forcing extensions of partial lattices abstract we prove the following result let k be a lattice let d be a distributive lattice with zero and let con c k d be a 0 homomorphism where con c k denotes the 0 semilattice of all finitely generated congruences of k then there are a lattice l a lattice homomorphism f k l and an isomorphism con c l d such that con c f furthermore l and f satisfy many additional properties for example i l is relatively complemented ii l has definable principal congruences iii if the range of is cofinal in d then the convex sublattice of l generated by f k equals l we mention the following corollaries that extend many results obtained in the last decades in that area 1 every lattice k such that con c k is a lattice admits a congruence preserving extension into a relatively complemented lattice 2 every 0 direct limit of a countable sequence of distributive lattices with zero is isomorphic to the semilattice of compact congruences of a relatively complemented lattice with zero

nonnegative splittings for rectangular matrices the extension of the nonnegative splitting for rectangular matrices called proper nonnegative splitting is proposed first different convergence and comparison theorems for the proper nonnegative splittings are established the notion of double nonnegative splitting is then generalized to rectangular matrices finally different convergence and comparison results are presented for this decomposition the case for singular square matrices is also studied

autoregressive and cross lagged model for bivariate non commensurate outcomes autoregressive and cross lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences but not much work has been carried out in modeling bivariate non commensurate e g mixed binary and continuous outcomes simultaneously we develop a likelihood based methodology combining ordinary autoregressive and cross lagged models with a shared subject specific random effect in the mixed model framework to model two correlated longitudinal non commensurate outcomes the estimates of the cross lagged and the autoregressive effects from our model are shown to be consistent with smaller mean squared error than the estimates from the univariate generalized linear models inclusion of the subject specific random effects in the proposed model accounts for between subject variability arising from the omitted and or unobservable but possibly explanatory subject level predictors our model is not restricted to the case with equal number of events per subject and it can be extended to different types of bivariate outcomes we apply our model to an ecological momentary assessment study with complex dependence and sampling data structures specifically we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections we find negative cross lagged effect between these two outcomes and positive autoregressive effect within each outcome copyright 2017 john wiley sons ltd

weighted max norms splittings and overlapping additive schwarz iterations summary weighted max norm bounds are obtained for algebraic additive schwarz iterations with overlapping blocks for the solution of ax b when the coefficient matrix a is an m matrix the case of inexact local solvers is also covered these bounds are analogous to those that exist using a norms when the matrix a is symmetric positive definite a new theorem concerningp regular splittings is presented which provides a useful tool for the a norm bounds furthermore a theory of splittings is developed to represent algebraic additive schwarz iterations this representation makes a connection with multisplitting methods with this representation and using a comparison theorem it is shown that a coarse grid correction improves the convergence of additive schwarz iterations when measured in weighted max norm

two step boundary value methods in the solution of odes abstract in this paper we study boundary value methods bvm methods for solving initial value problems these methods give some advantages with respect to usual initial value methods for odes for instance bvm methods may be implemented efficiently on parallel computers we propose two classes of bvm methods based on linear two step schemes and we study their bv stability regions the convergence will be approached by considering the simple case of a single linear differential equation numerical tests will be given both to illustrate the numerical features of these methods and to show the performance of the parallel implementation of some bvm methods with respect to usual codes for odes

factors affecting power of tests for multiple binary outcomes frequently in clinical studies a primary outcome is formulated from a vector of binary events several methods exist to assess treatment effects on multiple correlated binary outcomes including comparing groups on the occurrence of at least one among the outcomes collapsed composite on the count of outcomes observed per subject on individual outcomes adjusting for multiplicity or with multivariate tests postulating either common or distinct effects across outcomes we focus on a 1 df distinct effects test in which the estimated outcome specific treatment effects from a gee model are simply averaged and compare it with other methods on clinical and statistical grounds using a flexible method to simulate multivariate binary data we show that the relative efficiencies of the assessed tests depend in a complex way on the magnitudes and variabilities of component incidences and treatment effects as well as correlations among component events while other tests are easily driven by high frequency components the average effect gee test is not since it averages the log odds ratios unweighted by the component frequencies thus the average effect test is relatively more powerful than other tests when lower frequency components have stronger associations with a treatment or other predictor but less powerful when higher frequency components are more strongly associated in studies when relative effects are at least as important as absolute effects or when lower frequency components are clinically most important this test may be preferred two clinical trials are discussed and analyzed and recommendations for practice are made sons ltd

bayesian latent variable models for clustered mixed outcomes a general framework is proposed for modelling clustered mixed outcomes a mixture of generalized linear models is used to describe the joint distribution of a set of underlying variables and an arbitrary function relates the underlying variables to be observed outcomes the model accommodates multilevel data structures general covariate effects and distinct link functions and error distributions for each underlying variable within the framework proposed novel models are developed for clustered multiple binary unordered categorical and joint discrete and continuous outcomes a markov chain monte carlo sampling algorithm is described for estimating the posterior distributions of the parameters and latent variables because of the flexibility of the modelling framework and estimation procedure extensions to ordered categorical outcomes and more complex data structures are straightforward the methods are illustrated by using data from a reproductive toxicity study

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

bd splittings of matrices abstract a new matrix decomposition of real square singular matrices called b d splitting is proposed by extending the notion of b splitting 16 for nonsingular matrices then different convergence and comparison theorems for these splittings are discussed another convergence theorem using a generalized regular splitting is also proved as a result a new characterization of monotone matrices using regular splitting is obtained as a corollary

the possible values of critical points between strongly congruence proper varieties of algebras abstract we denote by con c a the 0 semilattice of all finitely generated congruences of an universal algebra a and we define con c v as the class of all isomorphic copies of all con c a for a v for any variety v of algebras let v and w be locally finite varieties of algebras such that for each finite algebra a v there are up to isomorphism only finitely many b w such that con c a con c b and every such b is finite if con c v con c w then there exists a 0 semilattice of cardinality 2 in con c v con c w our result extends to quasivarieties of first order structures with finitely many relation symbols and relative congruence lattices in particular if w is a finitely generated variety of algebras then this occurs in case w omits the tame congruence theory types 1 and 5 which in turn occurs in case w satisfies a nontrivial congruence identity the bound 2 is sharp

response models for mixed binary and quantitative variables summary a number of special representations are considered for the joint distribution of qualitative mostly binary and quantitative variables in addition to the conditional gaussian models and to conditional gaussian regression chain models some emphasis is placed on models derived from an underlying multivariate normal distribution and on models in which discrete probabilities are specified linearly in terms of unknown parameters the possibilities for choosing between the models empirically are examined as well as the testing of independence and conditional independence and the estimation of parameters often the testing of independence is exactly or nearly the same for a number of different models

positive cones and convergence conditions for iterative methods based on splittings the study of convergence conditions to solve large and sparse linear systems ax b by iterative methods has been discussed by many authors in this paper by using the partial order induced by positivity cone of matrices and conditions on the matrices and splittings we obtain the convergence of the iterative method the usual partial orders of nonnegative matrices and nonnegative definite matrices satisfy the conditions presented for this new order and hence we unify the theory moreover we also show that the new conditions apply to other partial orders as well thus extending the usual convergence theory to a new situation

on the perron frobenius theory for complex matrices abstract we extend here the perron frobenius theory of nonnegative matrices to certain complex matrices following the generalization of the perron frobenius theory to matrices that have some negative entries given by noutsos 14 we introduce here two types of extensions of the perron frobenius theory to complex matrices we present and prove here some sufficient conditions and some necessary and sufficient conditions for a complex matrix to have a perron frobenius eigenpair we apply this theory by introducing perron frobenius splittings as well as complex perron frobenius splittings for the solution of complex linear systems a x b by classical iterative methods perron frobenius splittings constitute an extension of the well known regular splittings weak regular splittings and nonnegative splittings convergence and comparison properties are also given and proved

stability of a three point scheme for linear second order singularly perturbed bvps with turning points in this paper we study stability properties of a numerical method applied to linear second order perturbed boundary value problems with boundary or interior layers the method consists of a three point difference scheme with variable stepsize the stability of which may be investigated by studying that of an lu factorization for the coefficient matrix of a suitable tridiagonal system we also propose a mesh selection strategy for treating boundary and interior layers which furnishes a good mesh on which the three point scheme is stable

multivariate mean parameter estimation by using a partly exponential model summary a class of partly exponential models is proposed for the regression analysis of multivariate response data the class is parameterized in terms of the response mean and a general shape parameter it includes the generalized linear error model and exponential dispersion models as special cases maximum likelihood equations for mean parameters are shown to be of the same form as certain generalized estimating equations and maximum likelihood estimates of mean and shape parameters are asymptotically independent some results are given on the efficiency of the estimating equation procedure under misspecification of the response covariance matrix

tridiagonal matrices invertibility and conditioning abstract tridiagonal matrices arise in a large variety of applications most of the time they are diagonally dominant and this is indeed the case most extensively studied in this paper we study in a unified approach the invertibility and the conditioning of such matrices the results presented provide practical criteria for a tridiagonal and irreducible matrix to be both invertible and well conditioned an application to a singular perturbation boundary value problem is then presented

a scaled linear mixed model for multiple outcomes summary we propose a scaled linear mixed model to assess the effects of exposure and other covariates on multiple continuous outcomes the most general form of the model allows a different exposure effect for each outcome an important special case is a model that represents the exposure effects using a common global measure that can be characterized in terms of effect sizes correlations among different outcomes within the same subject are accommodated using random effects we develop two approaches to model fitting including the maximum likelihood method and the working parameter method a key feature of both methods is that they can be easily implemented by repeatedly calling software for fitting standard linear mixed models e g sas proc mixed compared to the maximum likelihood method the working parameter method is easier to implement and yields fully efficient estimators of the parameters of interest we illustrate the proposed methods by analyzing data from a study of the effects of occupational pesticide exposure on semen quality in a cohort of chinese men

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

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

a new lattice construction the box product in a recent paper the authors have proved that for lattices a and b with zero the isomorphism conc a otimes b cong conc a otimes conc b holds provided that the tensor product satis es a very natural condition of being capped implying that a otimes b is a lattice in general a otimes b is not a lattice for instance we proved that m 3 otimes f 3 is not a lattice in this paper we introduce a new lattice construction the box product for arbitrary lattices the tensor product construction for complete lattices introduced by g n raney in 1960 and by r wille in 1985 and the tensor product construction of a fraser in 1978 for semilattices bear some formal resemblance to the new construction for lattices a and b while their tensor product a otimes b as semilattices is not always a lattice the box product a bp b is always a lattice furthermore the box product and some of its ideals behave like an improved tensor product for example if a and b are lattices with unit then the isomorphism conc a bp b cong conc a otimes conc b holds there are analogous results for lattices a and b with zero and for a bounded lattice a and an arbitrary lattice b a join semilattice s with zero is called 0 representable if there exists a lattice l with zero such that conc l cong s the above isomorphism results yield the following consequence the tensor product of two 0 representable semilattices is 0 representable

correlated bivariate continuous and binary outcomes issues and applications increasingly multiple outcomes are collected in order to characterize treatment effectiveness or to evaluate the impact of large policy initiatives often the multiple outcomes are non commensurate e g measured on different scales the common approach to inference is to model each outcome separately ignoring the potential correlation among the responses we describe and contrast several full likelihood and quasi likelihood multivariate methods for non commensurate outcomes we present a new multivariate model to analyze binary and continuous correlated outcomes using a latent variable we study the efficiency gains of the multivariate methods relative to the univariate approach for complete data all approaches yield consistent parameter estimates when the mean structure of all outcomes depends on the same set of covariates efficiency gains by adopting a multivariate approach are negligible in contrast when the mean outcomes depend on different covariate sets large efficiency gains are realized three real examples illustrate the different approaches

comparison theorems for splittings of matrices this paper investigates the comparisons of asymptotic rates of convergence of two iteration matrices on the basis of nonnegative matrix theory comparisons between two nonnegative splittings and between two parallel multisplitting methods are derived when the coefficient matrix a is hermitian positive semi definite comparison theorems about two p regular splittings and two parallel multisplitting methods are proved

comparisons of regular splittings of matrices in this article new comparison theorems for regular splittings of matrices are derived in so doing the initial results of varga in 1960 on regular splittings of matrices and the subsequent unpublished results of wo nicki in 1973 on regular splittings of matrices will be seen to be special cases of these new comparison theorems

distributive congruence lattices of congruence permutable algebras abstract we prove that every distributive algebraic lattice with at most 1 compact elements is isomorphic to the normal subgroup lattice of some group and to the submodule lattice of some right module the 1 bound is optimal as we find a distributive algebraic lattice d with 2 compact elements that is not isomorphic to the congruence lattice of any algebra with almost permutable congruences hence neither of any group nor of any module thus solving negatively a problem of e t schmidt from 1969 furthermore d may be taken as the congruence lattice of the free bounded lattice on 2 generators in any non distributive lattice variety some of our results are obtained via a functorial approach of the semilattice valued distances used by b jonsson in his proof of whitman s embedding theorem in particular the semilattice of compact elements of d is not the range of any distance satisfying the v condition of type 3 2 on the other hand every distributive 0 semilattice is the range of a distance satisfying the v condition of type 2 this can be done via a functorial construction

a solution to dilworth s congruence lattice problem we construct a distributive algebraic lattice d that is not isomorphic to the congruence lattice of any lattice this solves a long standing open problem traditionally attributed to r p dilworth from the forties the lattice d has compact top element and aleph omega 1 compact elements our results extend to all algebras possessing a polynomially definable structure of a join semilattice with a largest element

optimal dose finding designs with correlated continuous and discrete responses in dose finding clinical studies it is common that multiple endpoints are of interest for instance in phase i ii studies efficacy and toxicity are often the primary endpoints which are observed simultaneously and which need to be evaluated together motivated by this we confine ourselves to bivariate responses and focus on the most analytically difficult case a mixture of continuous and categorical responses we adopt the bivariate probit dose response model and quantify our goal by a utility function we study locally optimal designs two stage optimal designs and fully adaptive designs under different ethical and cost constraints in the experiments we assess the performance of two stage designs and fully adaptive designs via simulations our simulations suggest that the two stage designs are as efficient as and may be more efficient than the fully adaptive designs if there is a moderate sample size in the initial stage in addition two stage designs are easier to construct and implement and thus can be a useful approach in practice copyright 2011 john wiley sons ltd

regular splittings and monotone iteration functions in this paper we introduce the set of so called monotone iteration functions mi functions belonging to a given function we prove necessary and sufficient conditions in order that a given mi function is in a precisely defined sense at least as fast as a second one regular splittings of a function which were initially introduced for linear functions by r s varga in 1960 are generating mi functions in a natural manner for linear functions every mi function is generated by a regular splitting for nonlinear functions however this is generally not the case

on algebraic multi level methods for non symmetric systems comparison results abstract we establish theoretical comparison results for algebraic multi level methods applied to non singular non symmetric m matrices we consider two types of multi level approximate block factorizations or amg methods the amli and the mamli method we compare the spectral radii of the iteration matrices of these methods this comparison shows that the spectral radius of the mamli method is less than or equal to the spectral radius of the amli method moreover we establish how the quality of the approximations in the block factorization effects the spectral radii of the iteration matrices we prove comparisons results for different approximations of the fine grid block as well as for the used schur complement we also establish a theoretical comparison between the amg methods and the classical block jacobi and block gauss seidel methods

tridiagonal splittings in the conditioning and parallel solution of banded linear systems abstract we study the conditioning and the parallel solution of banded linear systems of algebraic equations we propose an iterative method for solving the linear system au b based on a tridiagonal splitting of the real coefficient matrix a which permits the study of the conditioning and the parallel solution of banded linear systems using the theoretical results known for tridiagonal systems sufficient conditions for the convergence of this method are studied and the definition of tridiagonal dominant matrices is introduced observing that for this class of matrices the iterative method converges when the iterative method converges the conditioning of a may be studied using that of its tridagonal part finally we consider a parallel version of this iterative method and show some parallel numerical tests

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

regression models for a bivariate discrete and continuous outcome with clustering abstract developmental toxicity studies of laboratory animals play a crucial role in the testing and regulation of chemicals and pharmaceutical compounds exposure to developmental toxicants typically causes a variety of adverse effects such as fetal malformations and reduced fetal weight at term in this article we discuss regression methods for jointly analyzing bivariate discrete and continuous outcomes that are motivated by the statistical problems that arise in analyzing data from developmental toxicity studies we focus on marginal regression models that is models in which the marginal expectation of the bivariate response vector is related to a set of covariates by some known link functions in these models the regression parameters for the marginal expectation are of primary scientific interest whereas the association between the binary and continuous response is considered to be a nuisance characteristic of the data we describe a likelihood based approach based on the general location mode

exact convergence and divergence domains for the symmetric successive overrelaxation iterative ssor method applied to h matrices abstract in this paper exact convergence and divergence domains for the ssor iterative method as applied to the class of h matrices are obtained the theory of regular splittings and the recent results of varga niethammer and cai are used as tools in establishing these convergence and divergence domains

a nice labelling for tree like event structures of degree 3 we address the problem of finding nice labellings for event structures of degree 3 we develop a minimum theory by which we prove that the index of an event structure of degree 3 is bounded by a linear function of the height the main theorem of the paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors we exemplify how to use this theorem to construct upper bounds for the index of other event structures of degree 3

estimates for the inverse of tridiagonal matrices arising in boundary value problems by considering tridiagonal matrices as three term recurrence relations with dirichlet boundary conditions one can formulate their inverses in terms of green s functions this analysis is applied to three point difference schemes for 1 d problems and five point difference schemes for 2 d problems we derive either an explicit inverse of the jacobian or a sharp estimate for both uniform and nonuniform grids

conditions for strict inequality in comparisons of spectral radii of splittings of different matrices we present new comparison theorems for the spectral radii of matrices arising from splittings of different matrices under nonnegativity assumptions our focus is on establishing strict inequalities of the spectral radii without imposing strict inequalities of the matrices but we also obtain new results for nonstrict inequalities of the spectral radii we emphasize two different approaches one combinatorial and the other analytic and discuss their merits in the light of the results obtained we try to get fairly general results and indicate by counter examples that some of our hypotheses cannot be relaxed in certain directions

on domains of superior convergence of the ssor method to that of the sor method let v denote the spectral radius of jab the block jacobi iteration matrix for the classes of 1 nonsingular m matrices and 2 p cyclic p 3 consistently ordered matrices we study domains in the v plane when v 1 where the block ssor iteration method has at least as favorable an asymptotic rate of convergence as the block sor method let la and sa denote respectively the block sor and ssor iteration matrices for the class of nonsingular m matrices a we determine conditions when the spectral radii satisfy sa la 0 21 v and 0 v 1 under these conditions we also show that the optimal sor iteration parameter is b 1 for the class of p cyclic p 3 consistently ordered matrices a we determine for which s and v s sa 1 la our investigations make use of the equality case in wielandt s inequality between the spectral radii of a complex matrix and its nonnegative and irreducible majorizers and of rouche s theorem for the location of zeros of complex functions

optimization of the spectral radius of a product for nonnegative matrices abstract let a be an n n irreducible nonnegative matrix we show that over the set n of all n n doubly stochastic matrices s the multiplicative spectral radius sa attains a minimum and a maximum at a permutation matrix for the case when a is a symmetric nonnegative matrix a by product of our technique of proof yields a result allowing us to show that s 1 a s 2 a when s 1 and s 2 are two symmetric matrices such that both s 1 a and s 2 a are nonnegative matrices and s 1 s 2 is a positive semidefinite matrix this result has several corollaries one corollary is that s 1 a s 2 a when s 1 1 n j and s 2 1 n 1 j i where j is the matrix of all 1 s a second corollary is a comparison theorem for weak regular splittings of two monotone matrices

comparison theorems for the convergence factor of iterative methods for singular matrices abstract iterative methods for the solution of consistent singular systems of linear equations are governed by the convergence factor of the iteration matrix t i e by the quantity t max t 1 where t is the spectrum of t theorems are presented comparing the convergence factor of two iterative methods the comparison is based on the relationship between the matrices of the splittings a cone other than the usual nonnegative hyperoctant is used to define the order used in this comparison although this cone is based on the unknown projection onto the null space of a matrix the characterization provided in the paper allows in specific instances the cone to be readily computable

bounds for the solutions of a class of tridiagonal linear systems we derive bounds for the solution of an irreducible tridiagonal linear system of dimension n which arises in many areas of numerical analysis the conditions for which the linear system is invertible and its solution bounded by a constant independent of n or dependent weakly on n are established the results derived are strictly related to the study of the condition number for the coefficient matrix of the system two examples which lead to this kind of linear systems are given the second of which derives from the solution of boundary value problems by means of difference methods

a note on comparison theorems for nonnegative matrices in a recent paper 4 csordas and varga have unified and extended earlier theorems of varga in 10 and wo nicki in 11 on the comparison of the asymptotic rates of convergence of two iteration matrices induced by two regular splittings the main purpose of this note is to show a connection between the csordas varga paper and a paper by beauwens 1 in which a comparison theorem is developed for the asymptotic rate of convergence of two nonnegative iteration matrices induced by two splittings which are not necessarily regular monotonic norms already used in 1 play an important role in our work here

comparisons of weak regular splittings and multisplitting methods comparison results for weak regular splittings of monotone matrices are derived as an application we get upper and lower bounds for the convergence rate of iterative procedures based on multisplittings this yields a very simple proof of results of neumann plemmons on upper bounds and establishes lower bounds which has in special cases been conjectured by these authors

comparison theorems for weak splittings in respect to a proper cone of nonsingular matrices the asymptotic rates of convergence of two iteration matrices induced by two splittings of the same nonsingular matrix have been compared in the works of many authors in this paper new comparison theorems which extend song s results y song numer math 65 1993 245 252 for weak splittings of the same or different types are presented these new comparison theorems are derived by using nonnegativity in respect to a proper cone k n ew converses which partially solve an open question asked by v a miller m neumann numer math 47 1985 427 434 are also presented 1999 elsevier science inc all rights reserved

multivariate linear mixed models for multiple outcomes we propose a multivariate linear mixed mlmm for the analysis of multiple outcomes which generalizes the latent variable model of sammel and ryan the proposed model assumes a flexible correlation structure among the multiple outcomes and allows a global test of the impact of exposure across outcomes in contrast to the sammel ryan model the mlmm separates the mean and correlation parameters so that the mean estimation will remain reasonably robust even if the correlation is misspecified the model is applied to birth defects data where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls

copula based regression models for a bivariate mixed discrete and continuous outcome this paper is concerned with regression models for correlated mixed discrete and continuous outcomes constructed using copulas our approach entails specifying marginal regression models for the outcomes and combining them via a copula to form a joint model specifically we propose marginal regression models e g generalized linear models to link the outcomes marginal means to covariates to account for associations between outcomes we adopt the gaussian copula to indirectly specify their joint distributions our approach has two advantages over current methods one regression parameters in models for both outcomes are marginally meaningful and two the association is margin free in the sense that it is characterized by the copula alone by assuming a latent variable framework to describe discrete outcomes the copula used still uniquely determines the joint distribution in addition association measures between outcomes can be interpreted in the usual way we report results of simulations concerning the bias and efficiency of two likelihood based estimation methods for the model finally we illustrate the model using data on burn injuries

regression models for mixed discrete and continuous responses with potentially missing values in this paper a likelihood based method for analyzing mixed discrete and continuous regression models is proposed we focus on marginal regression models that is models in which the marginal expectation of the response vector is related to covariates by known link functions the proposed model is based on an extension of the general location model of olkin and tate 1961 annals of mathematical statistics 32 448 465 and can accommodate missing responses when there are no missing data our particular choice of parameterization yields maximum likelihood estimates of the marginal mean parameters that are robust to misspecification of the association between the responses this robustness property does not in general hold for the case of incomplete data there are a number of potential benefits of a multivariate approach over separate analyses of the distinct responses first a multivariate analysis can exploit the correlation structure of the response vector to address intrinsically multivariate questions second multivariate test statistics allow for control over the inflation of the type i error that results when separate analyses of the distinct responses are performed without accounting for multiple comparisons third it is generally possible to obtain more precise parameter estimates by accounting for the association between the responses finally separate analyses of the distinct responses may be difficult to interpret when there is nonresponse because different sets of individuals contribute to each analysis furthermore separate analyses can introduce bias when the missing responses are missing at random mar a multivariate analysis can circumvent both of these problems the proposed methods are applied to two biomedical datasets

spectral spaces of countable abelian lattice ordered groups a compact topological space x is spectral if it is sober i e every irreducible closed set is the closure of a unique singleton and the compact open subsets of x form a basis of the topology of x closed under finite intersections theorem a topological space x is homeomorphic to the spectrum of some countable abelian l group with unit resp mv algebra iff x is spectral has a countable basis of open sets and for any points x and y in the closure of a singleton z either x is in the closure of y or y is in the closure of x we establish this result by proving that a countable distributive lattice d with zero is isomorphic to the lattice of all principal ideals of an abelian l group we say that d is l representable iff for all a b d there are x y d such that a b a y b x and x y 0 on the other hand we construct a non l representable bounded distributive lattice of cardinality 1 with an l representable countable l elementary sublattice in particular there is no characterization of the class of all l representable distributive lattices in arbitrary cardinality by any class of l sentences

a note on weak splittings of matrices in this note an open question proposed by marek and szyld is solved i marek d b szyld comparison theorems for weak splittings of bounded operators numer math 58 1990 387 397 at the same time some new comparison theorems are presented

parallel factorizations for tridiagonal matrices the authors analyze the problem of solving tridiagonal linear systems on parallel computers a wide class of efficient parallel solvers is derived by considering different parallel factorizations of partitioned matrices these solvers have a minimum requirement of data transmission in fact communication is only needed for solving a reduced system whose dimension depends on the number of parallel processors used moreover for a given partitioned tridiagonal matrix the reduced system which is again tridiagonal is the same and represents the only sequential part of the corresponding parallel solver three examples are discussed in more detail one of them derives a very efficient parallel method based on the cyclic reduction algorithm

new convergence results for alternating methods abstract the alternating methods for solving the large system of linear equations ax b are investigated the convergence and the monotone convergence theories for the alternating method are formulated when the coefficient matrix is an h matrix or a monotone matrix sufficient conditions are established for the induced splitting by the alternating method to be a regular splitting furthermore new comparison theorems which improve previous comparison theorems are proved and several concrete applications are given

on stein rosenberg type theorems for nonnegative and perron frobenius splittings abstract the stein rosenberg theorem is extended and generalized to the class of nonnegative splittings a m 1 n 1 m 2 n 2 as well as to the most generalized class of perron frobenius splittings two types of the stein rosenberg theorem are stated and proved for both classes these theorems allow us to obtain comparison results for the rate of convergence of the associated iterative methods specific assumptions are given under which the inequalities of the spectral radii become equalities or strict inequalities the theoretical results are confirmed by numerical examples

semilattices of finitely generated ideals of exchange rings with finite stable rank we find a distributive v 0 1 semilattice s of size aleph 1 that is not isomorphic to the maximal semilattice quotient of any riesz monoid endowed with an order unit of finite stable rank we thus obtain solutions to various open problems in ring theory and in lattice theory in particular there is no exchange ring thus no von neumann regular ring and no c algebra of real rank zero with finite stable rank whose semilattice of finitely generated idempotent generated two sided ideals is isomorphic to s there is no locally finite modular lattice whose semilattice of finitely generated congruences is isomorphic to s these results are established by constructing an infinitary statement denoted here by urpsr that holds in the maximal semilattice quotient of every riesz monoid endowed with an order unit of finite stable rank but not in the semilattice s

the possible values of critical points between varieties of lattices abstract we denote by con c l the 0 semilattice of all finitely generated congruences of a lattice l for varieties i e equational classes v and w of lattices such that v is contained neither in w nor in its dual and such that every simple member of w contains a prime interval we prove that there exists a bounded lattice a v with at most 2 elements such that con c a is not isomorphic to con c b for any b w the bound 2 is optimal as a corollary of our results there are continuum many congruence classes of locally finite varieties of bounded modular lattices

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

multivariate analysis of longitudinal ordinal data with mixed effects models with application to clinical outcomes in osteoarthritis our objective was to evaluate the efficacy of robenacoxib in osteoarthritic dogs using four ordinal responses measured repeatedly over time we propose a multivariate probit mixed effects model to describe the joint evolution of endpoints and to evidence the intrinsic correlations between responses that are not due to treatment effect maximum likelihood computation is intractable within reasonable time frames we therefore use a pairwise modeling approach in combination with a stochastic em algorithm multidimensional ordinal responses with longitudinal measurements are a common feature in clinical trials however the standard methods for data analysis use unidimensional models resulting in a loss of information our methodology provides substantially greater insight than these methods for the evaluation of treatment effects and shows a good performance at low computational cost we thus believe that it could be used in routine practice to optimize the evaluation of treatment efficacy

explicit and asymptotic formulas for ldmt factorization of banded toeplitz matrices abstract we study the ldmt factorization of banded toeplitz matrices we show that under fairly general conditions the l m and d factors exhibit exponential convergence along diagonals we also give explicit formulas for the limiting values our method of proof involves a generalization to matrices of the theory of continued fractions of quadratic irrationals