a multilevel mixed effects varying coefficient model with multilevel predictors and random effects for modeling hospitalization risk in patients on dialysis for patients on dialysis hospitalizations remain a major risk factor for mortality and morbidity we use data from a large national database united states renal data system to model time varying effects of hospitalization risk factors as functions of time since initiation of dialysis to account for the three level hierarchical structure in the data where hospitalizations are nested in patients and patients are nested in dialysis facilities we propose a multilevel mixed effects varying coefficient model mme vcm where multilevel patient and facility level random effects are used to model the dependence structure of the data the proposed mme vcm also includes multilevel covariates where baseline demographics and comorbidities are among the patient level factors and staffing composition and facility size are among the facility level risk factors to address the challenge of high dimensional integrals due to the hierarchical structure of the random effects we propose a novel two step approximate em algorithm based on the fully exponential laplace approximation inference for the varying coefficient functions and variance components is achieved via derivation of the standard errors using score contributions the finite sample performance of the proposed estimation procedure is studied through simulations

the computational complexity of knot genus and spanning area we investigate the computational complexity of some problems in three dimensional topology and geometry we show that the problem of determining a bound on the genus of a knot in a 3 manifold is np complete using similar ideas we show that deciding whether a curve in a metrized pl 3 manifold bounds a surface of area less than a given constant c is np hard

a hybrid estimator in nonlinear and generalised linear mixed effects models summary a hybrid method that combines laplace s approximation and monte carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family an asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results this hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models

inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains let rnbe an arbitrary smooth bounded domain we prove the existence of a polynomial functiona x on rnsuch that an arbitrary and sufficiently small vector field on rn 1can be realized on the center manifold of the semilinear parabolic equation formula with an appropriate nonlinearityg x s w r rn g x s w r this extends earlier results of polacik and rybakowski and shows that arbitrary chaotic behavior is possible for semilinear scalar parabolic bvps on arbitrary bounded domains to prove this we establish some spectral perturbation and convergence results and solve an abstract inverse eigenvalue problem

estimation of covariate effects in generalized linear mixed models with informative cluster sizes in standard regression analyses of clustered data one typically assumes that the expected value of the response is independent of cluster size however this is often false for example in studies of surgical interventions investigators have frequently found surgery volume and outcomes to be related to the skill level of the surgeons this paper examines the effect of ignoring response dependent informative cluster sizes on standard analytical methods such as mixed effects models and conditional likelihood methods using analytic calculations simulation studies and an example from a study of periodontal disease we consider the case in which cluster sizes and responses share random effects which we assume to be independent of the covariates our focus is on maximum likelihood methods that ignore informative cluster sizes and we show that they exhibit little bias in estimating covariate effects that are uncorrelated with the random effects associated with cluster sizes however estimation of covariate effects that are associated with the random effects can be biased in particular for models with random intercepts only ignoring informative cluster sizes can yield biased estimators of the intercept but little bias in estimation of all covariate effects

marginalized binary mixed effects models with covariate dependent random effects and likelihood inference les modeles marginaux et les modeles a effets mixtes conditionnels sont couramment utilises pour des donnees binaires agregees cependant les parametres de regression et les predictions de modeles non lineaires a effets mixtes n ont pas habituellement une interpretation marginale directe des que la forme fonctionnelle conditionnelle ne peut etre transposee a la marge une approche unifiee est interessante des que l on est interesse a la fois par des inferences marginales et conditionnelles a cette fin nous avons etudie une parametrisation de modeles lineaires generalises mixtes avec une distribution structuree de l intercept aleatoire qui apparie les formes conditionnelles et marginales nous modelisons la distribution des reponses moyennes marginales et selectionnons la distribution des intercept pour realiser l appariement et aussi pour modeliser des effets aleatoires de covariables nous discutons la relation entre cette approche et quelques modeles existant et comparons ces approches sur deux jeux de donnees

group sequential methods for an ordinal logistic random effects model under misspecification interim analyses in clinical trials are planned for ethical as well as economic reasons general results have been published in the literature that allow the use of standard group sequential methodology if one uses an efficient test statistic e g when wald type statistics are used in random effects models for ordinal longitudinal data these models often assume that the random effects are normally distributed however this is not always the case we will show that when the random effects distribution is misspecified in ordinal regression models the joint distribution of the test statistics over the different interim analyses is still a multivariate normal distribution but a sandwich type correction to the covariance matrix is needed in order to obtain the correct covariance matrix the independent increment structure is also investigated a bias in estimation will occur due to the misspecification however we will also show that the treatment effect estimate will be unbiased under the null hypothesis thus maintaining the type i error extensive simulations based on a toenail dermatophyte onychomycosis trial are used to illustrate our results

an algorithm for computing the nonparametric mle of a mixing distribution abstract a fast algorithm for calculating the nonparametric maximum likelihood estimate mle of a mixing distribution g in a mixture model is discussed the literature contains several methods for computing the nonparametric mle of g but these methods are slow in this article we develop an algorithm for maximizing the log likelihood l g over the family of all distribution functions that yields the nonparametric mle of g in some semiparametric problems a structural or fixed parameter is of interest and we are interested in computing profile likelihood sup gl g for a grid of values of the algorithm that we propose is fast enough for this purpose examples illustrate and compare the algorithms one taken from an article by laird the common mean problem and one taken from the literature on optimal experimental design it is also noted that routines from the literature on semi infinite programming may be used to compute the profile log likelihood

bridging conditional and marginal inference for spatially referenced binary data spatially referenced binary data are common in epidemiology and public health owing to its elegant log odds interpretation of the regression coefficients a natural model for these data is logistic regression to account for missing confounding variables that might exhibit a spatial pattern say socioeconomic biological or environmental conditions it is customary to include a gaussian spatial random effect conditioned on the spatial random effect the coefficients may be interpreted as log odds ratios however marginally over the random effects the coefficients no longer preserve the log odds interpretation and the estimates are hard to interpret and generalize to other spatial regions to resolve this issue we propose a new spatial random effect distribution through a copula framework which ensures that the regression coefficients maintain the log odds interpretation both conditional on and marginally over the spatial random effects we present simulations to assess the robustness of our approach to various random effects and apply it to an interesting dataset assessing periodontal health of gullah speaking african americans the proposed methodology is flexible enough to handle areal or geo statistical datasets and hierarchical models with multiple random intercepts

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

stable actions of groups on real trees this paper further develops rips s work on real trees we study a class of actions called stable which includes actions with trivial arc stabilizers and small actions of hyperbolic groups

jsj splittings for finitely presented groups over slender groups we generalize the jsj splitting of rips and sela to give decompositions of finitely presented groups which capture splittings over certain classes of small subgroups such classes include the class of all 2 ended groups and the class of all virtually z z groups the approach called track zipping is relatively elementary and differs from the rips sela approach in that it does not rely on the theory of r trees but rather on an understanding of certain embedded 1 complexes called patterns in a presentation 2 complex for the ambient group

a logistic bivariate normal model for overdispersed two state markov processes we describe a logistic bivariate normal mixture model for a two state markov chain in which each individual makes transitions between states according to a subject specific transition probability matrix the use of the bivariate normal mixing distribution facilitates inferences regarding the correlation of the random effects and hence provides insight as to the nature of the subject to subject variability in the transition probabilities tests regarding the correlation can be based on likelihood ratio score or wald statistics estimates of the transition intensities of a latent continuous time conditionally markov process may also be computed we illustrate this methodology by application to a parasitic infection field study and contrast our findings with those previously published on this data set

reml and ml estimation for clustered grouped survival data clustered grouped survival data arise naturally in clinical medicine and biological research for example in a randomized clinical trial the variable of interest is the time to occurrence of a certain event with or without a new treatment and the data are collected from possibly correlated subjects from independent clusters however it is sometimes impossible or too expensive to monitor the experimental subjects continuously the subjects are examined regularly and the continuous survival data are thus grouped into a discrete time scale with such a design researchers are mainly interested in the effectiveness of the new treatment as well as the correlation among subjects from the same cluster namely the intracluster correlation this paper suggests a random effects approach to the estimation of the regression parameter with various choices of regression model and also the dependence parameter which characterizes the intracluster correlation time dependent covariates can be accommodated in the proposed model and the estimation procedure will not be further complicated with large cluster sizes the proposed method is applied to the data from the diabetic retinopathy study the objective of which is to evaluate the effectiveness of laser photocoagulation in delaying or preventing the onset of blindness in the left and right eyes of individuals with diabetes associated retinopathy the intracluster correlation using a grouped proportional hazards regression model can be estimated and the relationship between the regression parameter estimates based on the random effects approach and the marginal approach using a dynamic logistic regression model are discussed results from a simulation study of the proposed method are also presented

modeling multivariate survival data by a semiparametric random effects proportional odds model summary in this article the focus is on the analysis of multivariate survival time data with various types of dependence structures examples of multivariate survival data include clustered data and repeated measurements from the same subject such as the interrecurrence times of cancer tumors a random effect semiparametric proportional odds model is proposed as an alternative to the proportional hazards model the distribution of the random effects is assumed to be multivariate normal and the random effect is assumed to act additively to the baseline log odds function this class of models which includes the usual shared random effects model the additive variance components model and the dynamic random effects model as special cases is highly flexible and is capable of modeling a wide range of multivariate survival data a unified estimation procedure is proposed to estimate the regression and dependence parameters simultaneously by means of a marginal likelihood approach unlike the fully parametric case the regression parameter estimate is not sensitive to the choice of correlation structure of the random effects the marginal likelihood is approximated by the monte carlo method simulation studies are carried out to investigate the performance of the proposed method the proposed method is applied to two well known data sets including clustered data and recurrent event times data

an estimation method for the semiparametric mixed effects model summary a semiparametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous ordinal or binary outcome the common assumption of gaussian random effects is relaxed by using a predictive recursion method newton and zhang 1999 to provide a nonparametric smooth density estimate a new strategy is introduced to accelerate the algorithm parameter estimates are obtained by maximizing the marginal profile likelihood by powell s conjugate direction search method monte carlo results are presented to show that the method can improve the mean squared error of the fixed effects estimators when the random effects distribution is not gaussian the usefulness of visualizing the random effects density itself is illustrated in the analysis of data from the wisconsin sleep survey the proposed estimation procedure is computationally feasible for quite large data sets

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

matching conditional and marginal shapes in binary random intercept models using a bridge distribution function summary random effects logistic regression models are often used to model clustered binary response data regression parameters in these models have a conditional subject specific interpretation in that they quantify regression effects for each cluster very often the logistic functional shape conditional on the random effects does not carry over to the marginal scale thus parameters in these models usually do not have an explicit marginal population averaged interpretation we study a bridge distribution function for the random effect in the random intercept logistic regression model under this distributional assumption the marginal functional shape is still of logistic form and thus regression parameters have an explicit marginal interpretation the main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework the generality of the results and some properties of the bridge distribution functions are discussed an example is used for illustration

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

convergence to equilibrium for a parabolic hyperbolic phase field system with dynamical boundary condition abstract this paper is concerned with the well posedness and the asymptotic behavior of solutions to the following parabolic hyperbolic phase field system 0 1 t 0 t t t 0 in 0 subject to the neumann boundary condition for 0 2 0 on 0 the dynamical boundary condition for 0 3 t 0 on 0 and the initial conditions 0 4 0 0 0 0 t 0 1 in where is a bounded domain in r 3 with smooth boundary is the outward normal direction to the boundary and is a real analytic function in this paper we first establish the existence and uniqueness of a global strong solution to 0 1 0 4 then we prove its convergence to an equilibrium as time goes to infinity and we provide an estimate of the convergence rate

semiparametric estimation of marginal hazard function from case control family studies estimating marginal hazard function from the correlated failure time data arising from case control family studies is complicated by noncohort study design and risk heterogeneity due to unmeasured shared risk factors among the family members accounting for both factors in this article we propose a two stage estimation procedure at the first stage we estimate the dependence parameter in the distribution for the risk heterogeneity without obtaining the marginal distribution first or simultaneously assuming that the dependence parameter is known at the second stage we estimate the marginal hazard function by iterating between estimation of the risk heterogeneity frailty for each family and maximization of the partial likelihood function with an offset to account for the risk heterogeneity we also propose an iterative procedure to improve the efficiency of the dependence parameter estimate the simulation study shows that both methods perform well under finite sample sizes we illustrate the method with a case control family study of early onset breast cancer

non parametric inference for clustered binary and count data when only summary information is available summary data in the form of pairs x y where the response y is a count arise in many applications including problems involving stratified or two stage sampling such data are often analysed by using random effects models where the distribution of y conditional on x and on an unobserved random parameter is taken to be either binomial or poisson and the distribution of is connected through a link function to a random effect the latter is sometimes supposed to be normally distributed but that assumption can lead to serious biases if it is not satisfied this difficulty has motivated an extensive literature on non parametric techniques for cases where the random effect distribution is unknown but that methodology requires detailed cluster level data no non parametric techniques are available for instances where only summary data are accessible we show that the random effect distribution is actually non parametrically identifiable from crude summary data and we suggest a sieve method for inference in this case non parametric approaches to both parameter estimation and prediction are introduced and empirical techniques are developed for choosing tuning parameters these methods are shown to outperform their parametric counterparts when the model is misspecified and to perform almost as well as parametric methods when the model is correct

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

analysis of a cluster randomized trial with binary outcome data using a multi level model the use of multi level logistic regression models was explored for the analysis of data from a cluster randomized trial investigating whether a training programme for general practitioners reception staff could improve women s attendance at breast screening twenty six general practices were randomized with women nested within them requiring a two level model which allowed for between practice variability comparisons were made with fixed effect fe and random effects re cluster summary statistic methods ordinary logistic regression and a marginal model based on generalized estimating equations with robust variance estimates an fe summary statistic method and ordinary logistic regression considerably understated the variance of the intervention effect thus overstating its statistical significance the marginal model produced a higher statistical significance for the intervention effect compared to that obtained from the re summary statistic method and the multi level model because there was only a moderate number of practices and these had unbalanced cluster sizes reliable asymptotic properties for the robust standard errors used in the marginal model may not have been achieved while the re summary statistic method cannot handle multiple covariates easily marginal and multi level models can do so in contrast to multi level models however marginal models do not provide direct estimates of variance components but treat these as nuisance parameters estimates of the variance components were of particular interest in this example additionally parametric bootstrap methods within the multi level model framework provide confidence intervals for these variance components as well as a confidence interval for the effect of intervention which allows for the imprecision in the estimated variance components the assumption of normality of the random effects can be checked and the models extended to investigate multiple sources of variability

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

the effects of mixture distribution misspecification when fitting mixed effects logistic models summary mixed effects logistic models are often used to analyze binary response data which have been gathered in clusters or groups responses are assumed to follow a logistic model within clusters with an intercept which varies across clusters according to a specified probability distribution g in this paper we examine the performance of mixed effects logistic regression analysis when a main component of the model the mixture distribution is misspecified we show that when the mixture distribution is misspecified estimates of model parameters including the effects of covariates typically are asymptotically biased i e inconsistent however we present some approximations which suggest that the magnitude of the bias in the estimated covariate effects is typically small these findings are corroborated by a set of simulations which also suggest that valid variance estimates of estimated covariate effects can be obtained when the mixture distribution is misspecified

bayesian methods of analysis for cluster randomized trials with binary outcome data we explore the potential of bayesian hierarchical modelling for the analysis of cluster randomized trials with binary outcome data and apply the methods to a trial randomized by general practice an approximate relationship is derived between the intracluster correlation coefficient icc and the between cluster variance used in a hierarchical logistic regression model by constructing an informative prior for the icc on the basis of available information we are thus able implicitly to specify an informative prior for the between cluster variance the approach also provides us with a credible interval for the icc for binary outcome data several approaches to constructing informative priors from empirical icc values are described we investigate the sensitivity of results to the prior specified and find that the estimate of intervention effect changes very little in this data set while its interval estimate is more sensitive the bayesian approach allows us to assume distributions other than normality for the random effects used to model the clustering this enables us to gain insight into the robustness of our parameter estimates to the classical normality assumption in a model with a more complex variance structure bayesian methods can provide credible intervals for a difference between two variance components in order for example to investigate whether the effect of intervention varies across clusters we compare our results with those obtained from classical estimation discuss the relative merits of the bayesian framework and conclude that the flexibility of the bayesian approach offers some substantial advantages although selection of prior distributions is not straightforward

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

rejoinder to a note on type ii error under random effects misspecification in generalized linear mixed models summary in this rejoinder we discuss the impact of misspecifying the random effects distribution on inferences obtained from generalized linear mixed models glmms special attention is paid to the power of the tests for the fixed effect parameters to study this misspecification researchers often use simulation designs in which several choices for the true underlying random effects distribution are considered while the assumed distribution is kept fixed neuhaus mcculloch and boylan 2010 biometrics 00 000 000 argue that a logically correct approach should consist of varying the assumed fitted distribution while holding the true fixed we argue that both simulation designs can bring valuable insights into the impact of the misspecification furthermore using both designs we illustrate that the power associated with the tests for the fixed effect parameters in glmm may be affected by misspecifying the random effects distribution

convergence to steady states in asymptotically autonomous semilinear evolution equations abstract we study the convergence to equilibrium of bounded solutions of the nonautonomous first order problem u m u g t t r and of the second order problem u u m u g t t r applications to diffusion wave cahn hilliard and kirchhoff carrier equations are described

realization of arbitrary vector fields on center manifolds of parabolic dirichlet bvps abstract consider the following parabolic equation u t lu x u u t 0 x u x t 0 t 0 x here r n is a smooth bounded domain l is a second order self adjoint uniformly elliptic differential operator and r r n r is some nonlinearity which explicitly depends on the gradient of the solution using the nash moser implicit function theorem we prove in this paper that if l and satisfy the so called polacik condition and x 1 denotes the kernel of l with dirichlet boundary conditions in this case the dimension of x 1 is necessarily n or n 1 then for every sufficiently smooth and small vector field defined in a neighborhood of zero in x 1 there exists a nonlinearity and a local center manifold m of p such that is exactly the reduced vector field of p on m this result implies in particular that arbitrary chaotic behavior of solutions of odes is also observable in suitable scalar parabolic equations with dirichlet boundary conditions and gradient dependent nonlinearities

a diagnostic test for the mixing distribution in a generalised linear mixed model summary we introduce a diagnostic test for the mixing distribution in a generalised linear mixed model the test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimators of a subset of the fixed effects in the model we derive the asymptotic variance of this difference and propose a test statistic that has a limiting chi squared distribution under the null hypothesis that the mixing distribution is correctly specified this strategy uses an idea presented by hausman 1978 who considered analogous tests for the linear mixed model an important advantage of the methods outlined here is that the resulting diagnostic test is easily implemented in commercial software we illustrate the method by applying it to data from a clinical trial investigating the effect of hormonal contraceptives in women

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

estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes generalized linear mixed models with random intercepts and slopes provide useful analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects previous work for models with only random intercepts has shown that misspecifying the shape of this distribution may bias estimates of the intercept but typically leads to little bias in estimates of covariate effects very few papers have examined the effects of misspecifying the joint distribution of random intercepts and slopes however simulation results in a recent paper suggest that misspecifying the shape of the random slope distribution can yield severely biased estimates of all model parameters using analytic results simulation studies and fits to example data this paper examines the bias in parameter estimates due to misspecification of the shape of the joint distribution of random intercepts and slopes consistent with results for models with only random intercepts and contrary to the claims of severe bias in a recent paper we show that misspecification of the joint distribution typically yields little bias in estimates of covariate effects and is restricted to covariates associated with the misspecified random effects distributions we also show that misspecification of the distribution of random effects has little effect on confidence interval performance coverage rates based on the model based standard errors from fitted likelihoods were generally quite close to nominal

misspecified maximum likelihood estimates and generalised linear mixed models summary we investigate the impact of model violations on the estimate of a regression coefficient in a generalised linear mixed model specifically we evaluate the asymptotic relative bias that results from incorrect assumptions regarding the random effects we compare the impact of model violation for two parameterisations of the regression model substantial bias in the conditionally specified regression point estimators can result from using a simple random intercepts model when either the random effects distribution depends on measured covariates or there are autoregressive random effects a marginally specified regression structure that is estimated using maximum likelihood is much less susceptible to bias resulting from random effects model misspecification

the impact of a misspecified random effects distribution on the estimation and the performance of inferential procedures in generalized linear mixed models estimation in generalized linear mixed models glmms is often based on maximum likelihood theory assuming that the underlying probability model is correctly specified however the validity of this assumption is sometimes difficult to verify in this paper we study through simulations the impact of misspecifying the random effects distribution on the estimation and hypothesis testing in glmms it is shown that the maximum likelihood estimators are inconsistent in the presence of misspecification the bias induced in the mean structure parameters is generally small as far as the variability of the underlying random effects distribution is small as well however the estimates of this variability are always severely biased given that the variance components are the only tool to study the variability of the true distribution it is difficult to assess whether problems in the estimation of the mean structure occur the type i error rate and the power of the commonly used inferential procedures are also severely affected the situation is aggravated if more than one random effect is included in the model further we propose to deal with possible misspecification by way of sensitivity analysis considering several random effects distributions all the results are illustrated using data from a clinical trial in schizophrenia

on robustness of marginal regression coefficient estimates and hazard functions in multivariate survival analysis of family data when the frailty distribution is mis specified the shared frailty model is an extension of the cox model to correlated failure times and essentially a random effects model for failure time outcomes in this model the latent frailty shared by individual members in a cluster acts multiplicatively as a factor on the hazard function and is typically modelled parametrically one commonly used distribution is gamma where both shape and scale parameters are set to be the same to allow for unique identification of baseline hazard function it is popular because it is a conjugate prior and the posterior distribution possesses the same form as gamma in addition the parameter can be interpreted as a time independent cross ratio function a natural extension of odds ratio to failure time outcomes in this paper we study the effect of frailty distribution mis specification on the marginal regression estimates and hazard functions under assumed gamma distribution with an application to family studies the simulation results show that the biases are generally 10 and lower even when the true frailty distribution deviates substantially from the assumed gamma distribution this suggests that the gamma frailty model can be a practical choice in real data analyses if the regression parameters and marginal hazard function are of primary interest and individual cluster members are exchangeable with respect to their dependencies

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

the algorithmic theory of polycyclic by finite groups a group is said to be polycyclic by finite or a pf group for short if it has a polycyclic normal subgroup of finite index equivalently pf groups are exactly the groups which have a series of finite length whose infinite factors are cyclic by a well known theorem of p hall every pf group is finitely presented and in fact pf groups form the largest known sectionclosed class of finitely presented groups it is this fact that makes pf groups natural objects of study from the algorithmic standpoint the general aim of the algorithmic theory of pf groups can be described as the collection of information about a pf group which can in principle

complicated dynamics of parabolic equations with simple gradient dependence let q c jr2 be a smooth bounded domain given positive integers n k and ql 0 x y y u 01 1 1 t o x s c 9q where a x y and al x y are smooth functions by refining and extending previous results of polaik we show that arbitrary k jets of vector fields in rn can be realized in equations of the form e in particular taking ql 1 we see that very complicated chaotic behavior is possible for reaction diffusionconvection equations with linear dependence on vu introduction let q c r2 be a smooth bounded domain we consider the semilinear parabolic equation ut uxx uyy 4a x y u f x y u uy t o x y e q u 0 t 0 x y e where a 1r2 r is continuous and f r4 r x y s w f x y s w is a smooth function more precisely f is continuous together with all its partial derivatives with respect to s w set x lp q p 2 and let a w2p q nwo p q x be the linear operator defined as au uxx uyy a x y u being a sectorial operator a generates the family x a 0 of fractional power spaces choosing a with 2 p a 1 we have that x c c01 q with continuous p inclusion define the nemitski operator f x x by f u x y f x y 2 x y uy x y received by the editors may 16 1996 1991 mathematics subject classification primary 35k20 secondary 35b40

a correlated probit model for joint modeling of clustered binary and continuous responses a difficulty in joint modeling of continuous and discrete response variables is the lack of a natural multivariate distribution for joint modeling of clustered observations on binary and continuous responses we study a correlated probit model that has an underlying normal latent variable for the binary responses catalano and ryan have factored the model into a marginal and a conditional component and used generalized estimating equations methodology to estimate the effects we propose a monte carlo expectation conditional maximization algorithm for finding maximum likelihood estimates of the mixed model itself extending and accelerating an algorithm for models with binary responses we demonstrate the methodology with a developmental toxicity study measuring fetal weight and a binary malformation status for several litters of mice a simulation study suggests that efficiency gains of joint fittings over separate fittings of the response variables occur mainly for small datasets with strong correlation

diagnosis of random effect model misspecification in generalized linear mixed models for binary response summary generalized linear mixed models glmms are widely used in the analysis of clustered data however the validity of likelihood based inference in such analyses can be greatly affected by the assumed model for the random effects we propose a diagnostic method for random effect model misspecification in glmms for clustered binary response we provide a theoretical justification of the proposed method and investigate its finite sample performance via simulation the proposed method is applied to data from a longitudinal respiratory infection study

diagnosing misspecification of the random effects distribution in mixed models it is traditionally assumed that the random effects in mixed models follow a multivariate normal distribution making likelihood based inferences more feasible theoretically and computationally however this assumption does not necessarily hold in practice which may lead to biased and unreliable results we introduce a novel diagnostic test based on the so called gradient function proposed by verbeke and molenberghs 2013 to assess the random effects distribution we establish asymptotic properties of our test and show that under a correctly specified model the proposed test statistic converges to a weighted sum of independent chi squared random variables each with one degree of freedom the weights which are eigenvalues of a square matrix can be easily calculated we also develop a parametric bootstrap algorithm for small samples our strategy can be used to check the adequacy of any distribution for random effects in a wide class of mixed models including linear mixed models generalized linear mixed models and non linear mixed models with univariate as well as multivariate random effects both asymptotic and bootstrap proposals are evaluated via simulations and a real data analysis of a randomized multicenter study on toenail dermatophyte onychomycosis

detecting free splittings in relatively hyperbolic groups we describe an algorithm which determines whether or not a group which is hyperbolic relative to abelian groups admits a nontrivial splitting over a finite group

peripheral splittings of groups we define the notion of a peripheral splitting of a group this is essentially a representation of the group as the fundamental group of a bipartite graph of groups where all the vertex groups of one colour are held fixed the peripheral subgroups we develop the theory of such splittings and prove an accessibility result the theory mainly applies to relatively hyperbolic groups with connected boundary where the peripheral subgroups are precisely the maximal parabolic subgroups we show that if such a group admits a non trivial peripheral splitting then its boundary has a global cut point moreover the non peripheral vertex groups of such a splitting are themselves relatively hyperbolic these results together with results from elsewhere show that under modest constraints on the peripheral subgroups the boundary of a relatively hyperbolic group is locally connected if it is connected in retrospect one further deduces that the set of global cut points in such a boundary has a simplicial treelike structure

acylindrical accessibility for groups we define the notion of acylindrical graph of groups of a group we bound the combinatorics of these graphs of groups for f g freely indecomposable groups our arguments imply the finiteness of acylindrical surfaces in closed 3 manifolds ha finiteness of isomorphism classes of small splittings of torsion free freely indecomposable hyperbolic groups as well as finiteness results for small splittings of f g kleinian and semisimple discrete groups acting on non positively curved simply connected manifolds in order to get our accessibility for f g groups we generalize parts of rips analysis of stable actions of f p groups on real trees to f g groups the concepts we present play an essential role in constructing the canonical jsj decomposition se1 ri se2 in obtaining the hopf property for hyperbolic groups se2 and in our study of sets of solutions to equations in a free group se3

nonconvergent bounded solutions of semilinear heat equations on arbitrary domains abstract we consider the dirichlet problem for the semilinear heat equation 0 1 u t u g x u x where is an arbitrary bounded domain in r n n 2 with c 2 boundary we find a c function g x u such that 0 1 has a bounded solution whose limit set is a continuum of equilibria this extends and improves an earlier result of the first author with rybakowski in which is a disk in r 2 and g is of finite differentiability class we also show that 0 1 can have an infinite dimensional manifold of nonconvergent bounded trajectories

convergence asymptotic periodicity and finite point blow up in one dimensional semilinear heat equations abstract we consider the initial value problem for the semilinear heat equation u t u xx f u t 0 x l t 0 under the dirichlet the neumann or the periodic boundary conditions we show that each solution whether it exists globally for t 0 or blows up in a finite time possesses an asymptotic profile in a certain sense and tends to this profile as time increases in the special case where f u t t f u t for some t 0 among other things the above statement is interpreted as saying that any bounded global solution converges as t to a time t periodic solution having some specific spatial structure in the case where the solution blows up in a finite time say at t t 0 assuming simply that f is a smooth function satisfying some growth conditions and that the initial data is a nonconstant bounded function we prove that the blow up set is a finite set and that lim t t 0 u x t x exists with being a smooth function having at most finitely many singular points

conditional inference functions for mixed effects models with unspecified random effects distribution in longitudinal studies mixed effects models are important for addressing subject specific effects however most existing approaches assume a normal distribution for the random effects and this could affect the bias and efficiency of the fixed effects estimator even in cases where the estimation of the fixed effects is robust with a misspecified distribution of the random effects the estimation of the random effects could be invalid we propose a new approach to estimate fixed and random effects using conditional quadratic inference functions qifs the new approach does not require the specification of likelihood functions or a normality assumption for random effects it can also accommodate serial correlation between observations within the same cluster in addition to mixed effects modeling other advantages include not requiring the estimation of the unknown variance components associated with the random effects or the nuisance parameters associated with the working correlations we establish a

deciding isomorphy using dehn fillings the splitting case we solve dehn s isomorphism problem for virtually torsion free relatively hyperbolic groups with nilpotent parabolic subgroups we do so by reducing the isomorphism problem to three algorithmic problems in the parabolic subgroups namely the isomorphism problem separation of torsion in their outer automorphism groups by congruences and the mixed whitehead problem an automorphism group orbit problem the first step of the reduction is to compute canonical jsj decompositions dehn fillings and the given solutions of the algorithmic problems in the parabolic groups are then used to decide if the graphs of groups have isomorphic vertex groups and if so whether a global isomorphism can be assembled for the class of finitely generated nilpotent groups we give solutions to these algorithmic problems by using the arithmetic nature of these groups and of their automorphism groups

type i and type ii error under random effects misspecification in generalized linear mixed models generalized linear mixed models glmms have become a frequently used tool for the analysis of non gaussian longitudinal data estimation is based on maximum likelihood theory which assumes that the underlying probability model is correctly specified recent research is showing that the results obtained from these models are not always robust against departures from the assumptions on which these models are based in the present work we have used simulations with a logistic random intercept model to study the impact of misspecifying the random effects distribution on the type i and ii errors of the tests for the mean structure in glmms we found that the misspecification can either increase or decrease the power of the tests depending on the shape of the underlying random effects distribution and it can considerably inflate the type i error rate additionally we have found a theoretical result which states that whenever a subset of fixed effects parameters not included in the random effects structure equals zero the corresponding maximum likelihood estimator will consistently estimate zero this implies that under certain conditions a significant effect could be considered as a reliable result even if the random effects distribution is misspecified

convergence to equilibrium for the cahn hilliard equation with dynamic boundary conditions this paper is concerned with the asymptotic behavior of solution to the cahn hilliard equation 0 1 u t u u u3 x t r subject to the following dynamic boundary conditions 0 2 s u u hs gsu 1 sut t 0 x 0 t 0 x and the initial condition 0 3 u t 0 u0 x x where is a bounded domain in rn n 3 with smooth boundary and s 0 s 0 gs 0 hs are given constants is the tangential laplacian operator and is the outward normal direction to the boundary this problem has been considered in the recent paper by racke and zheng adv differential equations 8 1 2003 83 where the global existence and uniqueness were proved in a very recent manuscript by pruss racke and zheng konstanzer schrift math inform 189 2003 the results on existence of global attractor and maximal regularity of solution have been obtained in this paper convergence of solution of this problem to an equilibrium as time goes to infinity is proved

flexible parametric models for random effects distributions it is commonly assumed that random effects in hierarchical models follow a normal distribution this can be extremely restrictive in practice we explore the use of more flexible alternatives for this assumption namely the t distribution and skew extensions to the normal and t distributions implemented using markov chain monte carlo methods models are compared in terms of parameter estimates deviance information criteria and predictive distributions these methods are applied to examples in meta analysis and health professional variation where the distribution of the random effects is of direct interest the results highlight the importance of allowing for potential skewing and heavy tails in random effects distributions especially when estimating a predictive distribution we describe the extension of these random effects models to the bivariate case with application to a meta analysis examining the relationship between treatment effect and baseline response we conclude that inferences regarding the random effects can crucially depend on the assumptions made and recommend using a distribution such as those suggested here which is more flexible than the normal

discovering subpopulation structure with latent class mixed models the linear mixed model is a well known method for incorporating heterogeneity for example subject to subject variation into a statistical analysis for continuous responses however heterogeneity cannot always be fully captured by the usual assumptions of normally distributed random effects latent class mixed models offer a way of incorporating additional heterogeneity which can be used to uncover distinct subpopulations to incorporate correlated non normally distributed outcomes and to classify individuals the methodology is motivated with examples in health care studies and a detailed illustration is drawn from the nutritional prevention of cancer trials latent class models are used with longitudinal data on prostate specific antigen psa as well as incidence of prostate cancer the models are extended to accommodate prostate cancer as a survival endpoint this is compared to treating it as a binary endpoint four subpopulations are identified which differ both with regard to their psa trajectories and their incidence rates of prostate cancer

ignoring overdispersion in hierarchical loglinear models possible problems and solutions poisson data frequently exhibit overdispersion and for univariate models many options exist to circumvent this problem nonetheless in complex scenarios for example in longitudinal studies accounting for overdispersion is a more challenging task recently molenberghs et al presented a model that accounts for overdispersion by combining two sets of random effects however introducing a new set of random effects implies additional distributional assumptions for intrinsically unobservable variables which has not been considered before using the combined model as a framework we explored the impact of ignoring overdispersion in complex longitudinal settings via simulations furthermore we evaluated the effect of misspecifying the random effects distribution on both the combined model and the classical poisson hierarchical model our results indicate that even though inferences may be affected by ignored overdispersion the combined model is a promising tool in this scenario copyright 2012 john wiley sons ltd

asymptotic behavior of a nonisothermal viscous cahn hilliard equation with inertial term we consider a differential model describing nonisothermal fast phase separation processes taking place in a three dimensional bounded domain this model consists of a viscous cahn hilliard equation characterized by the presence of an inertial term tt being the order parameter which is linearly coupled with an evolution equation for the relative temperature the latter can be of hyperbolic type if the cattaneo maxwell heat conduction law is assumed the state variables and the chemical potential are subject to the homogeneous neumann boundary conditions we first provide conditions which ensure the well posedness of the initial and boundary value problem then we prove that the corresponding dynamical system is dissipative and possesses a global attractor moreover assuming that the nonlinear potential is real analytic we establish that each trajectory converges to a single steady state by using a suitable version of the eojasiewicz simon inequality we also obtain an estimate of the decay rate to equilibrium

random effects modeling of multiple binomial responses using the multivariate binomial logit normal distribution summary the multivariate binomial logit normal distribution is a mixture distribution for which i conditional on a set of success probabilities and sample size indices a vector of counts is independent binomial variates and ii the vector of logits of the parameters has a multivariate normal distribution we use this distribution to model multivariate binomial type responses using a vector of random effects the vector of logits of parameters has a mean that is a linear function of explanatory variables and has an unspecified or partly specified covariance matrix the model generalizes and provides greater flexibility than the univariate model that uses a normal random effect to account for positive correlations in clustered data the multivariate model is useful when different elements of the response vector refer to different characteristics each of which may naturally have its own random effect it is also useful for repeated binary measurement of a single response when there is a nonexchangeable association structure such as one often expects with longitudinal data or when negative association exists for at least one pair of responses we apply the model to an influenza study with repeated responses in which some pairs are negatively associated and to a developmental toxicity study with continuation ratio logits applied to an ordinal response with clustered observations

prediction of random effects in linear and generalized linear models under model misspecification statistical models that include random effects are commonly used to analyze longitudinal and correlated data often with the assumption that the random effects follow a gaussian distribution via theoretical and numerical calculations and simulation we investigate the impact of misspecification of this distribution on both how well the predicted values recover the true underlying distribution and the accuracy of prediction of the realized values of the random effects we show that although the predicted values can vary with the assumed distribution the prediction accuracy as measured by mean square error is little affected for mild to moderate violations of the assumptions thus standard approaches readily available in statistical software will often suffice the results are illustrated using data from the heart and estrogen progestin replacement study using models to predict future blood pressure values

on systems of equations over free products of groups using an analogue of the makanin razborov diagrams we give a description of the solution set of systems of equations over an equationally noetherian free product of groups g equivalently we give a parametrisation of the set hom h g of all homomorphisms from a finitely generated group h to g furthermore we show that every algebraic set over g can be decomposed as a union of finitely many images of algebraic sets of ntq systems if the universal horn theory of g the theory of quasi identities is decidable then our constructions are effective 2010 elsevier inc

structure of the set of steady state solutions and asymptotic behaviour of semilinear heat equations soit un domaine borne lisse connexe de r n on considere a la fois le probleme aux valeurs initiales u t u f u dans 0 u x t 0 sur 0 u x o u 0 x dans et le probleme stationnaire u g u dans u 0 sur ou u 0 est une condition initiale donnee et f une non linearite donnee de classe c 1

existence multiplicity shape and attractivity of heterogeneous steady states for bistable reaction diffusion equations in the plane abstract we consider a class of bistable reaction diffusion equations in the plane first we introduce a partition of the plane into infinitely many sectors and consider dirichlet problems in these sectors by establish some a priori estimates for nontrivial solutions to these sub systems we obtain the existence and attractivity of a heterogeneous steady state of the dirichlet problem in each of the sectors and prove the existence of a maximum positive steady state and describe the asymptotic behaviours of positive steady states at the infinities we also estimate limit sets at the vicinities of the boundaries of the sectors near origin and at infinities further assuming the sub linearity for the reaction term we obtain the uniqueness and attractivity of a heterogeneous steady state by applying the dynamical and sliding methods these results help us describe the multiplicity shape and attractivity of the heterogeneous steady states for the equation

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

nonignorable models for intermittently missing categorical longitudinal responses a class of nonignorable models is presented for handling nonmonotone missingness in categorical longitudinal responses this class of models includes the traditional selection models and shared parameter models this allows us to perform a broader than usual sensitivity analysis in particular instead of considering variations to a chosen nonignorable model we study sensitivity between different missing data frameworks an appealing feature of the developed class is that parameters with a marginal interpretation are obtained while algebraically simple models are considered specifically marginalized mixed effects models heagerty 1999 biometrics 55 688 698 are used for the longitudinal process that model separately the marginal mean and the correlation structure for the correlation structure random effects are introduced and their distribution is modeled either parametrically or non parametrically to avoid potential misspecifications

a simple unified approach to some convergence theorems of l simon abstract we give a new and easier proof for the convergences result of l simon 15 concerning global and bounded solutions of a heat equation with analytic nonlinearity by constructing a new liapunov functional for the elliptic equation we are able to prove the second convergence theorem of 15 in the same way as the first theorem the results are more general and can be applied to other problems such as fourth order equation and vector valued systems of gradient type

a model for repeated measurements of a multivariate binary response abstract this article presents a logit model for a vector of binary variables observed for each subject under multiple conditions the model contains a vector of random effects to account for correlations among the repeated measurements a nonparametric treatment of the random effects implies a multivariate log linear model having quasi symmetric structure for the cross classification of responses at the various conditions the fit yields estimates of within subject effects comparing the conditions for each variable the estimates are identical to conditional maximum likelihood estimates for a fixed effects version of the logit model extensions incorporate independent groups or allow variables to have multiple response categories

convergence and decay rate to equilibrium of bounded solutions of quasilinear parabolic equations abstract we study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation u t div a x u f x u 0 on a bounded domain subject to dirichlet boundary and to initial conditions the data are supposed to satisfy suitable regularity and growth conditions our approach to the convergence result and decay estimate is based on the ojasiewicz simon gradient inequality which in the case of the semilinear heat equation is known to give optimal decay estimates the abstract results and their applications are discussed also in the framework of orlicz sobolev spaces

invariant manifolds for flows in banach spaces on presente une theorie des varietes invariantes lisses basee sur la methode classique de lyapunov penon pour des semi flots continus dans des espaces de banach

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

the nielsen method for groups acting on trees we use nielsen methods to study generating sets of subgroups of groups that act on simplicial trees and give several applications in particular we exhibit an explicit bound for the complexity of acylindrical splittings of a finitely generated group in terms of its rank this is applied to jsj splittings of word hyperbolic groups and 3 manifolds as a last application we construct examples of amalgamated products that show that there exists no non trivial rank formula for amalgamated products 2000 mathematical subject classification 20e06 20e08 57m27