statistical models for autocorrelated count data a generalized linear mixed model is an increasingly popular choice for the modelling of correlated non normal responses in a regression setting a number of methods are currently available for fitting a generalized linear mixed model including monte carlo markov chain maximum likelihood algorithms approximate maximum likelihood pql iterative bias correction and others of interest in this paper is to compare the parameter estimation of the various methods in the modelling of a count data set the incidence of polio in the usa over the period 1970 1983 using a longlinear generalized linear mixed model with an autoregressive correlation structure despite the fact that all of these methods are considered valid modelling techniques we find that parameter estimates and standard errors differ substantially between analyses particularly in the estimation of the parameters describing the random effects distribution a small simulation study is helpful in understanding some of these differences the methods lead to reasonably similar predictions for future observations with small differences observed in some monthly counts

boundary circles for area preserving maps abstract we report on numerical observations of various properties of boundary circles for area preserving maps we find that the continued fraction expansion of their rotation number generally has a special form we describe how their rotation number changes as parameters are varied we observe a statistically self similar structure in the neighbourhood of boundary circles which is probably relevant to the long time tails of the decay of correlations in the irregular components

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

an approximate generalized linear model with random effects for informative missing data this paper develops a class of models to deal with missing data from longitudinal studies we assume that separate models for the primary response and missingness e g number of missed visits are linked by a common random parameter such models have been developed in the econometrics heckman 1979 econometrica 47 153 161 and biostatistics wu and carroll 1988 biometrics 44 175 188 literature for a gaussian primary response we allow the primary response conditional on the random parameter to follow a generalized linear model and approximate the generalized linear model by conditioning on the data that describes missingness the resultant approximation is a mixed generalized linear model with possibly heterogeneous random effects an example is given to illustrate the approximate approach and simulations are performed to critique the adequacy of the approximation for repeated binary data

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

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

generalized estimating equation model for binary outcomes with missing covariates summary this paper presents an approach to handling missing covariates in the generalized estimating equation gee model for binary outcomes when the probability of missingness depends on the observed outcomes and covariates the proposed method is to replace the missing quantities in the estimating function with consistent estimates in special cases the proposed model reduces to a weighted gee model for the completely observed units where the weight is the inverse of the probability of missingness our method can be viewed as an extension of the mean score method by reilly and pepe 1995 biometrika 82 299 314 to the gee context under certain regularity conditions the estimates of the regression coefficients obtained by the proposed method are consistent and asymptotically normally distributed the finite sample properties of the estimates are illustrated via computer simulations an application to the study of dementia among stroke patients is presented

the discrete frenkel kontorova model and its extensions i exact results for the ground states abstract we present a rigorous study of the classical ground states under boundary conditions of a class of one dimensional models generalizing the discrete frenkel kontorova model the extremalization equations of the energy of these models turn out to define area preserving twist maps which exhibits periodic quasi periodic and chaotic orbits for all boundary conditions we select among all the extremum solutions of the energy of the model those which correspond to the ground states of the infinite system we prove that these ground states are either periodic commensurate or quasi periodic incommensurate but are never chaotic we also prove the existence of elementary discommensurations which are minimum energy configuration of the model for certain special boundary conditions the topological structure of the whole set of ground states is described in details in addition to physical applications consequences for twist map homeomorphisms are mentioned part ii s aubry p y ledaeron and g andre will be mostly devoted to exact results on the transition by breaking of analyticity which occurs on the incommensurate ground states when the model parameters vary and on its connection with the stochasticity threshold in the corresponding twist map

a note on fitting a marginal model to mixed effects log linear regression data via gee marginal generalized linear models for correlated data are often fit by generalized estimating equations liang k y and zeger s l 1986 biometrika 73 13 22 which requires the marginal expectation to be correctly specified while the covariance structure is allowed to be misspecified this note is concerned with the correct specification of the marginal mean for data from a mixed log linear regression model and the relationship between the true subject specific parameters and the true marginal parameters

a bayesian population model with hierarchical mixture priors applied to blood count data abstract population pharmacokinetic and pharmacodynamic studies require analyzing nonlinear growth curves fit to multiple measurements from study subjects we propose a class of nonlinear population models with nonparametric second stage priors for analyzing such data the proposed models apply a flexible class of mixtures to implement the nonparametric second stage the discussion is based on a pharmacodynamic study involving longitudinal data consisting of hematologic profiles i e blood counts measured over time of cancer patients undergoing chemotherapy we describe a full posterior analysis in a bayesian framework this includes prediction of future observations profiles and end points for new patients estimation of the mean response function for observed individuals and inference on population characteristics the mixture model is specified and given a hyperprior distribution by means of a dirichlet processes prior on the mixing measure estimation is implemented by a combination of various m

robust estimation in generalized linear mixed models generalized linear mixed models glmms are widely used to analyse non normal response data with extra variation but non robust estimators are still routinely used we propose robust methods for maximum quasi likelihood and residual maximum quasi likelihood estimation to limit the influence of outlying observations in glmms the estimation procedure parallels the development of robust estimation methods in linear mixed models but with adjustments in the dependent variable and the variance component the methods proposed are applied to three data sets and a comparison is made with the nonparametric maximum likelihood approach when applied to a set of epileptic seizure data the methods proposed have the desired effect of limiting the influence of outlying observations on the parameter estimates simulation shows that one of the residual maximum quasi likelihood proposals has a smaller bias than those of the other estimation methods we further discuss the equivalence of two glmm formulations when the response variable follows an exponential family their extensions to robust glmms and their comparative advantages in modelling are described some possible modifications of the robust glmm estimation methods are given to provide further flexibility for applying the method

bayesian covariance selection in generalized linear mixed models repeated measures and longitudinal data are commonly collected for analysis in epidemiology clinical trials biology sociology and economic sciences in such studies a response is measured repeatedly over time for each subject under study and the number and timing of the observations often varies among subjects in contrast to cross sectional studies that collect a single measurement per subject longitudinal studies have the extra complication of within subject dependence in the repeated measures such dependence can be thought to arise due to the impact of unmeasured predictors main effects of unmeasured predictors lead to variation in the average level of response among subjects while interactions with measured predictors lead to heterogeneity in the regression coefficients this justification has motivated random effects models which allow the intercept and slopes in a regression model to be subject specific random effects models are broadly useful for modeling of dependence not only for longitudinal data but also in multicenter studies meta analysis and functional data analysis

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

estimation in generalized linear models with random effects summary a conceptually very simple but general algorithm for the estimation of the fixed effects random effects and components of dispersion in generalized linear models with random effects is proposed conditions are described under which the algorithm yields approximate maximum likelihood or quasi maximum likelihood estimates of the fixed effects and dispersion components and approximate empirical bayes estimates of the random effects the algorithm is applied to two data sets to illustrate the estimation of components of dispersion and the modelling of overdispersion

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

nonparametric and semiparametric models for missing covariates in parametric regression robustness of covariate modeling for the missing covariate problem in parametric regression is studied under the missing at random assumption for a simple missing covariate pattern nonparametric covariate model is proposed and is shown to yield a consistent and semiparametrically efficient estimator for the regression parameter total robustness is achieved in this situation for more general missingcovariate patterns a novel semiparametric modeling approach is proposed for the covariates in this approach the covariate distribution is first decomposed into the product of a series of conditional distributions according to the overall missing data patterns and the conditional distributions are then represented in the general odds ratio form the general odds ratios are modeled parametrically and the other components of the covariate distribution are modeled nonparametrically maximum semiparametric likelihood is used to find the parameter estimates the proposed method yields a consistent estimator f

efficiency of estimating equations and the use of pivots summary methods are proposed for deriving unbiased estimating equations for the parameters of interest in a statistical model which includes further incidental or nuisance parameters we start with pivot like quantities which eliminate the dependence on the incidental parameters and derive functions of these which give estimating equations which are most efficient in a certain sense these equations involve the incidental parameters which are then replaced by estimators the methods overcome some of the difficulties encountered in likelihood and least squares estimation when there are many incidental parameters and our theory reduces to likelihood and least squares estimation when there are none thus the optimality results apply to these methods too some examples are discussed

a test of missing completely at random for generalised estimating equations with missing data we consider inference from generalised estimating equations when data are incomplete a test for missing completely at random is proposed to help decide whether or not we should adjust estimating equations to correct the possible bias introduced by a missing data mechanism that is not missing completely at random likelihood ratio tests have been introduced to test the missing completely at random hypothesis fuchs 1982 little 1988 for the estimating equation setting following the basic idea of little 1988 we propose a wald type test based on an information decomposition and recombination procedure which also provides an alternative method for estimating parameters one application of the test is to assess the adequacy of the marginal generalised estimating equation for longitudinal data with missing values simulations are done to evaluate its performance

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

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

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

stability of semilinear stochastic evolution equations stability of moments of the mild solution of a semilinear stochastic evolution equation is studied and sufficient conditions are given for the exponential stability of the pth moment in terms of liapunov function sufficient conditions for sample continuity of the solution are also obtained and the exponential stability of sample paths is proved three examples are given to illustrate the theory

adjusting for unmeasured confounding due to either of two crossed factors with a logistic regression model motivated by an investigation of the effect of surface water temperature on the presence of vibrio cholerae in water samples collected from different fixed surface water monitoring sites in haiti in different months we investigated methods to adjust for unmeasured confounding due to either of the two crossed factors site and month in the process we extended previous methods that adjust for unmeasured confounding due to one nesting factor such as site which nests the water samples from different months to the case of two crossed factors first we developed a conditional pseudolikelihood estimator that eliminates fixed effects for the levels of each of the crossed factors from the estimating equation using the theory of u statistics for independent but non identically distributed vectors we show that our estimator is consistent and asymptotically normal but that its variance depends on the nuisance parameters and thus cannot be easily estimated consequently we apply our estimator in conjunction with a permutation test and we investigate use of the pigeonhole bootstrap and the jackknife for constructing confidence intervals we also incorporate our estimator into a diagnostic test for a logistic mixed model with crossed random effects and no unmeasured confounding for comparison we investigate between within models extended to two crossed factors these generalized linear mixed models include covariate means for each level of each factor in order to adjust for the unmeasured confounding we conduct simulation studies and we apply the methods to the haitian data copyright 2016 john wiley sons ltd

model selection for multi component frailty models various frailty models have been developed and are now widely used for analysing multivariate survival data it is therefore important to develop an information criterion for model selection however in frailty models there are several alternative ways of forming a criterion and the particular criterion chosen may not be uniformly best in this paper we study an akaike information criterion aic on selecting a frailty structure from a set of possibly non nested frailty models we propose two new aic criteria based on a conditional likelihood and an extended restricted likelihood erl given by lee and nelder j r statist soc b 1996 58 619 678 we compare their performance using well known practical examples and demonstrate that the two criteria may yield rather different results a simulation study shows that the aic based on the erl is recommended when attention is focussed on selecting the frailty structure rather than the fixed effects

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

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

robust reml estimation for k component poisson mixture with random effects application to the epilepsy seizure count data and urinary tract infections data a robust version of residual maximum likelihood estimation for poisson log linear mixed model is developed and the method is extended to k component poisson mixture with random effects the method not only provides the robust estimators for the fixed effects and variance component parameters but also gives the robust prediction of random effects simulation results show that the proposed method is effective in limiting the impact of outliers under different data contamination schemes the method is adopted to analyze the epilepsy seizure count data and the urinary tract infections data which are deemed to contain several potential outliers the results show that the proposed method provides better goodness of fit to the data and demonstrate the effect of the robust tuning mechanism copyright 2012 john wiley sons ltd

approximate inference in generalized linear mixed models statistical approaches to overdispersion correlated errors shrinkage estimation and smoothing of regression relationships may be encompassed within the framework of the generalized linear mixed model glmm given an unobserved vector of random effects observations are assumed to be conditionally independent with means that depend on the linear predictor through a specified link function and conditional variances that are specified by a variance function known prior weights and a scale factor the random effects are assumed to be normally distributed with mean zero and dispersion matrix depending on unknown variance components for problems involving time series spatial aggregation and smoothing the dispersion may be specified in terms of a rank deficient inverse covariance matrix approximation of the marginal quasi likelihood using laplace s method leads eventually to estimating equations based on penalized quasilikelihood or pql for the mean parameters and pseudo likelihood for the variances im

sieve maximum likelihood estimation for regression models with covariates missing at random missing covariates are common in regression problems we propose a new semiparametric method based on a fully nonparametric distribution for the missing covariates that are assumed to be missing at random the method of sieve maximum likelihood estimation is used to obtain the estimators of the regression coefficients these estimators are shown to be consistent and asymptotically normal with their asymptotic covariance matrix that achieves the semiparametric efficiency bound a bootstrap approach is used to estimate the asymptotic covariance matrix some practical modeling approaches for high dimensional covariates are proposed extensive simulation studies are conducted to examine the finite sample properties of the estimates and a real data set from a liver cancer clinical trial is analyzed using the proposed method

minimum hellinger distance estimation for k component poisson mixture with random effects the k component poisson regression mixture with random effects is an effective model in describing the heterogeneity for clustered count data arising from several latent subpopulations however the residual maximum likelihood estimation reml of regression coefficients and variance component parameters tend to be unstable and may result in misleading inferences in the presence of outliers or extreme contamination in the literature the minimum hellinger distance mhd estimation has been investigated to obtain robust estimation for finite poisson mixtures this article aims to develop a robust mhd estimation approach for k component poisson mixtures with normally distributed random effects by applying the gaussian quadrature technique to approximate the integrals involved in the marginal distribution the marginal probability function of the k component poisson mixture with random effects can be approximated by the summation of a set of finite poisson mixtures simulation study shows that the mhd estimates perform satisfactorily for data without outlying observation s and outperform the reml estimates when data are contaminated application to a data set of recurrent urinary tract infections uti with random institution effects demonstrates the practical use of the robust mhd estimation method

consistent estimators in generalized linear mixed models abstract a simple method based on simulated moments is proposed for estimating the fixed effects and variance components in a generalized linear mixed model glmm it is shown that the method is not only computationally attractive but also leads to consistent estimators on the other hand simulation shows that the method can be quite inefficient

absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty this paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty the uncertainty in the system is assumed to have a stochastic character and to satisfy certain stochastic integral constraints it is shown that a minimax optimal guaranteed cost state feedback controller for a stochastic system can be synthesized as a state feedback controller absolutely stabilizing this system for each initial state of the system this controller can be found by parametric optimization of solutions of a parameter dependent generalized matrix riccati equation arising in stochastic h infty theory

data driven selection of the spline dimension in penalized spline regression a number of criteria exist to select the penalty in penalized spline regression but the selection of the number of spline basis functions has received much less attention in the literature we propose a likelihood based criterion to select the number of basis functions in penalized spline regression the criterion is easy to apply and we describe its theoretical and practical properties

robustness of feedback stabilized systems in the presence of non linear and random perturbations the general robustness problem is discussed for a controlled discrete time system subject to a lur e type feedback non linearity together with random multiplicative noises effective on state input and the non linearity a sufficient condition is given utilizing the discrete stochastic version of the second method of lyapunov to guarantee that any stabilizing controller designed for the deterministic linear part of the system renders the closed loop system with perturbations asymptotically stable with probability one then specializations to systems given in controllability and controller canonical forms are made independent noise signals are assumed to be effective on individual parameters of these canonical forms whose inputs are designed to assign the closed loop poles to zero in these cases stronger results are obtained in terms of system parameters and known characteristics of perturbations

absolute stability approach to stochastic stability of infinite dimensional nonlinear systems recent applications of absolute stability methods to robustness analysis have led to a rebirth of interest in this topic this paper is concerned with the robust stability of feedback distributed parameter systems against nonlinear and random disturbances our analysis is based on the lyapunov direct method to derive a stochastic lyapunov function we introduce the special stochastic infinite dimensional counterparts of the kalman yakubovich lemma they are proved by use of dynamic programming methods in combination with the properties of hilbert space valued wiener processes examples exhibit extensions of the popov and circle criteria to the feedback stochastic heat and delay equations respectively

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12

the analysis of binomial data by a generalized linear mixed model summary methods for generalized linear models are extended to provide estimates of location and variance parameters for mixed models fitted to binomial data formed by classifying samples from an underlying normal distribution the method estimates the parameters directly on the underlying scale for a balanced one way random effects model the variance estimator simplifies to the usual analysis of variance one the estimation of variances and the prediction of random effects for binomial traits is required by animal breeders the predictors given are analogous to best linear unbiased predictors henderson 1973 but differ from those presented by harville mee 1984

maximum likelihood estimation for probit linear mixed models with correlated random effects the probit normal model for binary data mcculloch 1994 journal of the american statistical association 89 330 335 is extended to allow correlated random effects to obtain maximum likelihood estimates we use the em algorithm with its m step greatly simplified under the assumption of a probit link and its e step made feasible by gibbs sampling standard errors are calculated by inverting a monte carlo approximation of the information matrix rather than via the sem algorithm a method is also suggested that accounts for the monte carlo variation explicitly as an illustration we present a new analysis of the famous salamander mating data unlike previous analyses we find it necessary to introduce different variance components for different species of animals finally we consider models with correlated errors as well as correlated random effects

reml estimation with exact covariance in the logistic mixed model residual maximum likelihood reml estimation is adapted to certain logistic mixed models for which representation of the unconditional mean as a linear function of the fixed effects is possible only the first two moments of the unconditional distribution need be evaluated and except for the form of the covariance the maximization algorithm carries over directly from linear models the exact unconditional covariance is computed from the logistic normal mixture for input into the algorithm residual log likelihood plots provide a means of inference for the dispersion components the taylor series approximation to this covariance besides exhibiting insufficient accuracy fails to be positive definite for large values of the dispersion components as a consequence reml loglikelihood plots based on this approximate covariance attribute misleadingly high precision to the dispersion component estimates the method is presented in the context of a salamander mating experiment in which random effects corresponding to male and female animals occur in a crossed design analyses of these data by several methods are compared

analysis of ulcer data using hierarchical generalized linear models in multi centre clinical trials heterogeneities in individual hospital treatment effects can be modelled as random effects estimates of the individual hospital treatment effects and estimate of the mean treatment effect allowing for the presence of overall hospital differences are required together with some measure of their uncertainty systematic inferences from the hierarchical likelihood are now possible using hierarchical generalized linear models we show how to construct profile likelihoods for the treatment effects of individual hospitals

robust estimation of variance components outliers may occur with respect to any of the random components in the mixed linear model a procedure for limiting the influence of these outliers on the estimates of the model parameters is described given the variances or estimates of them the model effects are estimated by augmenting the original observations with auxiliary observations that contain the prior information represented by the variances large residuals among either the original or the auxiliary observations are interpreted as outlying random errors or outlying random effects as appropriate and winsorized the robust estimation of the variances is obtained by modifying the defining equations for the restricted maximum likelihood estimates under normality along the lines of huber s proposal 2 a numerical example illustrates the use of the methodology both as a diagnostic and as an estimation tool

a generalized linear model with nested strata of extra poisson variation on etend la definition de quasivraisemblance pour tenir compte de plusieurs strates de variation emboitees dans un modele lineaire generalise

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

stochastic linear quadratic regulators with indefinite control weight costs ii in part i of this paper s chen x li and x zhou siam j control optim 36 1998 pp 1685 1702 an optimization model of stochastic linear quadratic regulators lqrs with indefinite control cost weighting matrices is proposed and studied in this sequel the problem of solving lqr models with system diffusions dependent on both state and control variables which is left open in part i is tackled first the solvability of the associated stochastic riccati equations sres is studied in the normal case namely all the state and control weighting matrices and the terminal matrix in the cost functional are nonnegative definite with at least one positive definite which in turn leads to an optimal state feedback control of the lqr problem in the general indefinite case the problem is decomposed into two optimal lqr problems one with a forward dynamics and the other with a backward dynamics the well posedness and solvability of the original lqr problem are then obtained by solving these two subproblems and an optimal control is explicitly constructed examples are presented to illustrate the results

quasi likelihood regression models with missing covariates summary this paper presents methods to handle missing covariates when the quasi likelihood equations for the complete data are available our suggestion is to replace the functions of the missing data appearing in the quasi likelihood equation with their conditional means given the observed data or with unbiased predictors so that the resulting equation is unbiased we focus on two models one is a random effects model for count data where random effects are treated as missing covariates the other is the overdispersed binomial regression model with partially missing covariates we also investigate the efficiency of the proposed estimates relative to the maximum likelihood estimators

variational time integrators the purpose of this paper is to review and further develop the subject of variational integration algorithms as it applies to mechanical systems of engineering interest in particular the conservation properties of both synchronous and asynchronous variational integrators avis are discussed in detail we present selected numerical examples which demonstrate the excellent accuracy conservation and convergence characteristics of avis in these tests avis are found to result in substantial speed ups at equal accuracy relative to explicit newmark a mathematical proof of convergence of the avis is also presented in this paper finally we develop the subject of horizontal variations and configurational forces in discrete dynamics this theory leads to exact path independent characterizations of the configurational forces acting on discrete systems notable examples are the configurational forces acting on material nodes in a finite element discretisation and the j integral at the tip of a crack in a finite element mesh

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

group sequential analysis incorporating covariate information abstract in this article we survey existing results concerning the joint distribution of the sequence of estimates of the parameter vector when a model is fitted to accumulating data and provide a unified theory that explains the independent increments structure commonly seen in group sequential test statistics our theory covers normal linear models including the case of correlated observations and asymptotic results extend to generalized linear models and the proportional hazards regression model for survival data the asymptotic results are derived using standard methods for the nonsequential case and they hold as long as these nonsequential techniques are applicable at each individual analysis in all cases the joint distribution of the sequence of parameter estimates has the same form exactly or asymptotically as that of the sequence of means of an increasing number of independent identically distributed normal variables thus our results provide the formal basis for extending the scope of s

calculation of cantori for hamiltonian flows cantori are the invariant sets remaining after the destruction of kam surfaces and create partial barriers to transport in chaotic regions cantori may be approximated by high order periodic orbits however field line tracing methods for locating periodic orbits perform poorly in chaotic regions to approximate cantori for continuous flow dynamics high order periodic orbits are determined by lagrangian variational methods the method is robust to chaos converges quadratically and the computational cost scales linearly with the periodicity length of the orbit minimizing periodic orbits with periodicities in the tens of thousands that closely approximate cantori have been constructed

estimation in forest yield models using composite link functions with random effects a sigmoidal forest yield model is estimated from longitudinal measurements of sample plots where measurement times and intervals vary the projection form of the yield model is fitted as a generalized linear model glm with composite link functions and an offset this allows age and additional covariates to be easily incorporated in a more flexible nonlinear structure than that provided by single link glms also existing algorithms for fitting generalized linear mixed models glmms are easily adapted to fit the projection model thereby allowing incorporation of random plot effects estimation for the composite link glmm is described as well as an alternative to the glmm in which random effects are incorporated as linear components on the same scale as the response this model is referred to as an additive generalized linear mixed model aglmm unlike the glmm the fixed effect parameter estimates in the aglmm are population average pa the aglmm is fitted using a modification of a subject specific ss algorithm using marginal expectation the random effects in the aglmm may have a natural interpretation or may provide a means of generating a marginal covariance structure as is the case with linear mixed models a simple example of an aglmm for binomial data and logit link is given in both this and the forest yield example a single artificial random effect is constructed to give exchangeable correlation for observations within subjects and a comparison of fit of the aglmm and glmm is made using a conditional quasi deviance if the fit is similar and pa parameter estimates are required the aglmm is preferred

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

a mean score method for missing and auxiliary covariate data in regression models summary we consider regression analysis when incomplete or auxiliary covariate data are available for all study subjects and in addition for a subset called the validation sample true covariate data of interest have been ascertained the term auxiliary data refers to data not in the regression model but thought to be informative about the true missing covariate data of interest we discuss a method which is nonparametric with respect to the association between available and missing data allows missingness to depend on available response and covariate values and is applicable to both cohort and case control study designs the method previously proposed by flanders greenland 1991 and by zhao lipsitz 1992 is generalised and asymptotic theory is derived our expression for the asymptotic variance of the estimator provides intuition regarding performance of the method optimal sampling strategies for the validation set are also suggested by the asymptotic results