exact approaches for testing hypotheses based on the intra class kappa coefficient testing involving the intra class kappa coefficient is commonly performed in order to assess agreement involving categorical ratings a number of procedures have been proposed which make use of the limiting null distribution as the sample size goes to infinity in order to compute the observed significance as with many tests based on asymptotic null distributions these tests are associated with problematic type i error control for selected sample sizes and points in the parameter space we propose and study a collection of exact testing approaches for both the one sample and k sample scenarios for the one sample case p values are obtained using the exact distribution of the test statistic conditional on a sufficient statistic in addition unconditional approaches are considered on the basis of maximization across the nuisance parameter space numerical evaluation reveals advantages with the exact unconditional procedures copyright 2014 john wiley sons ltd

random lie point symmetries of stochastic differential equations we study the invariance of stochastic differential equations under random diffeomorphisms and establish the determining equations for random lie point symmetries of stochastic differential equations both in ito and in stratonovich forms we also discuss relations with previous results in the literature

dose response models for teratological experiments in a recent paper hereinafter referred to as rvr rai and van ryzin 1985 propose a dose response model for use in low dose extrapolation from teratological experiments involving quantal responses suppose n litters are divided into m 1 dose groups the ith group consisting of ni litters exposed to dose di o do di dn the group i 0 being a zero dose control let sij denote the size of the jth litter in the ith group j 1 ni and let rij denote the number of foetuses or pups in the litter exhibiting the toxic response of interest the model proposed by rvr assumes that the conditional distribution of rij given sij sij is binomial sij p1j where

picard vessiot extensions of artinian simple module algebras abstract this paper pursues takeuchi s hopf algebraic approach m takeuchi a hopf algebraic approach to the picard vessiot theory j algebra 122 1989 481 509 to the picard vessiot pv theory for differential equations to involve the pv extensions of difference equations differential fields and total difference rings in the standard pv theory are unified here by artinian simple as module algebras over a cocommutative pointed smooth hopf algebra

on hopf algebras with cocommutative coradicals 1 zf k is a right coideal subalgebra of h such that s k k h is faithfully flat as a right or left k module 2 zf x h n h is a quotient left h module coalgebra h is faithfully coflat as a right or left x h comodule 3 k h nk and 7 h h establish a 1 1 correspondence between the right coideal subalgebras k of h such that s k ko and the quotient left h module coalgebras n h n h 4 suppose k x in 3 there is a left x h comodule and right k module isomorphism h n x h q k if either a h is pointed or b k is finite dimensional over k

bivariate latent variable models for clustered discrete and continuous outcomes abstract we use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome and then extend the model to allow for clustered data the model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable this factorization suggests a convenient approach to parameter estimation using quasi likelihood techniques our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters fetal weight and malformation data illustrate the results

geometric characterization of strongly normal extensions this paper continues previous work in which we developed the galois theory of strongly normal extensions using differential schemes in the present paper we derive two main results first we show that an extension is strongly normal if and only if a certain differential scheme splits i e is obtained by base extension of a scheme over constants this gives a geometric characterization to the notion of strongly normal second we show that picard vessiot extensions are characterized by their galois group being affine our proofs are elementary and do not use group chunks or cohomology we end by recalling some important results about strongly normal extensions with the hope of spurring future research

normal forms symmetry and linearization of dynamical systems we discuss how the presence of a suitable symmetry can guarantee the perturbative linearizability of a dynamical system or a parameter dependent family via the poincare normal form approach we discuss this formally at first and later pay attention to the convergence of the linearizing procedure we also discuss some generalizations of our main result

determining small parameters for quasi steady state for a parameter dependent system of ordinary dierential equations we present a systematic approach to the determination of parameter values near which singular perturbation scenarios in the sense of tikhonov and fenichel arise we call these special values tikhonov parameter values the principal application we intend is to equations that describe chemical reactions in the context of quasi steady state or partial equilibrium settings such equations have rational or even polynomial right hand side we determine the structure of the set of tikhonov parameter values as a semi algebraic set and present an algorithmic approach to their explicit determination using groebner bases examples and applications which include the irreversible and reversible michaelis menten systems illustrate that the approach is rather easy to implement msc 2010 92c45 34e15 80a30 13p10

on convergent normal form transformations in presence of symmetries abstract we prove a convergence criterion for transformations to poincare dulac normal form that involves the centralizer of the given vector field

testing the effect of treatment in experiments with correlated binary outcomes this paper considers the problem of testing for treatment effect in a randomized experiment with correlated binary outcomes representing success or failure for different parts of a randomized unit attention is restricted to tests that are based on a summary score for each individual randomized and thus are valid regardless of the precise nature of the correlation among parts the focus is on the efficiency of such tests under various correlation structures with special emphasis on the case in which the correlation among parts within an individual differs across treatment groups a class of summary score statistics is defined and optimal testing is discussed for some simple situations three potential general purpose tests also are described 1 the ratio estimate test discussed by henderson et al 1988 controlled clinical trials 9 189 205 2 a modified ratio estimate test with adjusted weighting based on the within individual correlation between parts 3 a test defined by applying the mantel haenszel procedure to the proportion of individuals with at least one failure stratifying by the number of parts for these general purpose tests numerical calculations of asymptotic efficiency are presented under a wide range of designs and correlation structures on the basis of these results some practical recommendations for choosing a test are made

picard vessiot theory of differentially simple rings abstract in picard vessiot theory the galois theory for linear differential equations the picard vessiot ring plays an important role since it is the picard vessiot ring which is a torsor principal homogeneous space for the galois group scheme like fields are simple rings having only 0 and 1 as ideals the picard vessiot ring is a differentially simple ring i e a differential ring having only 0 and 1 as differential ideals having in mind that the classical galois theory is a theory of extensions of fields i e of simple rings it is quite natural to ask whether one can also set up a picard vessiot theory where the base is not a differential field but more generally a differentially simple ring it is the aim of this article to give a positive answer to this question i e to set up such a differential galois theory

a hopf algebraic approach to the picard vessiot theory abstract this paper shows what is really happening in picard vessiot theory our hopf algebraic approach simplifies and generalizes the theory among other things the generalization gives a picard vessiot theory for positive characteristic for fields with not necessarily commuting derivations and even for fields with a set of higher derivations

non perturbative linearization of dynamical systems we consider the classical problem of linearizing a vector field x around a fixed point we adopt a non perturbative point of view based on the symmetry properties of linear vector fields

on the use of stochastic ordering to test for trend with clustered binary data we introduce the use of stochastic ordering for defining treatment related trend in clustered exchangeable binary data for both when cluster sizes are fixed and when they vary randomly in the latter case there is a well documented tendency for such data to be sparse a problem we address by making an assumption of interpretability or equivalently marginal compatibility our procedures are based on a representation of the joint distribution of binary exchangeable random variables by a saturated model and may hence be considered nonparametric the definition of trend by stochastic ordering is proposed to ensure a flexibility that allows for various forms of monotone increases in response to the cluster as a whole to be included in the evaluation of the trend we obtain maximum likelihood estimates of probability functions under stochastic ordering using mixture likelihood based algorithms since the data are sparse we avoid the use of asymptotic results and obtain p values of the likelihood ratio procedures by permutation resampling we demonstrate how the proposed framework can be used in risk assessment and provide comparisons with existing procedures

a general class of distributions on the simplex summary the dirichlet class of distributions on the simplex is overstructured for practical work because of its many strong independence properties a persistent problem of distribution theory has thus been to extend this class to include members free of these independence properties an alternative approach has been the recent introduction of the logistic normal class which contains members with and without the independence properties unfortunately this class is separate from the dirichlet class and so cannot sustain discussion of some strong forms of independence these difficulties are overcome in this paper by the introduction of a more general class which includes as special cases the dirichlet and logistic normal classes the role of this new class in relation to the analysis of compositional data in particular the investigation of independence hypotheses is discussed and illustrated

reduction and reconstruction for symmetric ordinary differential equations we discuss the reduction and reconstruction problem for ordinary differential equations that admit a linear symmetry group the goal is to prove that modulo reduction there remain only linear differential equations and to construct these explicitly extending previous work on one parameter groups we show this for certain unipotent and solvable groups and for all semisimple groups some applications to relative equilibria are given

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

estimation of sparse directed acyclic graphs for multivariate counts data the next generation sequencing data called high throughput sequencing data are recorded as count data which are generally far from normal distribution under the assumption that the count data follow the poisson log normal distribution this article provides an l1 penalized likelihood framework and an efficient search algorithm to estimate the structure of sparse directed acyclic graphs dags for multivariate counts data in searching for the solution we use iterative optimization procedures to estimate the adjacency matrix and the variance matrix of the latent variables the simulation result shows that our proposed method outperforms the approach which assumes multivariate normal distributions and the log transformation approach it also shows that the proposed method outperforms the rank based pc method under sparse network or hub network structures as a real data example we demonstrate the efficiency of the proposed method in estimating the gene regulatory networks of the ovarian cancer study

reduction of the semisimple 1 1 resonance the method of averaging is often used in hamiltonian systems of two degrees of freedom to find periodic orbits such periodic orbits can be reconstructed from the critical points of an associated reduced hamiltonian on a reduced space this paper details the construction of the reduced space and the reduced hamiltonian for the semisimple 1 1 resonance case the reduced space will be a 2 sphere in r3 and the reduced differential equations will be euler s equations restricted to this sphere the orbit projection from the energy surface in phase space to this sphere will be the hopf map the results of the paper are related to problems in physics on degeneracies due to symmetries of classical two dimensional harmonic oscillators and their quantum analogues for the hydrogen atom

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

spatial regression and spillover effects in cluster randomized trials with count outcomes this paper describes methodology for analyzing data from cluster randomized trials with count outcomes taking indirect effects as well spatial effects into account indirect effects are modeled using a novel application of a measure of depth within the intervention arm both direct and indirect effects can be estimated accurately even when the proposed model is misspecified we use spatial regression models with gaussian random effects where the individual outcomes have distributions overdispersed with respect to the poisson and the corresponding direct and indirect effects have a marginal interpretation to avoid spatial confounding we use orthogonal regression in which random effects represent spatial dependence using a homoscedastic and dimensionally reduced modification of the intrinsic conditional autoregression model we illustrate the methodology using spatial data from a pair matched cluster randomized trial against the dengue mosquito vector aedes aegypti done in trujillo venezuela

lie algebras with finite dimensional polynomial centralizer we give criteria for finite or infinite dimensionality of the polynomial centralizer of the lie algebra of a linear lie group in terms of invariants and relative invariants of the group in the finite dimensional scenario some applications to normal forms and to certain equations with fundamental solutions are presented

multivariate gamma poisson models abstract this article extends the multivariate gamma poisson model of repeated events developed by arbous and kerrich 1951 and bates and neyman 1952 by a compounding it with a dirichlet distribution in the analysis of cross sectional data and by b allowing individual rates to shift at the start of the second period in the analysis of two period longitudinal data the first extension allows individuals to specialize in particular types of events the model is shown to describe multivariate distributions of work incapacities prison infractions and criminal victimizations the second extension provides a framework for estimating changes in individual rates it is used to describe the shift in victimization rates observed in longitudinal studies of the national crime survey

normal form and representation theory representation theory of lie algebras is called upon to develop a procedure for normalizing a dynamical system with two degrees of freedom in the neighborhood of an equilibrium when the hamiltonian h x y x y in the coordinates x y and their conjugate momenta x y is of the type h x2 y2 2 v x y x y the potential energy v being a sum of homogeneous polynomials in the phase variables of degree strictly greater than 2 the fact that the resulting potential v is a polynomial in the new coordinates x y and the angular momentum g x y y x implies that the normalization is a rotation in the configuration space from a fixed frame to an ideal frame the technique is intended for normalizing an hamiltonian in equilibrium at the origin when the lie derivative associated with the quadratic part is not semisimple e g the planar restricted problem of three bodies at the equilateral equilibrium l4 when the basic frequencies are equal routh s singular case

the differential galois theory of strongly normal extensions differential galois theory the theory of strongly normal extensions has unfortunately languished this may be due to its reliance on kolchin s elegant but not widely adopted axiomatization of the theory of algebraic groups this paper attempts to revive the theory using a differential scheme in place of those axioms we also avoid using a universal differential field instead relying on a certain tensor product we identify automorphisms of a strongly normal extension with maximal differential ideals of this tensor product thus identifying the galois group with the closed points of an affine differential scheme moreover the tensor product has a natural coring structure which translates into the galois group operation composition of automorphisms this affine differential scheme splits i e is obtained by base extension from a not differential not necessarily affine group scheme as a consequence the galois group is canonically isomorphic to the closed or rational points of a group scheme defined over constants we obtain the fundamental theorem of differential galois theory giving a bijective correspondence between subgroup schemes and intermediate differential fields on the way to this result we study certain aspects of differential algebraic geometry e g closed immersions products local ringed space of constants and split differential schemes

a dose response model for teratological experiments involving quantal responses this paper introduces a dose response model for teratological quantal response data where the probability of response for an offspring from a female at a given dose varies with the litter size the maximum likelihood estimators for the parameters of the model are given as the solution of a nonlinear iterative algorithm two methods of low dose extrapolation are presented one based on the litter size distribution and the other a conservative method the resulting procedures are then applied to a teratological data set from the literature

uber polynomiale insbesondere riccatische differentialgleichungen mit fundamentallosungen caracterisation algebrique d une classe d equations differentielles admettant des solutions fondamentales

on the convergence of normalizing transformations in the presence of symmetries it is shown that under suitable conditions involving in particular the existence of analytic constants of motion the presence of lie point symmetries can ensure the convergence of the transformation of a vector field or dynamical system into normal form

convergent normal forms of symmetric dynamical systems it is shown that the presence of lie point symmetries of non hamiltonian dynamical systems can ensure the convergence of the coordinate transformations which take the dynamical system or vector field into poincare dulac normal form

distance based tests for homogeneity of multivariate dispersions the traditional likelihood based test for differences in multivariate dispersions is known to be sensitive to nonnormality it is also impossible to use when the number of variables exceeds the number of observations many biological and ecological data sets have many variables are highly skewed and are zero inflated the traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non euclidean dissimilarity would be more appropriate distance based tests of homogeneity of multivariate dispersions which can be based on any dissimilarity measure of choice are proposed here they rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes the tests are straightforward multivariate extensions of levene s test with p values obtained either using the traditional f distribution or using permutation of either least squares or lad residuals examples illustrate the utility of the approach including the analysis of stabilizing selection in sparrows biodiversity of new zealand fish assemblages and the response of indonesian reef corals to an el nino monte carlo simulations from the real data sets show that the distance based tests are robust and powerful for relevant alternative hypotheses of real differences in spread

tests for 2 x k contingency tables with clustered ordered categorical data ordered categorical data summarized in a 2 x k table usually consist of two sample multinomial or k sample binomial observations in analysing these data we usually assign scores to the k columns and perform a testing for the equality of two multinomial distributions in the former case and no trend among k binomial proportions in the latter case among the most popular score tests are the wilcoxon rank sum test and the armitage s linear trend test in this paper we extend the score tests to be used for clustered data under diverse study designs our methods do not require correct specification of the dependence structure within clusters the proposed tests are based on the asymptotic normality for large number of clusters and are a generalization of the standard tests used for independent data simulation studies are conducted to investigate the finite sample performance of the new methods the proposed methods are applied to real life data

multivariate methods for clustered binary data with more than one level of nesting abstract clustered data occur frequently in statistical practice in some areas of application such as ophthalmology clustered data are the rule rather than the exception in this setting standard multivariate methods such as logistic regression are invalid because of the lack of independence among outcomes for individual sample points within a cluster in rosner 1984 a polychotomous logistic regression model was presented to control for the effect of both cluster and individual specific covariates while accounting for the correlation among units within a cluster this model reduces to a beta binomial model in the absence of covariates and to an ordinary logistic model for clusters of size 1 and for larger clusters when no correlation is present a 1 level of nesting correlation structure is assumed as is typically found in ophthalmology where the person is the cluster and the individual eyes are the units within a cluster in this article this model is generalized to a 2 level of nesting struc

hopf module duality applied to x outer galois theory we work over a fixed ground field k in arbitrary characteristic let r be a prime algebra and let q denote the symmetric martindale quotient ring of r we know from 10 section 6 4 that to study group actions on r it is fundamental to consider the extended actions on q and those actions which are x outer or outer as automorphisms of q have nice properties which could be generalized for x outer in some appropriate sense hopf algebra actions to recall kharchenko s galois type correspondence theorem let g be a finite group of x outer automorphisms of r it was proved in 2 theorem 3 10 2 11 theorem b that

existence of parameterized picard vessiot extensions over fields with algebraically closed constants abstract the purpose of this short note is to establish the existence of parameterized picard vessiot extensions for systems of linear difference differential equations over difference differential fields with an algebraically closed field of constants

necessary conditions for the existence of quasi polynomial invariants the quasi polynomial and lotka volterra systems abstract we show that any quasi polynomial invariant of a quasi polynomial dynamical system can be transformed into a quasi polynomial invariant of a homogeneous quadratic lotka volterra dynamical system we show how this quasi polynomial invariant can be decomposed in a simple manner this decomposition permits to conclude that the existence of polynomial semi invariants in lotka volterra systems is a necessary condition for the existence of quasi polynomial invariants we derive a method which allows to construct the necessary conditions for existence of semi invariants on lotka volterra dynamical systems applications are given

binary regression using an extended beta binomial distribution with discussion of correlation induced by covariate measurement errors abstract the beta binomial distribution is extended to allow negative correlations among binary variates within an experimental unit regression models are proposed for both the binary variate response rate and for the pairwise correlation between binary variates and corresponding likelihood estimation procedures are described binary regression problems are also considered in which measurement errors in the regression variables represent the sole source of overdispersion some corresponding response rate estimation procedures are described and illustrated

a family of bivariate distributions generated by the bivariate bernoulli distribution abstract if x 1 x 2 is a sequence of independent bernoulli random variables the number of successes in the first n trials has a binomial distribution and the number of failures before the rth success has a negative binomial distribution from both the binomial and the negative binomial distributions the poisson distribution is obtainable as a limit moreover gamma distributions integer shape parameters are limits of negative binomial distributions and the normal distribution is a limit of negative binomial poisson and gamma distributions these basic facts from elementary probability have natural extensions to two dimensions because there is a unique natural bivariate bernoulli distribution in this article such extensions yielding a family of bivariate distributions are obtained and studied

on the poincare problem abstract we derive some restrictions on the possible degrees of algebraic invariant curves and on the possible form of algebraic integrating factors for plane polynomial vector fields whose stationary points at infinity satisfy a certain genericity condition the method is elementary and we show by example that it also yields strong results for certain non generic vector fields

painleve analysis and normal forms theory nonlinear vector fields have two important types of singularities the fixed points in phase space and the time singularities in the complex plane the first singularities are locally analyzed via normal form theory whereas the second ones are studied by the painleve analysis in this paper normal form theory is used to describe the solutions around their complex time singularities to do so a transformation mapping the local series around the singularities to the local series around a fixed point of a new system is introduced regular normal form theory is then used in this new system it is shown that a vector field has the painleve property only if the associated system is locally linearizable around its fixed points a problem analogous to the classical problem of the center moreover the connection between partial and complete integrability and the structure of local series around both types of singularities are established a new proof of the convergence of the local psi series is given and an explicit method to prove the existence of finite time blow up manifold in phase space is presented

galois theory for iterative connections and nonreduced galois groups this article presents a theory of modules with iterative connection this theory is a generalisation of the theory of modules with connection in characteristic zero as given by n katz to modules over rings of arbitrary characteristic we show that these modules with iterative connection and also the modules with integrable iterative connection form a tannakian category assuming some nice properties for the underlying ring and we show how this generalises to modules over schemes stratifications on modules as introduced by a grothendieck generalise the notion of integrable ordinary connections in another way however over smooth rings we obtain an equivalence of stratifications and integrable iterative connections furthermore over a regular ring in positive characteristic we show that the category of modules with integrable iterative connection is also equivalent to the category of flat bundles as defined by d gieseker in the second part of this article we set up a picard vessiot theory for fields of solutions for such a picard vessiot extension we obtain a galois correspondence which takes into account even nonreduced closed subgroup schemes of the galois group scheme on one hand and inseparable intermediate extensions of the picard vessiot extension on the other hand finally we compare our galois theory with the galois theory for purely inseparable field extensions given by s chase

integration of perturbed initial value problems through reduction theory we propose a method to integrate an initial value problem formed by the differential equations of a perturbed dynamical system plus the initial condition the approach consists of several steps first of all if the original system does not enjoy a continuous symmetry it is transformed up to a certain order of approximation m into an equivalent but equivariant one after truncation at order m second this new symmetry allows us to define a reduction map which produces in its whole phase space a splitting of the transformed equations specifically the latter system is decoupled into two subsystems also initial value problems one of them defined in the orbit space associated with the reduction and the other linear in its coordinates as a third step the reduced subsystems are analytically resolved or numerically integrated using standard methods finally the solution of the original system is recovered by inverting back the reduction map and thereafter the analytic transformations we apply our procedure to three examples

likelihood based modeling and analysis of data underdispersed relative to the poisson distribution summary by using a generalization of the poisson process distributions can be constructed that show appropriate amounts of underdispersion relative to the poisson distribution that may be apparent from observed data these are then used to examine the differences between the distributions of numbers of fetal implants in mice corresponding to different doses of the herbicide 2 4 5 t

a computationally tractable multivariate random effects model for clustered binary data summary we consider a multivariate random effects model for clustered binary data that is useful when interest focuses on the association structure among clustered observations based on a vector of gamma random effects and a complementary log log link function the model yields a likelihood that has closed form making a frequentist approach to model fitting straightforward this closed form yields several advantages over existing methods including easy inspection of model identifiability and straightforward adjustment for nonrandom ascertainment of subjects such as that which occurs in family studies of disease aggregation we use the proposed model to analyse two different binary datasets concerning disease outcome data from a familial aggregation study of breast and ovarian cancer in women and loss of heterozygosity outcomes from a brain tumour study

statistical inference for familial disease clusters in many epidemiologic studies the first indication of an environmental or genetic contribution to the disease is the way in which the diseased cases cluster within the same family units the concept of clustering is contrasted with incidence we assume that all individuals are exchangeable except for their disease status this assumption is used to provide an exact test of the initial hypothesis of no familial link with the disease conditional on the number of diseased cases and the distribution of the sizes of the various family units new parametric generalizations of binomial sampling models are described to provide measures of the effect size of the disease clustering we consider models and an example that takes covariates into account ascertainment bias is described and the appropriate sampling distribution is demonstrated four numerical examples with real data illustrate these methods

symmetries of dynamical systems and convergent normal forms it is shown that under suitable conditions involving in particular the existence of analytic constants of motion the presence of lie point symmetries can ensure the convergence of the transformation taking a vector field or dynamical system into normal form

using historical controls in the analysis of developmental toxicity data historical control data can often aid in the interpretation of the results from laboratory dose response experiments for example formal statistical methods for using historical data are well established for carcinogenicity studies in that case a score test derived from a beta binomial model yields a simple modification of the standard cochran armitage test for trend however this test cannot be used for developmental toxicity studies since it does not allow for the additional correlation structure induced by the presence of litter effects in this paper quasi likelihood methods are used to incorporate historical control information into a trend test for the types of correlated binary outcomes that typically arise in developmental toxicity studies the proposed test is asymptotically equivalent to the beta binomial score test in the special case when all the litter sizes are equal to 1 malformation data from a series of developmental toxicity studies illustrate the results

testing for homogeneity of multivariate dispersions using dissimilarity measures summary testing homogeneity of dispersions may be of its own scientific interest as well as an important auxiliary step verifying assumptions of a main analysis the problem is that many biological and ecological data are highly skewed and zero inflated also the number of variables often exceeds the sample size thus data analysts often do not rely on parametric assumptions but use a particular dissimilarity measure to calculate a matrix of pairwise differences this matrix is then the basis for further statistical inference anderson 2006 proposed a distance based test of homogeneity of multivariate dispersions for a one way anova design for which a matrix of pairwise dissimilarities can be taken as an input the key idea like in levene s test is to replace each observation with its distance to an estimated group center in this paper we suggest an alternative approach that is based on the means of within group distances and does not require group centre calculations to obtain the test statistic we show that this approach can have theoretical as well as practical advantages a permutation procedure that gives type i error close to the prescribed value even in small samples is described

analysis of proportions of affected foetuses in teratological experiments this paper is concerned with the analysis of proportions affected when an increasing dose of a compound is applied to a group of laboratory animals several sets of data including a set from a teratological experiment at the shell toxicology laboratory sittingbourne are analysed and some simulations are performed among the distributional models the beta binomial model is in general found to be the most sensitive to departures from the binomial for testing the equality of two proportions a comparison is made between the pseudo t test based on the jackknife method and the likelihood ratio test based on the beta binomial model from the limited comparison no definite advantage of one approach over the other has been found at the 5 level of significance both approaches lead to similar conclusions

difference galois theory of linear differential equations abstract we develop a galois theory for linear differential equations equipped with the action of an endomorphism this theory is aimed at studying the difference algebraic relations among the solutions of a linear differential equation the galois groups here are linear difference algebraic groups i e matrix groups defined by algebraic difference equations

tests of independence treatment heterogeneity dose related trend with exchangeable binary data abstract existing methods of testing for treatment effects for clustered binary data include the beta binomial quasilikelihood gee procedures all of these methods revolve around the mean response and the second order correlation however these two parameters alone do not fully determine the effect of treatment this article develops nonparametric likelihood ratio procedures to test for independence heterogeneity dose related trend in dose response studies involving exchangeable binary data the hypotheses of independence heterogeneity trend are expressed in terms of joint probabilities of similar responses among cluster mates constrained maximum likelihood estimates of these probabilities are computed and used to construct test statistics unlike the test statistics for independence and heterogeneity the asymptotic distribution of the likelihood ratio test for trend is not exactly a chi square however an upper bound of its p value is obtained by using a chi squared distribution a set of clustere

a simple method for the analysis of clustered binary data a simple method for comparing independent groups of clustered binary data with group specific covariates is proposed it is based on the concepts of design effect and effective sample size widely used in sample surveys and assumes no specific models for the intracluster correlations it can be implemented using any standard computer program for the analysis of independent binary data after a small amount of preprocessing the method is applied to a variety of problems involving clustered binary data testing homogeneity of proportions estimating dose response models and testing for trend in proportions and performing the mantel haenszel chi squared test for independence in a series of 2 x 2 tables and estimating the common odds ratio and its variance illustrative applications of the method are also presented

the multivariate poisson log normal distribution summary the statistical analysis of multivariate counts has proved difficult because of the lack of a parametric class of distributions supporting a rich enough correlation structure with increasing availability of powerful computing facilities an obvious candidate for consideration is now the multivariate log normal mixture of independent poisson distributions the multivariate poisson log normal distribution the properties of this discrete multivariate distribution are studied and its uses in a variety of applications to multivariate count data are illustrated

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

cluster sampling techniques in quantal response teratology and developmental toxicity studies summary this paper presents a model free approach for evaluating teratology and developmental toxicity data involving clustered binary responses in teratology studies a major statistical problem arises from the effect of intralitter correlation or the potential for littermates to respond similarly some statistical methods impose strict distributional assumptions to account for extra binomial variation while others rely on nonparametric resampling and empirical variance estimation techniques quasi likelihood methods and generalized estimating equations gee which model the marginal mean variance relationship also avoid strict distributional assumptions the proposed approach often used to analyze complex sample survey data is based on a first order taylor series approximation and a between cluster variance estimation procedure yielding consistent variance estimates for binomial based proportions and regression coefficients from dose response models the cluster sample technique presented here in the context of a logistic dose response model incorporates many of the advantages of quasi likelihood methods are valid for any underlying nested correlation structure and are adaptable to a variety of analytical settings the results of a simulation study show the cluster sample technique to be a viable competitor to gee methods currently receiving attention

on exchangeable multinomial distributions we derive an expression for the joint distribution of exchangeable multinomial random variables which generalizes the multinomial distribution based on independent trials while retaining some of its important properties unlike de finneti s representation theorem for a binary sequence the exchangeable multinomial distribution derived here does not require that the finite set of random variables under consideration be a subset of an infinite sequence using expressions for higher moments and correlations we show that the covariance matrix for exchangeable multinomial data has a different form from that usually assumed in the literature and we analyse data from developmental toxicology studies the proposed analyses have been implemented in r and are available on cran in the corrbin package

statistical interpretation of species composition the relative abundance of different species characterizes the structure of a biological community we analyze an experiment addressing the relationship between omnivorous feeding linkages and community stability our goal is to determine whether communities with different predator compositions respond similarly to environmental disturbance to evaluate these data we develop a hierarchical statistical model that combines aitchison s logistic normal distribution with a conditional multinomial observation distribution in addition we present an algebra for compositions that includes addition scalar multiplication and a metric for differences in compositions the algebra aids interpretation of treatment effects treatment interactions and covariates markov chain monte carlo mcmc is used for inference in a bayesian framework our experimental results indicate that a high degree of omnivory can help to stabilize community dynamics and prevent radical shifts in community composition this result is at od

a saturated model for analyzing exchangeable binary data applications to clinical and developmental toxicity studies abstract correlated binary data occur very frequently in statistical practice in many applications it is reasonable to assume that data from the same cluster are exchangeable such data are commonly encountered in cluster sample surveys teratological experiments ophthalmologic and otolaryngologic studies and other clinical trials the standard methods of analyzing these data include the use of beta binomial models and generalized estimating equations with third and fourth moments specified by working matrices the focus of these procedures is an estimation of the mean and variance parameters more information can be obtained when data are exchangeable by expressing the joint distribution of a set of exchangeable binary random variables in terms of the probability of similar response within cluster this article introduces a procedure for obtaining maximum likelihood estimates of population parameters such as the marginal means moments and correlations of orders two and higher applications are m

testing for order restricted hypotheses in longitudinal data an inherent ordering we propose a quadratic score test qst based on a quadratic inference function for detecting an order in treatment effects for correlated data the quadratic inference function is similar to the negative of a log likelihood and it provides test statistics in the spirit of a x2 test for testing nested hypotheses as well as for assessing the goodness of fit of model assumptions under the null hypothesis of no order restriction it is shown that the qst statistic has a wald type asymptotic representation and that the asymptotic distribution of the qst statistic is a weighted x2 distribution furthermore an asymptotic distribution of the qst statistic under an arbitrary convex cone alternative is provided the performance of the qst is investigated through monte carlo simulation experiments analysis of the polyposis data demonstrates that the qst outperforms the wald test when data are highly correlated with a small sample size and there is a significant amount of missing data with a small number of clusters the proposed test statistic accommodates both time dependent and time independent covariates in a model

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

embedding and splitting ordinary differential equations in normal form abstract we introduce an embedding of real or complex n dimensional space k n as an algebraic variety v which is determined by the action of a linear one parameter group every analytic vector field on k n corresponds to some embedded vector field on v for a symmetric vector field this embedded vector field splits into a reduced system and a direct sum of non autonomous linear systems examples and applications are mostly concerned with poincare dulac normal forms embeddings provide a natural setting for perturbations of symmetric systems in particular of systems in normal form up to some degree