a comparison of permutation and mixed model regression methods for the analysis of simulated data in the context of a group randomized trial our first purpose was to determine whether in the context of a group randomized trial grt with gaussian errors permutation or mixed model regression methods fare better in the presence of measurable confounding in terms of their monte carlo type i error rates and power our results indicate that given a proper randomization the type i error rate is similar for both methods whether unadjusted or adjusted even in small studies however our results also show that should the investigator face the unfortunate circumstance in which modest confounding exists in the only realization available the unadjusted analysis risks a type i error in this regard there was little to distinguish the two methods finally our results show that power is similar for the two methods and not surprisingly better for the adjusted tests our second purpose was to examine the relative performance of permutation and mixed model regression methods in the context of a grt when the normality assumptions underlying the mixed model are violated published studies have examined the impact of violation of this assumption at the member level only our findings indicate that both methods perform well when the assumption is violated so long as the icc is very small and the design is balanced at the group level however at icc 0 01 the permutation test carries the nominal type i error rate while the model based test is conservative and so less powerful binomial group and member level errors did not otherwise change the relative performance of the two methods with regard to confounding copyright 2005 john wiley sons ltd

a random effects model for binary data summary this paper presents a method based on maximizing the marginal likelihood for analyzing binary data with random effects with the assumption of a parametric family that allows for a wide variety of shapes for the distribution of the random effects the marginal likelihood can be computed without numerical integrations the method uses local independence models as well as those that incorporate additional dependence among the responses two examples a panel study with binary responses and an analysis of item response data will be used to illustrate the method

feature selection in possibilistic modeling feature selection is becoming increasingly important for the reduction of computing complexity in this context conventional approaches have random performances because they can succeed for some contexts and fail for others possibilistic modeling is a powerful paradigm being able to handle data imperfection or redundancy and is not affected by data variability therefore in this paper we propose a new feature selection strategy for possibilitic modeling the proposed approach is based on two issues in order to extract relevant features the measure of feature importance as well as the possibility distribution uncertainty degree the importance of one feature can be considered under two aspects the first one is related to the scattering within one class and the second one reflects the feature power for class discrimination therefore we apply here shapley index paradigm which selects features who minimize the intra class distance and who maximize the inter class distance the previous process is refined using possibility distribution uncertainty degree in order to resolve some conflict problems between feature s importance values highlightswe present a feature selection strategy for possibilitic modeling we examine feature importance within one class and for classes s discrimination resolving conflict between feature s importance using possibility uncertainty degree proposed strategy is able to handle data imperfection and gives good performances proposed strategy gives better and reliable results on any data set

estimation efficiency in a binary mixed effects model setting summary we investigate the efficiency of likelihood methods for estimating the regression parameters of mixed effects logistic regression models one approach uses a conditional likelihood which eliminates the random intercept terms a second uses the likelihood generated from the marginal distribution of the data where the random intercepts are integrated out parametric estimates result from assuming a parametric form for the intercept distribution whereas we obtain semiparametric estimates when the intercept distribution is left unspecified we present an expression which shows that the asymptotic relative efficiency of conditional likelihood estimators relative to parametric estimators is a decreasing function of within cluster covariate correlation simulation results show the same for the asymptotic relative efficiency of the semiparametric estimator relative to the conditional for fixed covariate correlation the asymptotic relative efficiency of the parametric versus the conditional increases as cluster sizes increase example data further illustrate our findings

stratified feature sampling method for ensemble clustering of high dimensional data high dimensional data with thousands of features present a big challenge to current clustering algorithms sparsity noise and correlation of features are common characteristics of such data another common phenomenon is that clusters in such high dimensional data often exist in different subspaces ensemble clustering is emerging as a prominent technique for improving robustness stability and accuracy of high dimensional data clustering in this paper we propose a stratified sampling method for generating subspace component data sets in ensemble clustering of high dimensional data instead of randomly sampling a subset of features for each component data set in this method we first cluster the features of high dimensional data into a few feature groups called feature strata using stratified sampling we randomly sample some features from each feature stratum and merge the sampled features from different feature strata to generate a component data set in this way the component data sets have better representations of the clustering structure in the original data set comparing with random sampling and random projection methods in synthetic data analysis the component clustering by stratified sampling has demonstrated that the average clustering accuracy was increased without sacrificing clustering diversity we carried out a series of experiments on eight real world data sets from microarray text and image domains to evaluate ensemble clustering methods using three subspace component data generation methods and four consensus functions the experimental results consistently showed that the stratified sampling method produced the best ensemble clustering results in all data sets the ensemble clustering with stratified sampling also outperformed three other ensemble clustering methods which generate component clusters from the entire space of the original data highlightsa new component generation approach is proposed to produce ensemble components stratified sampling is used to generate subspace component data sets the component data can well represent the characteristics of the original data the proposed method can achieve a consistent performance in ensemble clustering the proposed method is easy to implement

estimation in generalized mixed models regression models containing fixed and random effects may have a response variable which is not normally distributed the generalized mixed model includes both discrete and continuous response variables and is developed here for problems in which the regression variables enter linearly into the model best linear unbiased predictor methods are extended to maximum likelihood and residual maximum likelihood estimation procedures applications in modelling discrete response variables and in survival analysis are discussed

dimensionality reduction for data of unknown cluster structure dimensionality reduction that preserves certain characteristics of data is needed for numerous reasons in this work we focus on data coming from a mixture of gaussian distributions and we propose a method that preserves the distinctness of the clustering structure although this structure is assumed to be yet unknown the rationale behind the method is the following i had one known the clusters classes within the data one could facilitate further analysis and reduce space dimensionality by projecting the data to the fisher s linear subspace which by definition best preserves the structure of the given classes ii under some reasonable assumptions this can be done albeit approximately without prior knowledge of the clusters classes in this paper we show how this approach works we present a method of preliminary data transformation that brings the directions of largest overall variability close to the directions of the best between class separation hence for the transformed data simple pca provides an approximation to the fisher s subspace we show that the transformation preserves the distinctness of the unknown structure in the data to a great extent

latent model for correlated binary data with diagnostic error summary we propose a methodology for modeling correlated binary data measured with diagnostic error a shared random effect is used to induce correlations in repeated true latent binary outcomes and in observed responses and to link the probability of a true positive outcome with the probability of having a diagnosis error we evaluate the performance of our proposed approach through simulations and compare it with an ad hoc approach the methodology is illustrated with data from a study that assessed the probability of corneal arcus n patients with familial hypercholesterolemia

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

predicting longitudinal trajectories of health probabilities with random effects multinomial logit regression researchers often encounter longitudinal health data characterized with three or more ordinal or nominal categories random effects multinomial logit models are generally applied to account for potential lack of independence inherent in such clustered data when parameter estimates are used to describe longitudinal processes however random effects both between and within individuals need to be retransformed for correctly predicting outcome probabilities this study attempts to go beyond existing work by developing a retransformation method that derives longitudinal growth trajectories of unbiased health probabilities variances of the predicted probabilities are estimated by using the delta method additionally the covariates regression coefficients on the multinomial logit function not substantively meaningful are transformed to the conditional effects on the predicted probabilities the empirical illustration uses the longitudinal data from the asset and health dynamics among the oldest old ahead our analysis compares three sets of the predicted probabilities of three health states at six time points obtained from respectively the retransformation method the blup and the fixed effects approach the results demonstrate that neglect of retransforming random errors in the random effects multinomial logit model results in severely biased longitudinal trajectories of health probabilities as well as overestimated effects of covariates on the probabilities

clusterability assessment for gaussian mixture models there are numerous measures designed to evaluate quality of a given data grouping in terms of its distinctness and between cluster separation however there seems to be no efficient method to assess distinctness of the intrinsic structure within data clusterability before actual clustering is determined based on recent findings we propose such measure in terms of covariance matrix decomposition for appropriately transformed data the data is assumed to come from a gaussian mixture model the transformation reshapes the data so that unsupervised technique of principal component analysis is able to uncover information directly indicative of the data clusterability characteristics in this work we propose the measure and explain the motivation as well as the relation to supervised structure distinctness coefficients we also show how the measure can be applied for number of clusters and feature selection tasks

random effects logistic regression analysis with auxiliary covariates summary we study a semiparametric estimation method for the random effects logistic regression when there is auxiliary covariate information about the main exposure variable we extend the semiparametric estimator of pepe and fleming 1991 journal of the american statistical association86 108 113 to the random effects model using the best linear unbiased prediction approach of henderson 1975 biometrics31 423 448 the method can be used to handle the missing covariate or mismeasured covariate data problems in a variety of real applications simulation study results show that the proposed method outperforms the existing methods we analyzed a data set from the collaborative perinatal project using the proposed method and found that the use of ddt increases the risk of preterm births among us children

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

latent variables measurement error and methods for analysing longitudinal binary and ordinal data we explore structural equations with latent variables for modelling between individual variability and measurement error in the analysis of longitudinal binary and ordinal data the structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis introducing the concept of continuous latent variables makes it clear that marginal and cluster specific models differ because their predicted variables are scaled to different standard deviations and that adjustment for measurement error in the outcome involves a change in scale as well we apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders in the process we compare results from marginal modelling using an sas gee routine karim and zeger 1988 qu s gauss program qu 1992 for generalized mixed models using gee the mixor package for cluster specific mixed effects models hedeker and gibbons 1994 and liscomp for structural models muthen 1988

modelling the covariance structure of repeated measurements models for repeated measurements used by wilson hebel and sherwin 1981 biometrics 37 553565 and mansour nordheim and rutledge 1985 biometrics 41 287 294 are considered these two models are generalized by the a p e k model obtained by introducing an extra parameter k a more general class of models described by kenward unpublished ph d thesis university of reading 1981 is briefly discussed simulation results are presented in which model parameters are estimated by maximum likelihood and likelihood ratios are used as criteria for choosing between models a set of blood pressure data is used to illustrate model fitting

generalized linear models with random effects a gibbs sampling approach abstract generalized linear models have unified the approach to regression for a wide variety of discrete continuous and censored response variables that can be assumed to be independent across experimental units in applications such as longitudinal studies genetic studies of families and survey sampling observations may be obtained in clusters responses from the same cluster cannot be assumed to be independent with linear models correlation has been effectively modeled by assuming there are cluster specific random effects that derive from an underlying mixing distribution extensions of generalized linear models to include random effects has thus far been hampered by the need for numerical integration to evaluate likelihoods in this article we cast the generalized linear random effects model in a bayesian framework and use a monte carlo method the gibbs sampler to overcome the current computational limitations the resulting algorithm is flexible to easily accommodate changes in the number

a mixed effects model for overdispersed count data in animal breeding count data models are developed for animal breeding applications to account for more variability than in a poisson mixed effects model a gamma distribution is assigned to poisson parameters thereby leading to a negative binomial model the natural log of the expected value of the poisson parameter is expressed as a linear function of fixed and random polygenic effects the negative binomial and poisson mixed models were compared in two simulations in the first marginal maximum likelihood mml estimates of genetic variances obtained under a poisson sire model psm and under a poisson animal model pam accounting for half sib relationships were different contrary to what occurs in a gaussian mixed linear model mml estimates of genetic variance under a negative binomial sire model were less biased than estimates under a psm and had a slightly smaller mean squared error mse the second simulation compared animal models in which the variance of the residuals was larger than the genetic variance empirical relative bias and mse of mml estimates of genetic variance were larger under a pam that ignored the residuals than under a negative binomial animal model differences in performance widened as genetic variance increased an application to the analysis of number of artificial inseminations until conception in dairy heifers is presented to illustrate potential differences in genetic variance estimates under the two animal models

a complete axiomatisation for observational congruence of finite state behaviours abstract finite state automata with non determinism and silent transitions can be interpreted not as subsets of the free monoid as in classical automata theory but as congruence classes under a congruence relation based upon the notion of weak bisimulation or observational equivalence due to park and milner in this paper a complete axiomatisation for this congruence is presented it extends the previously known complete axiomatisation by hennessy and milner for the case when all computations are finite the extension consists of five simple rules for recursion

two stage methods for the analysis of pooled data epidemiologic studies of disease often produce inconclusive or contradictory results due to small sample sizes or regional variations in the disease incidence or the exposures to clarify these issues researchers occasionally pool and reanalyse original data from several large studies in this paper we explore the use of a two stage random effects model for analysing pooled case control studies and undertake a thorough examination of bias in the pooled estimator under various conditions the two stage model analyses each study using the model appropriate to the design with study specific confounders and combines the individual study specific adjusted log odds ratios using a linear mixed effects model it is computationally simple and can incorporate study level covariates and random effects simulations indicate that when the individual studies are large two stage methods produce nearly unbiased exposure estimates and standard errors of the exposure estimates from a generalized linear mixed model by contrast joint fixed effects logistic regression produces attenuated exposure estimates and underestimates the standard error when heterogeneity is present while bias in the pooled regression coefficient increases with interstudy heterogeneity for both models it is much smaller using the two stage model in pooled analyses where covariates may not be uniformly defined and coded across studies and occasionally not measured in all studies a joint model is often not feasible the two stage method is shown to be a simple valid and practical method for the analysis of pooled binary data the results are applied to a study of reproductive history and cutaneous melanoma risk in women using data from ten large case control studies

the intraclass correlation coefficient distribution free definition and test a definition of the intraclass correlation coefficient is given on the basis of a general class of random effect model the conventional intraclass correlation coefficient and the intracluster correlation coefficient for binary data are both particular cases of the generalized coefficient we derive the score test for the hypothesis of null intraclass correlation in the exponential family the statistic does not depend on the particular distribution in this family and is related to the pairwise correlation coefficient the test can be adjusted for explanatory variables

an approximate marginal logistic distribution for the analysis of longitudinal ordinal data subject specific and marginal models have been developed for the analysis of longitudinal ordinal data subject specific models often lack a population average interpretation of the model parameters due to the conditional formulation of random intercepts and slopes marginal models frequently lack an underlying distribution for ordinal data in particular when generalized estimating equations are applied to overcome these issues latent variable models underneath the ordinal outcomes with a multivariate logistic distribution can be applied in this article we extend the work of o brien and dunson 2004 who studied the multivariate t distribution with marginal logistic distributions we use maximum likelihood instead of a bayesian approach and incorporated covariates in the correlation structure in addition to the mean model we compared our method with gee and demonstrated that it performs better than gee with respect to the fixed effect parameter estimation when the latent variables have an approximately elliptical distribution and at least as good as gee for other types of latent variable distributions

the algebra of timed processes atp the algebra of timed processes atp uses a notion of discrete global time and suggests a conceptual framework for introducing time by extending untimed languages the action vocabularly of atp contains a special element representing the progress of time the algebra has apart from standard operators of process algebras such as prefixing by an action alternative choice and parallel composition a primitive unit delay operator for two arguments processes p and q this operator gives a process which behaves as p before the execution of a time event and behaves as q afterwards it is shown that several d unit delay constructs such as timeouts and watchdogs can be expressed in terms of the unit delay operator and standard process algebra operators a sound and complete axiomatization for bisimulation semantics is studied and two examples illustrating the adequacy of the language for the description of timed systems are given finally we provide a comparison with existing timed process algebras

dynamic stochastic models for time dependent ordered paired comparison systems abstract when paired comparisons are made sequentially over time as for example in chess competitions it is natural to assume that the underlying abilities do change with time previous approaches are based on fixed updating schemes where the increments and decrements are fixed functions of the underlying abilities the parameters that determine the functions have to be specified a priori and are based on rational reasoning we suggest an alternative scheme for keeping track with the underlying abilities our approach is based on two components a response model that specifies the connection between the observations and the underlying abilities and a transition model that specifies the variation of abilities over time the response model is a very general paired comparison model allowing for ties and ordered responses the transition model incorporates random walk models and local linear trend models taken together these two components form a non gaussian state space model based on recent results rec

latent variable models for mixed discrete and continuous outcomes we propose a latent variable model for mixed discrete and continuous outcomes the model accommodates any mixture of outcomes from an exponential family and allows for arbitrary covariate effects as well as direct modelling of covariates on the latent variable an em algorithm is proposed for parameter estimation and estimates of the latent variables are produced as a by product of the analysis a generalized likelihood ratio test can be used to test the significance of covariates affecting the latent outcomes this method is applied to birth defects data where the outcomes of interest are continuous measures of size and binary indicators of minor physical anomalies infants who were exposed in utero to anticonvulsant medications are compared with controls

impact of missing data due to drop outs on estimators for rates of change in longitudinal studies a simulation study many cohort studies and clinical trials are designed to compare rates of change over time in one or more disease markers in several groups one major problem in such longitudinal studies is missing data due to patient drop out the bias and efficiency of six different methods to estimate rates of changes in longitudinal studies with incomplete observations were compared generalized estimating equation estimates gee proposed by liang and zeger 1986 unweighted average of ordinary least squares olse of individual rates of change uwls weighted average of olse wls conditional linear model estimates cle a covariate type estimates proposed by wu and bailey 1989 random effect re and joint multivariate re jmre estimates the latter method combines a linear re model for the underlying pattern of the marker with a log normal survival model for informative drop out process the performance of these methods in the presence of missing data completely at random mcar at random mar and non ignorable nim were compared in simulation studies data for the disease marker were generated under the linear random effects model with parameter values derived from realistic examples in hiv infection rates of drop out assumed to increase over time were allowed to be independent of marker values or to depend either only on previous marker values or on both previous and current marker values under macr all six methods yielded unbiased estimates of both group mean rates and between group difference however the cross sectional view of the data in the gee method resulted in seriously biased estimates under mar and nim drop out process the bias in the estimates ranged from 30 per cent to 50 per cent the degree of bias in the gee estimates increases with the severity of non randomness and with the proportion of mar data under mcar and mar all the other five methods performed relatively well re and jmre estimates were more efficient that is had smaller variance than uwls wls and cl estimates under nim wls and particularly re estimates tended to underestimate the average rate of marker change bias approximately 10 per cent under nim uwls cl and jmre performed better in terms of bias 3 5 per cent with the jmre giving the most efficient estimates given that markers are key variables related to disease progression missing marker data are likely to be at least mar thus the gee method may not be appropriate for analysing such longitudinal marker data the potential biases due to incomplete data require greater recognition in reports of longitudinal studies sensitivity analyses to assess the effect of drop outs on inferences about the target parameters are important

the topography of multivariate normal mixtures multivariate normal mixtures provide a flexible method of fitting high dimensional data it is shown that their topography in the sense of their key features as a density can be analyzed rigorously in lower dimensions by use of a ridgeline manifold that contains all critical points as well as the ridges of the density a plot of the elevations on the ridgeline shows the key features of the mixed density in addition by use of the ridgeline we uncover a function that determines the number of modes of the mixed density when there are two components being mixed a followup analysis then gives a curvature function that can be used to prove a set of modality theorems

exchangeability in multivariate markov chain models time homogeneous markov chain models with state space 0 1 k are useful in analysis of binary follow up data on k individuals that interact the number of parameters increases exponentially with k so more restrictive models are imperative for statistical inference the hypothesis that the matrix of transition probabilities is invariant under permutation of individuals is discussed it is shown that if individuals are exchangeable then the process counting the number of individuals occupying a given state is a markov chain this reduction of data is sufficient if either at most a single individual may change state between two consecutive time points or if a state is absorbing similar results are obtained for exchangeability within two subgroups inference in the multivariate process reduces to a univariate problem if individuals are independent given the group s previous response it is shown how conditional independence could be tested assuming exchangeability the different hypotheses re examined in an analysis of the occurrence of bacteria in milk samples of danish dairy cattle

multivariate contingency tables and the analysis of exchangeability there are settings in the social and health sciences where it is natural to question whether a collection of discrete random variables is exchangeable in this paper the inter relationships between parameter symmetry parameter invariance and exchangeable discrete random variables are investigated within the log linear models framework we demonstrate how log linear models can be used to formulate and test hypotheses of various forms of exchangeability and to characterize departures from exchangeability conditions under which the observed cross classification collapses into a lower dimensional cross classification while preserving the essential probability structure of the higher dimensional cross classification and the model structure of this lower dimensional cross classification are presented the development is sufficiently general to allow for subsetting the variables into classes which is important for some applications for example in studying the spatial clustering of periodontal disease there is interest in studying differences among disease patterns between the upper and lower arches in terms of parameter symmetry parameter invariance and exchangeability cross sectional periodontal disease data from a study of pima indians residing in the gila river indian community are used to illustrate how log linear models may be used to examine for exchangeability and for specific departures from exchangeability

linear dimension reduction and bayes classification abstract this paper develops an explicit expression for a compression matrix t of smallest possible left dimension k consistent with preserving the n variate normal bayes assignment of x to a given one of a finite number of populations and the k variate bayes assignment of tx to that population the bayes population assignment of x and tx are shown to be equivalent for a compression matrix t explicitly calculated as a function of the means and covariances known of the given populations

a comparison of mixed effects logistic regression models for binary response data with two nested levels of clustering we compare mixed effects logistic regression models for binary response data with two nested levels of clustering the comparison of these models occurs in the context of developmental toxicity data sets for which multiple types of outcomes first level are measured on each rat pup second level nested within a litter third level because the nested nature of such data is occasionally accommodated by ignoring one level of clustering we consider three models i a three level model adjusting for clustering due to both pup and litter m1 ii a two level model adjusting for just pup m2 and iii another two level model adjusting for just litter m3 the three types of effects of interest are i differences among malformation types first level effects ii differences among groups of pups for example sex of pup second level effects and iii differences among groups of litters for example dose third level effects simulations and data analyses suggest that the m3 model leads to more bias than the m1 or m2 models for all three types of effects in terms of coverage of confidence intervals for fixed effects log odds ratio parameters the m1 model achieves nominal coverage whereas the m2 model reduces coverage for the third level effects and the m3 model obtains poor coverage for both first and second level effects these reductions in coverage for certain model parameter combinations worsen as baseline risk increases the data analyses support these simulation based conclusions to some extent copyright 1999 john wiley sons ltd

robust analysis of generalized linear mixed models the method of maximum likelihood ml is widely used for analyzing generalized linear mixed models glmm s a full maximum likelihood analysis requires numerical integration techniques for calculation of the log likelihood and to avoid the computational problems involving irreducibly high dimensional integrals several maximum likelihood algorithms have been proposed in the literature to estimate the model parameters by approximating the log likelihood function although these likelihood algorithms are useful for fitting the glmm s efficiently under strict model assumptions they can be highly influenced by the presence of unusual data points in this article the author develops a technique for finding robust maximum likelihood rml estimates of the model parameters in glmm s which appears to be useful in downweighting the influential data points when estimating the parameters the asymptotic properties of the robust estimators are investigated under some regularity conditions small simulations are

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

analysis of binary data from a multicentre clinical trial summary we develop several methods for estimating the treatment effect difference defined as the overall log odds ratio of favourable response in a multicentre clinical trial comparing two treatments with binary response a simulation study compares the bias and mean squared error of the point estimates and the exact coverage probabilities of confidence intervals obtained distributions multicentre randomized clinical trials are frequently used to test the efficacy of new medical regimens these trials are attractive due to the ease of getting the desired sample size in a short period of time and the broad coverage of the patient population and medical practitioners the analysis of data from such trials requires combining information from the centres in a way that properly accounts for the variation due to the centres and the differential efficacy of treatments between the centres in this paper we investigate several approaches to pooling the data across centres and for handling the effects associated with the centres chakravarthi grizzle 1975 and beitler landis 1985 argue for treating these effects as random and fleiss 1986 argues against because the centres are seldom chosen at random from a well defined population of clinics and therefore the effects cannot be associated with any population we prefer the random effect model approach for the following reasons the goal of a trial is to extend the results of the study to the general population duly accounting for variation in the patient population and the medical skills of practitioners hence if we believe that the variability between centres as estimated by the data is typical of the variability in the population of centres then the inference based on the random effects model is more appropriate than the one based on the fixed effects model furthermore the variation among the centres may be more than that predicted from samples from a binomial distribution treating the centre effects as random introduces this intra class correlation into our model assumptions let the outcome variable from each centre be a pair of binomial random variables xaj

high dimensional multivariate probit analysis a computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model the procedure is applied to five variables from the pneumoconiosis field trial two variables of which were previously analyzed by ashford and sowden 1970 biometrics 26 535 546

decentralized clustering by finding loose and distributed density cores abstract centroid based clustering approaches fail to recognize extremely complex patterns that are non isotropic we analyze the underlying causes and find some inherent flaws in these approaches including shape loss false distances and false peaks which typically cause centroid based approaches to fail when applied to complex patterns as an alternative to current methods we propose a hybrid decentralized approach named dcore which is based on finding density cores instead of centroids to overcome these flaws the underlying idea is that we consider each cluster to have a shrunken density core that roughly retains the shape of the cluster each such core consists of a set of loosely connected local density peaks of higher density than their surroundings borders edges and outliers are distributed around the outsides of these cores in a hierarchical structure experiments demonstrate that the promise of dcore lies in its power to recognize extremely complex patterns and its high performance in real applications for example image segmentation and face clustering regardless of the dimensionality of the space in which the data are embedded

random effect threshold models for dose response relationships with repeated measurements summary a random threshold model for dose response designs with repeated measurements is intro duced inference procedures for this model are discussed the framework of generalized linear models is used to propose a quasi likelihood inference procedure the feasibility of this approach is illustrated with the analysis of food science data concerning a forced choice sensory experiment we consider a dose response study involving m individuals for which repeated binary measurements are obtained by applying several stimuli to the same individual and observing the responses an example would be a sensory experiment in the area of food science and food technology the response of interest often is detection yes or no of odour or flavour from a solution of a chemical substance which is presented to an individual at various concentrations odour and flavour detection thresholds across the population are then of primary interest other examples occur in phase ii clinical studies where a number of subjects are given various doses of a drug some of them are treated repeatedly with varying doses and success or failure of the therapy or alternatively the occurrence of severe side effects yes or no is assessed again with interest focused on population average behaviour further examples for repeated binary measurement design are mentioned in anderson and aitkin 1985 compared with other repeated measurements dose response designs considered previously by elashoff 1981 stiratelli et al 1984 anderson and aitkin 1985 zeger et al 1988 randall 1989 or more recently breslow and clayton 1993 the novelty of our approach lies in the model and the algorithm proposed in the model it is assumed that the observed responses are determined by underlying unobservable

learning over sets using kernel principal angles we consider the problem of learning with instances defined over a space of sets of vectors we derive a new positive definite kernel f a b defined over pairs of matrices a b based on the concept of principal angles between two linear subspaces we show that the principal angles can be recovered using only inner products between pairs of column vectors of the input matrices thereby allowing the original column vectors of a b to be mapped onto arbitrarily high dimensional feature spaces we demonstrate the usage of the matrix based kernel function f a b with experiments on two visual tasks the first task is the discrimination of irregular motion trajectory of an individual or a group of individuals in a video sequence we use the svm approach using f a b where an input matrix represents the motion trajectory of a group of individuals over a certain fixed time frame we show that the classification irregular versus regular greatly outperforms the conventional representation where all the trajectories form a single vector the second application is the visual recognition of faces from input video sequences representing head motion and facial expressions where f a b is used to compare two image sequences

linear dimension reduction and bayes classification with unknown population parameters abstract odell and decell odell and coberly gave necessary and sufficient conditions for the smallest dimension compression matrix b such that the bayes classification regions are preserved that is they developed an explicit expression of a compression matrix b such that the bayes classification assignment are the same for both the original space x and the compressed space bx odell indicated that whenever the population parameters are unknown then the dimension of bx is the same as x with probability one furthermore odell posed the problem of finding a lower dimension q p which in some sense best fits the range space generated by the matrix m the purpose of this paper is to discuss this problem and provide a partial solution

association models for periodontal disease progression a comparison of methods for clustered binary data we investigate population averaged pa and cluster specific cs associations for clustered binary logistic regression in the context of a longitudinal clinical trial that investigated the association between tooth specific visual elastase kit results and periodontal disease progression within 26 weeks of follow up we address estimation of population averaged logistic regression models with generalized estimating equations gee and conditional likelihood cl and mixed effects me estimation of cs logistic regression models of particular interest is the impact of clusters that do not provide information for conditional likelihood methods non informative clusters on inferences based upon the various methodologies the empirical and analytical results indicate that cl methods yield smaller test statistics than me methods when non informative clusters exist and that cl estimates are less efficient than me estimates under certain conditions moreover previously reported relationships between population averaged and cluster specific parameters appear to hold for the corresponding estimates in the presence of these clusters

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

interpreting parameters in the logistic regression model with random effects summary logistic regression with random effects is used to study the relationship between explanatory variables and a binary outcome in cases with nonindependent outcomes in this paper we examine in detail the interpretation of both fixed effects and random effects parameters as heterogeneity measures the random effects parameters included in the model are not easily interpreted we discuss different alternative measures of heterogeneity and suggest using a median odds ratio measure that is a function of the original random effects parameters the measure allows a simple interpretation in terms of well known odds ratios that greatly facilitates communication between the data analyst and the subject matter researcher three examples from different subject areas mainly taken from our own experience serve to motivate and illustrate different aspects of parameter interpretation in these models

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

sampling bias and logistic models summary in a regression model the joint distribution for each finite sample of units is determined by a function px y depending only on the list of covariate values x x u1 x un on the sampled units no random sampling of units is involved in biological work random sampling is frequently unavoidable in which case the joint distribution p y x depends on the sampling scheme regression models can be used for the study of dependence provided that the conditional distribution p y x for random samples agrees with px y as determined by the regression model for a fixed sample having a non random configuration x the paper develops a model that avoids the concept of a fixed population of units thereby forcing the sampling plan to be incorporated into the sampling distribution for a quota sample having a predetermined covariate configuration x the sampling distribution agrees with the standard logistic regression model with correlated components for most natural sampling plans such as sequential or simple random sampling the conditional distribution p y x is not the same as the regression distribution unless px y has independent components in this sense most natural sampling schemes involving binary random effects models are biased the implications of this formulation for subject specific and population averaged procedures are explored

small area inference for binary variables in the national health interview survey abstract the national health interview survey is designed to produce precise estimates of finite population parameters for the entire united states but not for small geographical areas or subpopulations our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months to include all sources of variation in the model we carry out a bayesian hierarchical analysis for the desired finite population quantities first for each cluster county a separate logistic regression relates the individual s probability of a doctor visit to his or her characteristics second a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level we describe the numerical methods needed to obtain the desired posterior moments then we compare estimates produced using the exact numerical method with approximations finally we compare the hierarchical bayes estimates to empirical bayes estimates and to stand

bias correction in generalised linear mixed models with a single component of dispersion summary general expressions are derived for the asymptotic biases in three approximate estimators of regression coefficients and variance component for small values of the variance component in generalised linear mixed models with canonical link function and a single source of extraneous variation the estimators involve first and second order laplace expansions of the integrated likelihood and a related procedure known as penalised quasilikelihood numerical studies of a series of matched pairs of binary outcomes show that the first order estimators of the variance component are seriously biased easily computed correction factors produce satisfactory estimators of small variance components comparable to those obtained with a second order laplace expansion and markedly improve the asymptotic performance for larger values for a series of matched pairs of binomial observations the variance correction factors rapidly approach one as the binomial denominators increase these results greatly extend the range of parameter values for which the approximate estimation procedures have satisfactory asymptotic properties

approximate posterior distributions for incomplete data problems summary we consider the problem of developing a simple approximation to a posterior distribution arising from incomplete data sampling we compare approximations based on the normal distribution and upon conjugate distributions theoretically where feasible and in some numerical examples two general conclusions can be made on the basis of our numerical work first when there is missing data approximations which fail to take loss of information into account give overly concentrated posterior distributions second the gaussian approximation matching mode and observed fisher information is quite good with large sample sizes and true posteriors which are not highly skewed further work delimiting these conditions more precisely will be useful finally the use of a conjugate posterior which matches both mode and information performs well in all of our examples and is decidedly superior to the gaussian approximation with small samples

the beta geometric distribution applied to comparative fecundability studies a convenient measure of fecundability is time number of menstrual cycles required to achieve pregnancy couples attempting pregnancy are heterogeneous in their per cycle probability of success if success probabilities vary among couples according to a beta distribution then cycles to pregnancy will have a beta geometric distribution the likelihood ratio test can thus be employed in studies of exposures that may impair fecundability covariates are incorporated in a natural way the model is illustrated by applying it to data on cycles to pregnancy in smokers and nonsmokers with adjustment for covariates summary in fre excerpt

regression analysis with clustered data clustered data are found in many different types of studies for example studies involving repeated measures inter rater agreement studies household surveys crossover designs and community randomized trials analyses based on population average and cluster specific models are commonly used for estimating treatment exposure effects with clustered data this paper discusses conditions when one or both types of models are appropriate for estimating causal effects and when there is agreement between population average and cluster specific analyses applications of survey sampling methods to the robust estimation of standard errors of estimated treatment parameters are discussed

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

a complete axiomatization of finite state acsr processes a real time process algebra called acsr has been developed to facilitate the specification and analysis of real time systems acsr supports synchronous timed actions and asynchronous instantaneous events timed actions are used to represent the usage of resources and to model the passage of time events are used to capture synchronization between processes to be able to specify real time systems accurately acsr supports a notion of priority that can be used to arbitrate among timed actions competing for the use of resources and among events that are ready for synchronization in addition to operators common to process algebra acsr includes the scope operator which can be used to model timeouts and interrupts equivalence between acsr terms is based on the notion of strong bisimulation this paper briefly describes the syntax and semantics of acsr and then presents a set of algebraic laws that can be used to prove equivalence of acsr processes the contribution of this paper is the soundness and completeness proofs of this set of laws the completeness proof is for finite state acsr processes which are defined to be processes without free variables under parallel operator or scope operator

tree structured logistic model for over dispersed binomial data with application to modeling developmental effects this article proposes tree structured logistic regression modeling for over dispersed binomial data recursive partitioning is performed using a combination of statistical tests and residual analysis the splitting criterion in cross validation is based on the deviance function a nested grid algorithm to estimate the bootstrap parameters is developed the regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables the proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the national center for toxicological research a conditional gaussian chain model is used to account for the effect of fetal weight by dose

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

analysis of clustered binary outcomes using within cluster paired resampling summary conditional logistic regression clr is useful for analyzing clustered binary outcome data when interest lies in estimating a cluster specific exposure parameter while treating the dependency arising from random cluster effects as a nuisance clr aggregates unmeasured cluster specific factors into a cluster specific baseline risk and is invalid in the presence of unmodeled heterogeneous covariate effects or within cluster dependency we propose an alternative resampling based method for analyzing clustered binary outcome data within cluster paired resampling wcpr which allows for within cluster dependency not solely due to baseline heterogeneity for example dependency may be in part caused by heterogeneity in response to an exposure across clusters due to unmeasured cofactors when both clr and wcpr are valid our simulations suggest that the two methods perform comparably when clr is invalid wcpr continues to have good operating characteristics for illustration we apply both wcpr and clr to a periodontal data set where there is heterogeneity in response to exposure across clusters

chernoff information between gaussian trees abstract in this paper we deal with gaussian graphical classifiaction problem we aim to provide a systematic study of the relationship between chernoff information and topological as well as algebraic properties of the corresponding gaussian graphs for the underlying graphical testing problems we first show the relationship between chernoff information and generalized eigenvalues of the associated covariance matrices it is then proved that chernoff information between two gaussian trees sharing certain local subtree structures can be transformed into that of two smaller trees in this way we provide a sequence of equivalent gaussian tree pairs in terms of chernoff information under our proposed grafting operations bottleneck gaussian trees namely gaussian trees connected by one such operation can thus be simplified into two 3 node gaussian trees thereafter we provide a thorough study about how chernoff information changes when small differences are accumulated into bigger ones via concatenated grafting operations as well as partial ordering in the end we propose an optimal linear dimension reduction method based on generalized eigenvalues for the purpose of classification which is proved to achieve maximum chernoff information among all linear transformations

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

a mixed effects multinomial logistic regression model a mixed effects multinomial logistic regression model is described for analysis of clustered or longitudinal nominal or ordinal response data the model is parameterized to allow flexibility in the choice of contrasts used to represent comparisons across the response categories estimation is achieved using a maximum marginal likelihood mml solution that uses quadrature to numerically integrate over the distribution of random effects an analysis of a psychiatric data set in which homeless adults with serious mental illness are repeatedly classified in terms of their living arrangement is used to illustrate features of the model

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

empirical bayes estimation of individual growth curve parameters and their relationship to covariates summary the analysis of growth curves has long been important in biostatistics work has focused on two problems the estimation of individual curves based on many data points and the estimation of the mean growth curve for a group of individuals this paper extends a recent approach that seeks to combine data from a group of individuals in order to improve the estimates of individual growth parameters growth is modeled as polynomial in time and the group model is also linear incorporating growth related covariates into the model the estimation used is empirical bayes the estimation formulas are illustrated with a set of data on rat growth originally presented by box 1950 biometrics 6 362 389

analyzing repeated measures on generalized linear models via the bootstrap the analysis of longitudinal data for which the response variables have nonnormal error distributions previously has been complex and or dependent on restrictive assumptions in this paper simple methods are introduced for the class of generalized linear models glms regressions are fit to the data at each observation time functions of the resulting coefficients may be bootstrapped or the coefficients combined through closed form estimation of their covariances application is made to a data set on xerophthalmia in indonesian children

discharge rates of medicare stroke patients to skilled nursing facilities bayesian logistic regression with unobserved heterogeneity abstract we determine factors both hospital specific and market area specific associated with hospitals propensities for discharging medicare stroke patients to skilled nursing facilities snf s in california and florida logistic regression is generalized to the case of a betabinomial hierarchical model in which covariate information is included in the hyperparameters of the second stage beta distribution it is found that the posterior mean of the proportion discharged to snf is approximately a weighted average i e shrinkage estimator of the logistic regression estimator and the observed rate we develop fully bayesian inference that takes into account uncertainty about the hyperparameters and we find that this also allows us to test for overdispersion in a natural way the number of observed zeros i e hospitals that sent no stroke patients to a snf is excessive compared to the number expected from a standard logistic regression model and is fit better by the hierarchical betabinomial mod

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations

assessing the order of dependence for partially exchangeable binary data abstract the problem we consider is how to assess the order of serial dependence within partially exchangeable binary sequences we obtain exact conditional tests comparing any two orders by finding the conditional distribution of data given certain transition counts these tests are facilitated with a new monte carlo scheme asymptotic tests are also discussed in particular we show that the likelihood ratio tests have an asymptotic chi squared distribution thus generalizing the results of billingsley for the particular case of markov chains we apply these methods to several datasets and perform a simulation to study their properties

comparison of the proportions of affected relatives of cases and controls analysis and minimum sample size formula the problem of familial aggregation has frequently been approached by comparing the proportion of affected relatives of index cases with the proportion of affected relatives of index controls this type of study has an analogy with the case control design and is frequently analysed as if it was one it is however an essentially different design which may involve dependent observations we show that conventional tests for comparing proportions of affected subjects are still valid with this design we give a formula for computing the minimum sample size required to detect a given degree of aggregation measured by the intracluster correlation coefficient which can be estimated very simply by the difference in proportions of affected relatives in the two groups

mixed effects models with bivariate and univariate association parameters for longitudinal bivariate binary response data summary when two binary responses are measured for each study subject across time it may be of interest to model how the bivariate associations and marginal univariate risks involving the two responses change across time to achieve such a goal marginal models with bivariate log odds ratio and univariate logit components are extended to include random effects for all components specifically separate normal random effects are specified on the log odds ratio scale for bivariate responses and on the logit scale for univariate responses assuming conditional independence given the random effects facilitates the modeling of bivariate associations across time with missing at random incomplete data we fit the model to a dataset for which such structures are feasible a longitudinal randomized trial of a cardiovascular educational program where the responses of interest are change in hypertension and hypercholestemia status the proposed model is compared to a naive bivariate model that assumes independence between time points and univariate mixed effects logit models

power analyses for longitudinal study designs with missing data existing methods for power analysis for longitudinal study designs are limited in that they do not adequately address random missing data patterns although the pattern of missing data can be assessed during data analysis it is unknown during the design phase of a study the random nature of the missing data pattern adds another layer of complexity in addressing missing data for power analysis in this paper we model the occurrence of missing data with a two state first order markov process and integrate the modelling information into the power function to account for random missing data patterns the markov model is easily specified to accommodate different anticipated missing data processes we develop this approach for the two most popular longitudinal models the generalized estimating equations gee and the linear mixed effects model under the missing completely at random mcar assumption for gee we also limit our consideration to the working independence correlation model the proposed methodology is illustrated with numerous examples that are motivated by real study designs

semiparametric bayesian modeling of random genetic effects in family based association studies we consider the inference problem of estimating covariate and genetic effects in a family based case control study where families are ascertained on the basis of the number of cases within the family however our interest lies not only in estimating the fixed covariate effects but also in estimating the random effects parameters that account for varying correlations among family members these random effects parameters though weakly identifiable in a strict theoretical sense are often hard to estimate due to the small number of observations per family a hierarchical bayesian paradigm is a very natural route in this context with multiple advantages compared with a classical mixed effects estimation strategy based on the integrated likelihood we propose a fully flexible bayesian approach allowing nonparametric modeling of the random effects distribution using a dirichlet process prior and provide estimation of both fixed effect and random effects parameters using a markov chain monte carlo numerical integration scheme the nonparametric bayesian approach not only provides inference that is less sensitive to parametric specification of the random effects distribution but also allows possible uncertainty around a specific genetic correlation structure the bayesian approach has certain computational advantages over its mixed model counterparts data from the prostate cancer genetics project a family based study at the university of michigan comprehensive cancer center including families having one or more members with prostate cancer are used to illustrate the proposed methods a small scale simulation study is carried out to compare the proposed nonparametric bayes methodology with a parametric bayesian alternative

exact goodness of fit tests for markov chains goodness of fit tests are useful in assessing whether a statistical model is consistent with available data however the usual asymptotics often fail either because of the paucity of the data or because a nonstandard test statistic is of interest in this article we describe exact goodness of fit tests for first and higher order markov chains with particular attention given to time reversible ones the tests are obtained by conditioning on the sufficient statistics for the transition probabilities and are implemented by simple monte carlo sampling or by markov chain monte carlo they apply both to single and to multiple sequences and allow a free choice of test statistic three examples are given the first concerns multiple sequences of dry and wet january days for the years 1948 1983 at snoqualmie falls washington state and suggests that standard analysis may be misleading the second one is for a four state dna sequence and lends support to the original conclusion that a second order markov chain provides an adequate fit to the data the last one is six state atomistic data arising in molecular conformational dynamics simulation of solvated alanine dipeptide and points to strong evidence against a first order reversible markov chain at 6 picosecond time steps

combining historical and randomized controls for assessing trends in proportions abstract a statistical method for incorporating historical control data in the analysis of proportions is proposed and illustrated the method has as its extremes logistic regressions completely pooling and completely ignoring historical controls the degree of pooling used is determined by the variability from experiment to experiment in the control incidences the fit of historical control groups to an assumed normal logistic model is assessed using probability plotting techniques monte carlo studies evaluate the adequacy of the asymptotic approximation used sensitivity analyses show that results are insensitive to alternative priors the method is applied to several sets of tumor data from animal experiments

mixed model analysis of a censored normal distribution with reference to animal breeding a mixed model procedure for analysis of censored data assuming a multivariate normal distribution is described a bayesian framework is adopted which allows for estimation of fixed effects and variance components and prediction of random effects when records are left censored the procedure can be extended to right and two tailed censoring the model employed is a generalized linear model and the estimation equations resemble those arising in analysis of multivariate normal or categorical data with threshold models estimates of variance components are obtained using expressions similar to those employed in the em algorithm for restricted maximum likelihood reml estimation under normality

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

combining images across multiple subjects a study of direct cortical electrical interference this article introduces a bayesian hierarchical model for combining information across multiple images our work was motivated by an invasive functional brain mapping technique called direct cortical electrical interference that gives a sparse set of binary observations of an underlying true region at multiple sites on the brain surface to model region shapes that may vary widely across individuals we use mixtures of simple templates for example circles these subject specific templates are treated as random effects governed by a set of population templates that make up a population region the numbers of subject specific and population templates are treated as unknown variables to be estimated from the data conditional on the subject specific regions the observed data are modeled using logistic regression to estimate the variability among images across patients we develop a measure based on baddeley s error measure for binary images because the dimension of the parameter space changes as the

bias reduction of approximate maximum likelihood estimates for heritability in threshold models approximate maximum likelihood estimates such as penalized quasi likelihood and iterated reweighted reml estimates for heritability or intraclass correlation in threshold models for binary data can be seriously biased two approaches to correct for this bias are studied with emphasis on animal breeding models for binary data scope for reduction of bias of heritability estimates is found to be slim because of the commonly large number of fixed effects in animal breeding models minimal dimensions for the data are identified such that bias and root mean squared error are of modest size and useful inference on heritability or intraclass correlation is feasible

the evaluation of integrals of the form f t exp t 2 dt application to logistic normal models abstract logistic normal distributions and related functions arise in a variety of statistical applications of current interest including binary measurement error models and the analysis of teratogenicity experiments analytic intractability has led to the development of numerous approximations to the desired forms often with consequences that have not been well studied a method is developed to compute these forms to arbitrary accuracy and comparative calculations are made that show when the common numerical alternative 20 point gaussian quadrature begins to fail by using a simple matrix transformation this method can be used with multiple covariate regression models of the logistic normal form we conducted a simulation study that compares the ability of 20 point gaussian quadrature and our new method to obtain the maximum likelihood estimator of relative risk in the logistic normal measurement error model using standard subroutines to maximize the likelihood equations 27 of 50 trials failed to

generalized score test of homogeneity based on correlated random effects models summary we present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing in these models each subject has a particular random effect but the random effects between subjects are correlated we derive the general form of the score statistic for testing that the random effects have a variance equal to 0 we apply this result to both parametric and semiparametric models in both cases we show that under certain conditions the score statistic has an asymptotic normal distribution we consider several applications of this theory including overdispersion heterogeneity between groups spatial correlations and genetic linkage

using empirical bayes methods in biopharmaceutical research a compound sampling model where a unit specific parameter is sampled from a prior distribution and then observed are generated by a sampling distribution depending on the parameter underlies a wide variety of biopharmaceutical data for example in a multi centre clinical trial the true treatment effect varies from centre to centre observed treatment effects deviate from these true effects through sampling variation knowledge of the prior distribution allows use of bayesian analysis to compute the posterior distribution of clinic specific treatment effects frequently summarized by the posterior mean and variance more commonly with the prior not completely specified observed data can be used to estimate the prior and use it to produce the posterior distribution an empirical bayes or variance component analysis in the empirical bayes model the estimated prior mean gives the typical treatment effect and the estimated prior standard deviation indicates the heterogeneity of treatment effects in both the bayes and empirical bayes approaches estimated clinic effects are shrunken towards a common value from estimates based on single clinics this shrinkage produces more efficient estimates in addition the compound model helps structure approaches to ranking and selection provides adjustments for multiplicity allows estimation of the histogram of clinic specific effects and structures incorporation of external information this paper outlines the empirical bayes approach coverage will include development and comparison of approaches based on parametric priors for example a gaussian prior with unknown mean and variance and non parametric priors discussion of the importance of accounting for uncertainty in the estimated prior comparison of the output and interpretation of fixed and random effects approaches to estimating population values estimating histograms and identification of key considerations in the use and interpretation of empirical bayes methods

pca and svd with nonnegative loadings principal component analysis pca and singular value decomposition svd are widely used in multivariate statistical analysis for data reduction the work considers exponential logit and multinomial parameterization of the eigenvectors elements that always yields nonnegative loadings of shares for variable aggregation in contrast to regular pca and svd matrix decomposition by the positive shares shows explicitly which variables and with which percent are composed into each group so what is each variable contribution to data approximation the least squares objective of matrix fit is reduced to rayleigh quotient for variational description of the eigenvalues eigenvectors with the nonlinear parameterization can be found in newton raphson optimizing procedure numerical examples compare the classical and nonnegative loadings results with interpretation by the perron frobenius theory for each subset of variables identified by sparse loading vectors

a gee moving average analysis of the relationship between air pollution and mortality for asthma in barcelona spain several studies have assessed the association between air pollution and hospital admissions or emergency room visits for asthma because of both the presence of missing data and the small number of observations the relationship between air pollution and mortality for respiratory causes has been rarely analysed and when it has the results are very inconclusive or even inconsistent the objective of this study is to assess the relation between levels of air pollutants black smoke sulphur dioxide nitrogen dioxide and ozone meteorological variables 24th average temperature and relative humidity and daily mortality for asthma icd 9 493 2 to 45 years old in barcelona spain during the period 1986 1989 since the range of daily mortality for asthma 2 to 45 years old during the period 1986 1989 was 0 1 we have preferred to consider this variable as dichotomous first the relationship between air pollutants meteorological variables and daily mortality controlled for the occurrence of asthma epidemics was estimated using logistic regression models as was expected the residuals from this regression were autocorrelated showing a complex moving average ma structure if covariates were not time dependent the so called generalized linear mixed models could be applied in our case the covariates vary as a consequence the likelihood is numerically intractable because it involves the evaluation of n fold integral an alternative method that avoids these numerical problems is the generalized estimating equations method gee it is a multivariate analogue of quasilikelihood estimation in the absence of a likelihood function the parameters can be estimated by solving a multivariate analogue of the quasi score function we have modi ed the gee method in this paper allowing for a di erent structure in the error covariance matrix ma both air pollutants and meteorological variables are related with the occurrence of a death for asthma in this sense nitrogen dioxide no2 0 037 p 0 05 ozone o3 0 021 p 0 06 and high temperature the s were in the range 0 098 0 182 p 0 05 increased the probability of dying for asthma in barcelona during the period 1986 1989 copyright 1999 john wiley sons ltd

a two part random effects model for semicontinuous longitudinal data a semicontinuous variable has a portion of responses equal to a single value typically 0 and a continuous often skewed distribution among the remaining values in cross sectional analyses variables of this type may be described by a pair of regression models for example a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero we extend this two part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages fitting a two part random effects model poses computational challenges similar to those found with generalized linear mixed models we obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate fisher scoring procedure based on high order laplace approximations to illustrate we apply the technique to data from the adolescent alcohol prevention trial examining reported recent alcohol use for students in g

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures