score test for familial aggregation in probands studies application to alzheimer s disease when studying familial aggregation of a disease the following two stage design is often used first select index subjects cases and controls then record data on their relatives the likelihood corresponding to this design is derived and a score test of homogeneity is proposed for testing the hypothesis of no aggregation this test takes into account the selection procedure and allows adjustment to be made for explanatory variables it appears as the sum of three terms a pure test of homogeneity a test of comparison of observed minus expected cases in the two groups and a term which adjusts for the possible unequal probabilities of disease of the index subjects asymptotic efficiency and a simulation study show that the proposed test is superior to either the pure homogeneity test or tests based on the comparison of numbers of affected in the two groups the test statistic which has an asymptotically standard normal distribution is applied to a study of familial aggregation of early onset alzheimer s disease for which a highly significant value 9 46 is obtained this is the highest value among the three tests compared in agreement with the simulation study a logistic normal model is fitted to the data taking account of the selection procedure it allows to estimate the regression parameters and the variance of the random effect the likelihood ratio test for familial aggregation seems less powerful than the score test

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

adjusted score tests of homogeneity for poisson processes abstract tests of homogeneity are being increasingly used for the analysis of event time data but relatively little attention has been paid to their distributional properties in settings with small to moderate sample sizes here we consider tests of homogeneity for recurrent event data in which the null model is a poisson process and the alternative is a mixed poisson process we examine score and adjusted score statistics in the context of parametric and semiparametric regression models where the adjustments correct for the bias induced by substituting the maximum likelihood estimates of the parameters into the test statistic we report the results of simulation studies suggesting that the adjusted score statistics are superior in terms of size and power we also find that the adjusted score test in the semiparametric regression model does not perform particularly well in small samples but the adjusted score test based on a piecewise exponential model has satisfactory performance the latter thus prov

real royal road functions for constant population size evolutionary and genetic algorithms eas and gas are quite successful randomized function optimizers this success is mainly based on the interaction of different operators like selection mutation and crossover since this interaction is still not well understood one is interested in the analysis of the single operators jansen and wegener proceedings of gecco 2001 2001 pp 375 382 have described so called real royal road functions where simple steady state gas have a polynomial expected optimization time while the success probability of mutation based eas is exponentially small even after an exponential number of steps this success of the ga is based on the crossover operator and a population whose size is moderately increasing with the dimension of the search space here new real royal road functions are presented where crossover leads to a small optimization time although the ga works with the smallest possible population size namely 2

variance component testing in generalised linear models with random effects summary there is considerable interest in testing for overdispersion correlation and heterogeneity across groups in biomedical studies in this paper we cast the problem in the framework of generalised linear models with random effects we propose a global score test for the null hypothesis that all the variance components are zero this test is a locally asymptotically most stringent test and is robust in the special sense that the test does not require specifying the joint distribution of the random effects we also propose individual score tests and their approximations for testing the variance components separately both tests can be easily implemented using existing statistical software we illustrate these tests with an application to the study of heterogeneity of mating success across males and females in an experiment on salamander matings and evaluate their performance through simulation

on the insensitivity of the score test for heterogeneity to omitted covariates in multivariate failure time models the multivariate weibull distribution often provides a point of departure for modelling repeated or a sequence of failure times for a particular individual it is then natural to want to test the implied assumption of homogeneity and a number of authors have derived a score test for this purpose see for example kimber 1996 in the present paper it is shown that the proposed score test for neglected heterogeneity can be insensitive to specification error in the implied log linear regression structure

on the analysis of the 1 1 evolutionary algorithm many experimental results are reported on all types of evolutionary algorithms but only few results have been proved a step towards a theory on evolutionary algorithms in particular the so called 1 1 evolutionary algorithm is performed linear functions are proved to be optimized in expected time o nlnn but only mutation rates of size 1 n can ensure this behavior for some polynomial of degree 2 the optimization needs exponential time the same is proved for a unimodal function both results were not expected by several other authors finally a hierarchy result is proved moreover methods are presented to analyze the behavior of the 1 1 evolutionary algorithm

a disaggregate negative binomial regression procedure for count data analysis various research areas face the methodological problems presented by nonnegative integer count data drawn from heterogeneous populations we present a disaggregate negative binomial regression procedure for analysis of count data observed for a heterogeneous sample of cross sections possibly over some fixed time periods this procedure simultaneously pools or groups cross sections while estimating a separate negative binomial regression model for each group an e m algorithm is described within a maximum likelihood framework to estimate the group proportions the group specific regression coefficients and the degree of overdispersion in event rates within each derived group the proposed procedure is illustrated with count data entailing nonnegative integer counts of purchases events for a frequently bought consumer good

estimation of additive regression models with known links summary we consider estimation of an additive nonparametric regression model with known link function the asymptotic distribution of this regression estimate is given the practical performance is investigated via an application to the study of migration between east and west germany

comparing markov chains aggregation and precedence relations applied to sets of states with applications to assemble to order systems solving markov chains is in general difficult if the state space of the chain is very large or infinite and lacking a simple repeating structure one alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest we present a new bounding method for markov chains inspired by markov reward theory our method constructs bounds by redirecting selected sets of transitions facilitating an intuitive interpretation of the modifications of the original system we show that our method is compatible with strong aggregation of markov chains thus we can obtain bounds for an initial chain by analyzing a much smaller chain we illustrate our method by using it to prove monotonicity results and bounds for assemble to order systems

homogeneity tests against central mixture alternatives abstract a test of homogeneity is derived for a general sampling model the alternative hypothesis is a mixture over a parameter of the sampling model centered at the null hypothesis the test statistic is derived through a score test its functional form is independent of the particular mixing distribution suppose yi i 1 n are independent random variables with respective probability density or mass functions fi yi i under the null hypothesis suppose all i homogeneous and equal to the common value 0 under the alternative hypothesis suppose the i behave as random samples taken from a distribution with mean 0 and finite third moment the score statistic for testing these hypotheses rejects the null for large values of where is the maximum likelihood estimate of 0 under the null hypothesis and when the sample size n is large s is normally distributed under both the null hypothesis and a sequence of alternative hypotheses in which the variance of the mixing distribution tends

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

the effect of measurement error summary measurement error causes the distribution generating data to differ from the distribution that is of substantive interest to understand the effect of measurement error on the information produced by statistical procedures it is thus necessary to understand the distortions induced by measurement error this paper sheds light on this by providing small error variance approximations to the distribution of variates subject to contamination by measurement error these provide the basis for the analysis of the properties of estimators and tests and less formal procedures when measurement error is present and the basis for the development of tests to detect measurement error and of models which incorporate its influence

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

pseudo gaussian and rank based optimal tests for random individual effects in large n small t panels we consider the problem of detecting unobserved heterogeneity that is the problem of testing the absence of random individual effects in an n t panel we establish a local asymptotic normality property with respect to intercept regression coefficient the scale parameter of the error and the scale parameter u of individual effects which is the parameter of interest for given scaled density f 1 of the error terms when n tends to infinity and t is fixed this result allows via the hk representation theorem for developing asymptotically optimal rank based tests for the null hypothesis u 0 absence of individual effects these tests are locally asymptotically optimal at correctly specified innovation densities f 1 but remain valid irrespective of the actual underlying density the limiting distribution of our test statistics is obtained both under the null and under sequences of contiguous alternatives a local asymptotic linearity property is established in order to control for the effect of substituting estimators for nuisance parameters the asymptotic relative efficiencies of the proposed procedures with respect to the corresponding pseudo gaussian parametric tests are derived in particular the van der waerden version of our rank based tests uniformly dominates from the point of view of pitman efficiency the classical honda test small sample performances are investigated via a monte carlo study and confirm theoretical findings

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

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

a central limit theorem for generalized quadratic forms random variables of the form w n mathop sum limits 1 leqq i leqq n mathop sum limits text 1 leqq j leqq n w ijn x i x j are considered with x i independent not necessarily identically distributed and w ijn borel functions such that w ijn x i x j is square integrable and has vanishing conditional expectations e w ijn x i x j x i e w ijn x i x j x j 0 text a text s text a central limit theorem is proved under the condition that the normed fourth moment tends to 3 under some restrictions the condition is also necessary finally conditions on the individual tails of w ijn x i x j and an eigenvalue condition are given that ensure asymptotic normality of w n

generalized score test of homogeneity for mixed effects models many important problems in psychology and biomedical studies require testing for overdispersion correlation and heterogeneity in mixed effects and latent variable models and score tests are particularly useful for this purpose but the existing testing procedures depend on restrictive assumptions in this paper we propose a class of test statistics based on a general mixed effects model to test the homogeneity hypothesis that all of the variance components are zero under some mild conditions not only do we derive asymptotic distributions of the test statistics but also propose a resampling procedure for approximating their asymptotic distributions conditional on the observed data to overcome the technical challenge we establish an invariance principle for random quadratic forms indexed by a parameter a simulation study is conducted to investigate the empirical performance of the test statistics a real data set is analyzed to illustrate the application of our theoretical results

a simple method for analysing overdispersion in clustered poisson data a simple method is proposed for analysing grouped count data exhibiting overdispersion relative to a poisson model the method is similar to the approach suggested for the analysis of clustered binary data in rao and scott 1992 it requires no specific model for the overdispersion and it can be implemented easily using standard programs designed to handle independent poisson counts after a small amount of preprocessing

bayesian semiparametric analysis of developmental toxicology data modeling of developmental toxicity studies often requires simple parametric analyses of the dose response relationship between exposure and probability of a birth defect but poses challenges because of nonstandard distributions of birth defects for a fixed level of exposure this article is motivated by two such experiments in which the distribution of the outcome variable is challenging to both the standard logistic model with binomial response and its parametric multistage elaborations we approach our analysis using a bayesian semiparametric model that we tailored specifically to developmental toxicology studies it combines parametric dose response relationships with a flexible nonparametric specification of the distribution of the response obtained via a product of dirichlet process mixtures approach pdpm our formulation achieves three goals 1 the distribution of the response is modeled in a general way 2 the degree to which the distribution of the response adapts nonparametrically to the observations is driven by the data and 3 the marginal posterior distribution of the parameters of interest is available in closed form the logistic regression model as well as many of its extensions such as the beta binomial model and finite mixture models are special cases in the context of the two motivating examples and a simulated example we provide model comparisons illustrate overdispersion diagnostics that can assist model specification show how to derive posterior distributions of the effective dose parameters and predictive distributions of response and discuss the sensitivity of the results to the choice of the prior distribution

computer assisted analysis of mixtures c a man statistical algorithms summary this paper presents various algorithmic approaches for computing the maximum likelihood estimator of the mixing distribution of a one parameter family of densities and provides a unifying computeroriented concept for the statistical analysis of unobserved heterogeneity i e observations stemming from different subpopulations in a univariate sample the case with unknown number of population subgroups as well as the case with known number of population subgroups with emphasis on the first is considered in the computer package c a man computer assisted mixture analysis it includes an algorithmic menu with choices of the em algorithm the vertex exchange algorithm a combination of both as well as the vertex direction method to ensure reliable convergence a steplength menu is provided for the three latter methods each achieving monotonicity for the direction of choice c a man has the option to work with restricted support size that is the case when the number of components is known a priori in the latter case the em algorithm is used applications of mixture modelling in medical problems are discussed

estimating equations for parameters in means and covariances of multivariate discrete and continuous responses generalized estimating equations are introduced in an ad hoc fashion for the covariance matrix of a multivariate response these equations are to be solved jointly with score equations from a generalized linear model for mean parameters a class of quadratic exponential models is used to develop joint estimating equations for mean and covariance parameters in a more systematic fashion and proposals for the use of such equations are developed comments on the relative merits of the ad hoc and model based approaches to estimation are given and a regression illustration with a bivariate response is provided

testing the fit of a regression model via score tests in random effects models this paper considers testing the goodness of fit of regression models emphasis is on a goodness of fit test for generalized linear models with canonical link function and known dispersion parameter the test is based on the score test for extra variation in a random effects model by choosing a suitable form for the dispersion matrix a goodness of fit test statistic is obtained which is quite similar to test statistics based on non parametric kernel methods we consider the distribution of the test statistic and discuss the choice of the dispersion matrix the testing method can handle models with continuous and discrete covariates corrections for bias when parameters are estimated are available and extensions to models with unknown dispersion parameters and more general nonlinear models are discussed the proposed goodness of fit method is demonstrated in a simulation study and on real data of bone marrow transplant patients the individual contributions of observations to the test statistic are used to perform residual analyses

models for zero inflated correlated count data with extra heterogeneity when is it too complex statistical analysis of count data typically starts with a poisson regression however in many real life applications it is observed that the variation in the counts is larger than the mean and one needs to deal with the problem of overdispersion in the counts several factors may contribute to overdispersion 1 unobserved heterogeneity due to missing covariates 2 correlation between observations such as in longitudinal studies and 3 the occurrence of many zeros more than expected from the poisson distribution in this paper we discuss a model that allows one to explicitly take each of these factors into consideration the aim of this paper is twofold 1 investigate whether we can identify the cause of overdispersion via model selection and 2 investigate the impact of a misspecification of the model on the power of a covariate the paper is motivated by a study of the occurrence of drug induced arrhythmia in beagle dogs based on electrocardiogram recordings with the objective to evaluate the effect of potential drugs on the heartbeat irregularities copyright 2016 john wiley sons ltd

odds ratio inference with dependent data summary when data can be presented as a series of k 2 x 2 tables with cell counts xi ni xi yi mi yi it is often assumed that xi and yi are binomially distributed this paper deals with inference for the common odds ratio i l when the binomial assumption is invalid when k increases the consistency and asymptotic normality of the mantel haenszel 1959 estimator is derived the conditional maximum likelihood estimator is shown to be inconsistent and the asymptotic bias is computed when either the first order markov chain or beta binomial model is assumed the mantel haenszel test for testing f 1 is also shown to be inappropriate through some simulation studies two consistent test statistics are proposed and shown to be comparable to each other in terms of size and efficiency some possible further work is described

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

testing for overdispersion in poisson and binomial regression models abstract in this article a method for obtaining tests for overdispersion with respect to a natural exponential family is derived the tests are designed to be powerful against arbitrary alternative mixture models where only the first two moments of the mixed distribution are specified various tests for extra poisson and extra binomial variation are obtained as special cases the use of a particular test may be motivated by a consideration of the mechanism through which the overdispersion may arise the common occurrence of extra poisson and extra binomial variation has been noted by several authors however the poisson and binomial models remain valid in many instances and because of their simplicity and appeal it is of real interest to ascertain when they apply this paper develops a unifying theory for testing for overdispersion and generalizes tests previously derived including those by fisher 1950 collings and margolin 1985 and prentice 1986 it also shows the pearson statistic to be a sc

on a simple test for neglected heterogeneity in panel studies summary this paper deals with the performance of a simple test for the detection of unmeasured heterogeneity in regression models for panel data it is assumed that the unmeasured heterogeneity can be modeled by an individual specific random variable that does not vary over time conditionally on the individual specific effects and the regressor variables the distribution of the dependent variable is assumed to belong to a linear exponential family this class of distributions includes linear models for continuous dependent variables as well as nonlinear models for discrete outcomes the proposed test does not assume a special form of the distribution of the heterogeneity and the test statistic can be calculated with available computer programs the performance of the test is investigated in a simulation experiment

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

population size versus runtime of a simple evolutionary algorithm evolutionary algorithms eas find numerous applications and practical knowledge on eas is immense in practice sophisticated population based eas employing selection mutation and crossover are applied in contrast theoretical analysis of eas often concentrates on very simple algorithms such as the 1 1 ea where the population size equals 1 in this paper the question is addressed whether the use of a population by itself can be advantageous a population based ea that neither makes use of crossover nor any diversity maintaining operator is investigated on an example function it is shown that an increase of the population size by a constant factor decreases the expected runtime from exponential to polynomial thereby the best gap known so far is improved from superpolynomial vs polynomial to exponential vs polynomial moreover it is proved that the exponential and polynomial runtime bounds occur with a probability exponentially close to one if the population size is a constant resp a small polynomial finally a second example function where only a small population leads to a polynomial runtime and a hierarchy result on the appropriate population size are presented the analyses show formally how the population size can lead to different attractors in the search space

selecting factors predictive of heterogeneity in multivariate event time data in multivariate survival analysis investigators are often interested in testing for heterogeneity among clusters both overall and within specific classes we represent different hypotheses about the heterogeneity structure using a sequence of gamma frailty models ranging from a null model with no random effects to a full model having random effects for each class following a bayesian approach we define prior distributions for the frailty variances consisting of mixtures of point masses at zero and inverse gamma densities since frailties with zero variance effectively drop out of the model this prior allocates probability to each model in the sequence including the overall null hypothesis of homogeneity using a counting process formulation the conditional posterior distributions of the frailties and proportional hazards regression coefficients have simple forms posterior computation proceeds via a data augmentation gibbs sampling algorithm a single run of which can be used to obtain model averaged estimates of the population parameters and posterior model probabilities for testing hypotheses about the heterogeneity structure the methods are illustrated using data from a lung cancer trial

tests for detecting overdispersion in models with measurement error in covariates measurement error in covariates can affect the accuracy in count data modeling and analysis in overdispersion identification the true mean variance relationship can be obscured under the influence of measurement error in covariates in this paper we propose three tests for detecting overdispersion when covariates are measured with error a modified score test and two score tests based on the proposed approximate likelihood and quasi likelihood respectively the proposed approximate likelihood is derived under the classical measurement error model and the resulting approximate maximum likelihood estimator is shown to have superior efficiency simulation results also show that the score test based on approximate likelihood outperforms the test based on quasi likelihood and other alternatives in terms of empirical power by analyzing a real dataset containing the health related quality of life measurements of a particular group of patients we demonstrate the importance of the proposed methods by showing that the analyses with and without measurement error correction yield significantly different results copyright 2015 john wiley sons ltd

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

algorithms for an irreducible and lumpable strong stochastic bound despite considerable works the numerical analysis of large chains remains a difficult problem fortunately enough while modeling computer networks it is often sufficient to check if the studied mechanism satisfies the requirements of the quality of service qos we expect and exact values of the performance indices are not necessary so we advocate a new method based on the algorithmic derivation of a lumpable stochastic bounding matrix to analyze large state space problems because of the lumpability the numerical analysis deals with smaller matrices the stochastic bounds provide upper bounds for performance indices defined as reward functions our work is purely algorithmic and algebraic and does not require proofs based on the sample path theorem and coupling see stoyan comparison methods for queues and other stochastic models wiley 1983 for some examples we present the algorithms time complexity memory requirements and an example

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

estimating prevalence by group testing using generalized linear models a method is described for estimating prevalence by group testing using generalized linear models this provides a simple way of analysing such data using widely available software existing methodology to correct for overdispersion using quasi likelihoods is applied to the group testing model the methods are illustrated by an estimation of salmonella contamination in eggs and of yellow fever virus infection in a mosquito population

a locally most powerful test for homogeneity with many strata summary a locally most powerful test is proposed for homogeneity of nuisance parameters from many strata in the mixed model setting the test is based on the difference between the square of the score and the observed information about the nuisance parameters all evaluated at the null hypothesis several examples including constant normal mean with possibly different variances and matched case control studies are presented in detail the relative efficiencies of the unstratified estimator of parameter of interest versus the stratified one are calculated two data sets on matched case control studies are used for illustration

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

test of homogeneity of binary data with explanatory variables summary apparent heterogeneity of the risk of a disease in different groups may be explained by subjectspecific risk factors unequally distributed in these groups we propose a score test of homogeneity that allows adjustment for known risk factors of the disease the test is based oni a random effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method the score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3 318 subjects scattered in 75 parishes it is shown that an apparent heterogeneity disappears when taking into account subject specific risk factors this test may also be useful for studying familial aggregation of a disease testing homogeneity of the distribution of binary traits in different groups has long been recognized as an important problem particularly in conventional genetics smith 1951 and in genetic epidemiology where it may be used to investigate the familial aggregation of a disease the presence of familial aggregation suggests a genetic determinant testing homogeneity of geographical units is also of interest the presence of heterogeneity suggests the presence of an unmeasured environmental factor another application occurs if the possible correlation of the data is treated as a nuisance it is useful to test whether the groups are homogeneous before performing ordinary regression models liang 1987 chi squared tests are used for testing homogeneity when the number of groups is small however the chi squared test is not applicable when the sizes of the groups are not large haldane 1940 and when the number of groups is large in such cases random effect models are preferred the probability of disease within a group have a common distribution thus the null hypothesis is specified by a null variance of the random effect and alternative hypotheses are specified by a unique parameter the variance of the random effect whatever the number of groups see potthoff and whittinghill 1966 wisniewsky 1968 and tarone 1979 in epidemiologic studies however we often need to test for homogeneity while adjusting for other risk factors of the disease indeed risk factors if differently distributed in the different groups may play the role of confounding factors relative to the group effect it is of paramount importance in genetic studies to investigate whether an apparent familial aggregation may be explained by nongenetic factors such as educational level or nutritional habits which may also segregate in families similarly geographical clusters may be explained by nonenvironmental factors unequally distributed in the geographical units based on a random effect logistic regression model we derive a score test of homogeneity that allows adjustment on explanatory variables the score statistic is the same as that proposed by hamerle 1990 in the context of repeated measurements but the variance proposed in the present paper is different simulations show that it leads to a more powerful test we use this test to investigate the possible geographical heterogeneity of cognitive impairment as measured by the mini mental state score in 3 318 subjects scattered in 75 parishes in southwestern france

a goodness of fit test for cox s proportional hazards model based on martingale residuals a goodness of fit test for cox s proportional hazards model is proposed on the basis of martingale residuals the test is derived as the score test for the presence of an extra random effect in the exponential part of the hazard function assumptions about the distribution of the random effects are not made only the correlation matrix must be specified this can be done on the basis of an existing division of individuals into groups such as families or on the basis of the distance between observed covariates the variance of the test statistic is derived using a counting process approach corrections for the estimation of parameters are available the test is demonstrated in a simulated data set as well as in a real data set on ovarian cancer

comparison of partitioning techniques for two level iterative solvers on large sparse markov chains experimental results for large sparse markov chains especially the ill conditioned nearly completely decomposable ncd ones are few we believe there is need for further research in this area specifically to aid in the understanding of the effects of the degree of coupling of ncd markov chains and their nonzero structure on the convergence characteristics and space requirements of iterative solvers the work of several researchers has raised the following questions that led to research in a related direction how must one go about partitioning the global coefficient matrix into blocks when the system is ncd and a two level iterative solver such as block sor is to be employed are block partitionings dictated by the ncd form of the stochastic one step transition probability matrix necessarily superior to others is it worth investigating alternative partitionings better yet for a fixed labeling and partitioning of the states how does the performance of block sor or even that of point sor compare to the performance of the iterative aggregation disaggregation iad algorithm finally is there any merit in using two level iterative solvers when preconditioned krylov subspace methods are available we seek answers to these questions on a test suite of 13 markov chains arising in 7 applications

towards an analytic framework for analysing the computation time of evolutionary algorithms in spite of many applications of evolutionary algorithms in optimisation theoretical results on the computation time and time complexity of evolutionary algorithms on different optimisation problems are relatively few it is still unclear when an evolutionary algorithm is expected to solve an optimisation problem efficiently or otherwise this paper gives a general analytic framework for analysing first hitting times of evolutionary algorithms the framework is built on the absorbing markov chain model of evolutionary algorithms the first step towards a systematic comparative study among different eas and their first hitting times has been made in the paper

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

testing goodness of fit in regression a general approach for specified alternatives when fitting generalized linear models or the cox proportional hazards model it is important to have tools to test for lack of fit because lack of fit comes in all shapes and sizes distinguishing among different types of lack of fit is of practical importance we argue that an adequate diagnosis of lack of fit requires a specified alternative model such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis we know the direction of the departure from the model the goodness of fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases connections with penalized likelihood and random effects are discussed and the application of the proposed approach is illustrated with medical examples tailored functions for goodness of fit testing have been implemented in the r package globaltest copyright 2012 john wiley sons ltd

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

iterative methods based on splittings for stochastic automata networks abstract this paper presents iterative methods based on splittings jacobi gauss seidel successive over relaxation and their block versions for stochastic automata networks sans these methods prove to be better than the power method that has been used to solve sans until recently with the help of three examples we show that the time it takes to solve a system modeled as a san is still substantial and it does not seem to be possible to solve systems with tens of millions of states on standard desktop workstations with the current state of technology however the san methodology enables one to solve much larger models than those could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense

testing random effects in the linear mixed model using approximate bayes factors deciding which predictor effects may vary across subjects is a difficult issue standard model selection criteria and test procedures are often inappropriate for comparing models with different numbers of random effects due to constraints on the parameter space of the variance components testing on the boundary of the parameter space changes the asymptotic distribution of some classical test statistics and causes problems in approximating bayes factors we propose a simple approach for testing random effects in the linear mixed model using bayes factors we scale each random effect to the residual variance and introduce a parameter that controls the relative contribution of each random effect free of the scale of the data we integrate out the random effects and the variance components using closed form solutions the resulting integrals needed to calculate the bayes factor are low dimensional integrals lacking variance components and can be efficiently approximated with laplace s method we propose a default prior distribution on the parameter controlling the contribution of each random effect and conduct simulations to show that our method has good properties for model selection problems finally we illustrate our methods on data from a clinical trial of patients with bipolar disorder and on data from an environmental study of water disinfection by products and male reproductive outcomes

regression based tests for overdispersion in the poisson model abstract a property of the poisson regression model is mean variance equality conditional on explanatory variables regression based tests for this property are proposed in a very general setting unlike classical statistical tests these tests require specification of only the mean variance relationship under the alternative rather than the complete distribution whose choice is usually arbitrary the optimal regression based test is easily computed as the t test from an auxiliary regression if a distribution under the alternative hypothesis is in fact specified and is in the katz system of distributions or is cox s local approximation to the poisson the score test for the poisson distribution is equivalent to the optimal regression based test

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

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

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

the numerical solution of stochastic automata networks abstract stochastic automata networks san s have recently received attention in the literature as an efficient means of modelling parallel systems such as communicating processes concurrent processors shared memory etc the advantage that the san approach has over generalized stochastic petri nets and indeed over any markovian analysis that requires the generation of a transition matrix is that its representation remains compact even as the number of states in the underlying markov chain begins to explode our concern in this paper is with the numerical issues that are involved in solving san networks we introduce stochastic automata and consider the numerical difficulties that result from their interaction we examine how the product of a vector with a compact san descriptor may be formed for this operation is the basis of all iterative solution methods we describe possible solution methods including the power method the method of arnoldi and gmres and show that the two latter methods greatly out perform the power method the method usually used in conjunction with stochastic automata networks finally we consider one possible means of preconditioning but conclude that further research is needed

theory of genetic algorithms i we investigate spectral and geometric properties of the mutation crossover operator in a genetic algorithm with general size alphabet by computing spectral estimates we show how the crossover operator enhances the averaging procedure of the mutation operator in the random generator phase of the genetic algorithm by mapping our model to the multi set model often investigated in the literature we compute corresponding spectral estimates for mutation crossover in the multi set model ii various types of unscaled or scaled fitness selection mechanisms are considered such as proportional fitness selection rank selection and tournament fitness selection we allow fitness selection mechanisms where the fitness of an individual or creature depends upon the population it resides in we investigate contracting properties of these fitness selection mechanisms and combine them with the crossover operator to obtain a model for genetic drift this has applications to the study of genetic algorithms with zero or extremely low mutation rate iii we discuss a variety of convergent simulated annealing type algorithms with mutation crossover as generator matrix iv the theory includes proof of strong ergodicity for various types of scaled genetic algorithms using common fitness selection methods if the mutation rate converges to a positive value and the other operators of the genetic algorithm converge then the limit probability distribution over populations is fully positive at uniform populations whose members have not necessarily optimal fitness v in what follows suppose the mutation rate converges to zero sufficiently slow to assure weak ergodicity of the inhomogeneous markov chain describing the genetic algorithm unbounded power law scaling for the fitness selection is used mutation and crossover commute and the fitness function is injective which is a minor restriction in regard to function optimization va if a certain integrable convergence condition is satisfied such that the selection pressure increases fast then there is essentially no other restriction on the crossover operation and the algorithm asymptotically behaves as the following take the best search algorithm 1 mutate in every step with rate decreasing to zero and 2 map any population to the uniform population with the best creature the take the best search algorithm is investigated and its convergence is shown depending upon population size the take the best search algorithm does or does not necessarily converge to the optimal solution vb if population size is larger than length of genome and a certain logarithmic convergence condition is satisfied such that the selection pressure increases slowly but sufficiently fast then the algorithm asymptotically converges to the optimal solution

testing against a high dimensional alternative in the generalized linear model asymptotic type i error control summary testing a low dimensional null hypothesis against a high dimensional alternative in a generalized linear model may lead to a test statistic that is a quadratic form in the residuals under the null model using asymptotic arguments we show that the distribution of such a test statistic can be approximated by a ratio of quadratic forms in normal variables for which algorithms are readily available for generalized linear models the asymptotic distribution shows good control of type i error for moderate to small samples even when the number of covariates in the model far exceeds the sample size

estimation of the covariance matrix of random effects in longitudinal studies longitudinal studies are often conducted to explore the cohort and age effects in many scientific areas the within cluster correlation structure plays a very important role in longitudinal data analysis this is because not only can an estimator be improved by incorporating the within cluster correlation structure into the estimation procedure but also the within cluster correlation structure can sometimes provide valuable insights in practical problems for example it can reveal the correlation strengths among the impacts of various factors motivated by data typified by a set from bangladesh pertinent to the use of contraceptives we propose a random effect varying coefficient model and an estimation procedure for the within cluster correlation structure of the proposed model the estimation procedure is optimization free and the proposed estimators enjoy asymptotic normality under mild conditions simulations suggest that the proposed estimation is practicable for finite samples and resistent against mild forms of model m is specification finally we analyze the data mentioned above with the new random effect varying coefficient model together with the proposed estimation procedure which reveals some interesting sociological dynamics

how to analyse evolutionary algorithms many variants of evolutionary algorithms have been designed and applied the experimental knowledge is immense the rigorous analysis of evolutionary algorithms is difficult but such a theory can help to understand design and teach evolutionary algorithms in this survey first the history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed

random effects selection in linear mixed models nous presentons le probleme pratique important de la selection des effets aleatoires dans un modele lineaire mixte un modele bayesien hierarchique est utilise pour identifier tout effet aleatoire devariance nulle l approche proposee reparametrise le modele mixte de telle sorte que les fonctions des parametres de covariance de la distribution des effets aleatoires soient incorporees comme des coefficients de regression pour des variables latentes normales nous permettons aux effets aleatoires de sortir du modele en choisissant des melanges d a priori avec des masses ponctuelles en zero pour les variances des effets aleatoires du fait de la reparametrisation le modele prend une structure lineaire conditionnelle qui facilite l utilisation de lois a priori conjuguees et normales nous demontrons que les calculs a posteriori peuvent etre effectues via un algorithme simple et efficace de monte carlo par chaine de markov les methodes sont illustrees par des donnees simulees et par des donnees reelles d exposition prenatale au polychlorobiphenile et des donnees sur le developpement psychomoteur des enfants

transform both sides approach for overdispersed binomial data when n is unobserved abstract a common complication in analyzing binomial data is overdispersion where the observed variation exceeds that predicted from the binomial distribution with parameters n and p we consider the situation where n is not observed and variable to estimate the regression parameters associated with covariates we apply the transform both sides method based on the first order asymptotic variance stabilizing transformation we develop the arcsine transformation family indexed by a single parameter this family includes the square root and the arcsine transformations as special cases asymptotic properties of the transformation methods are obtained simulation study indicates that the arcsine transformation family is more efficient than the square root and arcsine transformations when there is moderate overdispersion these approaches are applied to a data set from radiobiology

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

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

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