complicated situations with all nuisance parameters eliminated the empirical bayes likelihood theory is extended to situations where the k s have a regression structure as well as an empiri

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

a remark on the c 2 cofiniteness condition on vertex algebras we show that a finitely strongly generated non negatively graded vertex algebra is c 2 cofinite if and only if it is lisse in the sense of beilinson et al preprint this shows that the c 2 cofiniteness is indeed a natural finiteness condition

analysis of contingency tables by ideal point discriminant analysis cross classified data are frequently encountered in behavioral and social science research the loglinear model and dual scaling correspondence analysis are two representative methods of analyzing such data an alternative method based on ideal point discriminant analysis da is proposed for analysis of contingency tables which in a certain sense encompasses the two existing methods a variety of interesting structures can be imposed on rows and columns of the tables through manipulations of predictor variables and or as direct constraints on model parameters this along with maximum likelihood estimation of the model parameters allows interesting model comparisons this is illustrated by the analysis of several data sets

response surfaces for overdispersion in the study of the conditions for fish eggs hatching summary response surface methodology originally developed for determining optimal conditions in industrial experiments was early adapted to experiments in marine ecology however these involved studying the shape of the complete response surface not only detecting the optimum and often had counts or durations as the response variable thus nonlinear nonnormal response models were required for counts binomial and beta binomial models have been used the latter because of substantial over dispersion in closely controlled experiments over dispersion among units held under the same conditions might indicate that some mishap has occurred in conducting the study one possible check is to model the dispersion as a second response surface this procedure is used to show that over dispersion in fish egg hatching experiments has a biological explanation in that it occurs only under suboptimal hatching conditions