analysis of rank measures of association for ordinal data from longitudinal studies abstract consideration is given to longitudinal data settings in which an ordinal response variable is observed at two or more visits for each subject in two or more ordered groups with at least moderately large sample sizes e g overall n 40 rank measures of association between group and response are constructed at each time and the covariance matrix of these measures is also estimated variation among the rank measures of association is then analyzed through weighted least squares methods with weights based on the estimated covariance matrix such methods permit evaluation of group visit interaction as well as other effects of interest extensions of this type of analysis to situations with stratification or concomitant variables or missing data are also considered examples are provided for illustrative purposes

multivariate non parametric methods for mann whitney statistics to analyse cross over studies with two treatment sequences a non parametric strategy for the analysis of ordinal data from cross over studies with two treatment sequences and d or 2 periods is examined through mann whitney rank measures of association for each period these statistics estimate the probability of larger response for a randomly selected patient in one group relative to a randomly selected patient in the other group such estimates are as well formed for comparisons between groups for u pairs of periods with the same treatment methods for u statistics are used to produce a consistent estimate of the covariance matrix for the d u mann whitney estimates the effects of periods and treatments on the respective mann whitney estimates are evaluated through linear or log linear models for estimation of the parameters in these models a modified weighted least squares method is applied through a 2d 1 or d u dimensional basis which effectively addresses potentially near singularities in the estimated covariance matrix of the mann whitney estimates the proposed methods are applicable to response variables with an interval or an ordered categorical scale their scope additionally has capabilities for controlling strata in the design of a cross over study or concomitant variables for which covariance adjustment is of interest for reduction of variance applications of the methods are illustrated through three cross over studies with different specifications for the two sequences of two treatments during two to four periods

homogeneous linear predictor models for contingency tables maximum likelihood ml inference for the class of homogeneous linear predictor hlp models for contingency tables is described hlp models constrain the expected table counts m through l m x where the link l is allowed to be a many to one nonlinear function generalized log linear association trend marginal cumulative probit and conditional marginal homogeneity models are given as specific examples ml fit results which include point estimates goodness of fit statistics and asymptotic based approximate distributions are described and compared for equivalent hlp models the results are valid for a wide variety of sampling plans including combinations of product multinomial and poisson sampling an important practical implication of this article is that the implementation of ml fitting and theory is straightforward and an attractive alternative to weighted least squares estimation for hlp models

analysing repeated measurements with possibly missing observations by modelling marginal distributions suppose that subjects are observed repeatedly over a common set of time points with possibly time dependent covariates and possibly missing observations at each time point we model the marginal distribution of the response variable and the effect of the covariates on that distribution using a class of quasi likelihood models studied in mccullagh and nelder no parametric model of dependence of the repeated observations of the subject is assumed for large samples the quasi likelihood estimates of the time specific regression coefficients over the set of predetermined time points are shown to be approximately jointly normal this coupled with various inference procedures provides a global picture about the effects of the covariates on the response variable over the entire study period a lack of fit test for testing the adequacy of the assumed quasi likelihood model is also provided all the methods considered here are illustrated with real life examples

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

on λ pure acyclic complexes in a grothendieck category abstract let a be a grothendieck category we prove that there is an infinite regular cardinal such that a has pure injective envelopes furthermore we show that any pure acyclic complex in a is a directed union of contractible subcomplexes this provides an answer to a question which is conjectured by simson in 14 conjecture 3 4

nesting inertial manifolds for reaction and diffusion equations with large diffusivity we study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations a priori we review both local and global dynamics of the system in scales of banach spaces of hilbert type and we prove the existence of a universal compact attractor for the equations extensions yield the existence of a family of nesting inertial manifolds dependent on the diffusion of the system of equations it is introduced an upper semicontinuity notion in large diffusivity for inertial manifolds the limit inertial manifold whose dimension is strictly less than those of the infinite dimensional system of semilinear evolution equations is obtained

maximum likelihood variance components estimation for binary data abstract we consider a class of probit normal models for binary data and describe ml and reml estimation of variance components for that class as well as best prediction for the realized values of the random effects ml estimates are calculated using an em algorithm for complicated models em includes a gibbs step the computations are illustrated through two examples

combining dependent tests with incomplete repeated measurements summary in comparing the effectiveness of two treatments repeated measurements of the same characteristic are often taken under two or more distinct conditions for each experimental subject a locally best linear combination of individual test statistics obtained under different conditions is proposed to test the equality of the two treatments the test procedure allows different patterns of missing observations for the two groups to be compared special cases such as combining wilcoxon tests t tests and 2 x 2 tables are discussed in detail with real examples

flat complexes pure periodicity and pure acyclic complexes abstract the paper can be viewed as an addition and extension of the recent paper of emmanouil 2016 5 among others an alternative functor category approach to emmanouil s results is presented by applying an idea of neeman 2008 16 and the main results obtained there we prove that a chain complex f in a locally finitely presented grothendieck category a is pure acyclic if and only if any chain map f p f from a complex p of pure projective objects in a to f is null homotopic as a consequence we prove that any pure periodic object in a is pure projective moreover we show that a is pure semisimple if and only if a has the pure qf property that is every pure injective object in a is pure projective

a survey of models for repeated ordered categorical response data we survey models for analysing repeated observations on an ordered categorical response variable the models presented are univariate models that permit correlation among repeated measurements the models describe simultaneously the dependence of marginal response distributions on values of explanatory variables and on the occasion of response we present models for three transformations of the response distribution cumulative logits adjacent category logits and the mean for scores assigned to response categories we discuss three methods for fitting the models maximum likelihood weighted least squares and semi parametric weighted least squares is easily implemented with sas as illustrated with a study designed to compare a drug with a placebo for the treatment of insomnia

the analysis of panel data under a markov assumption abstract methods for the analysis of panel data under a continuous time markov model are proposed we present procedures for obtaining maximum likelihood estimates and associated asymptotic covariance matrices for transition intensity parameters in time homogeneous models and for other process characteristics such as mean sojourn times and equilibrium distributions generalizations to handle covariance analysis and to the fitting of certain nonhomogeneous models are presented and an example based on a longitudinal study of the smoking habits of school children is discussed questions of embeddability and estimation are examined

impact of missing data due to drop outs on estimators for rates of change in longitudinal studies a simulation study many cohort studies and clinical trials are designed to compare rates of change over time in one or more disease markers in several groups one major problem in such longitudinal studies is missing data due to patient drop out the bias and efficiency of six different methods to estimate rates of changes in longitudinal studies with incomplete observations were compared generalized estimating equation estimates gee proposed by liang and zeger 1986 unweighted average of ordinary least squares olse of individual rates of change uwls weighted average of olse wls conditional linear model estimates cle a covariate type estimates proposed by wu and bailey 1989 random effect re and joint multivariate re jmre estimates the latter method combines a linear re model for the underlying pattern of the marker with a log normal survival model for informative drop out process the performance of these methods in the presence of missing data completely at random mcar at random mar and non ignorable nim were compared in simulation studies data for the disease marker were generated under the linear random effects model with parameter values derived from realistic examples in hiv infection rates of drop out assumed to increase over time were allowed to be independent of marker values or to depend either only on previous marker values or on both previous and current marker values under macr all six methods yielded unbiased estimates of both group mean rates and between group difference however the cross sectional view of the data in the gee method resulted in seriously biased estimates under mar and nim drop out process the bias in the estimates ranged from 30 per cent to 50 per cent the degree of bias in the gee estimates increases with the severity of non randomness and with the proportion of mar data under mcar and mar all the other five methods performed relatively well re and jmre estimates were more efficient that is had smaller variance than uwls wls and cl estimates under nim wls and particularly re estimates tended to underestimate the average rate of marker change bias approximately 10 per cent under nim uwls cl and jmre performed better in terms of bias 3 5 per cent with the jmre giving the most efficient estimates given that markers are key variables related to disease progression missing marker data are likely to be at least mar thus the gee method may not be appropriate for analysing such longitudinal marker data the potential biases due to incomplete data require greater recognition in reports of longitudinal studies sensitivity analyses to assess the effect of drop outs on inferences about the target parameters are important

a combined score test for binary and ordinal endpoints from clinical trials there is growing interest especially for trials in stroke in combining multiple endpoints in a single clinical evaluation of an experimental treatment the endpoints might be repeated evaluations of the same characteristic or alternative measures of progress on different scales often they will be binary or ordinal and those are the cases studied here in this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each endpoint the correlations between the score statistics are derived and used to allow a valid combined score test to be applied a sample size formula is deduced and application in sequential designs is discussed the method is compared with an alternative approach based on generalized estimating equations in an illustrative analysis and replicated simulations and the advantages and disadvantages of the two approaches are discussed

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

the analysis of longitudinal polytomous data generalized estimating equations and connections with weighted least squares in recent years methods have been developed for modelling repeated observations of a categorical response obtained over time on the same individual although situations in which the repeated response is binary or poisson have been studied extensively relatively little attention has been given to polytomous categorical response variable in this paper we extend the estimating equations initially developed for clustered discrete data by liang and zeger 1986 biometrika 73 13 22 and subsequently extended by prentice 1988 biometrics 44 1033 1048 to polytomous response variables under certain assumptions we illustrate that these estimating equations simplify to the weighted least squares wls equations formalized by koch et al 1977 biometrics 33 133 158 this connection provides a formal framework for obtaining iterated weighted least squares model parameter estimates cumulative logit models are developed and applied to a representative longitudinal data set simulation results comparing wls an iterative form of wls and independence estimating equations using a robust estimate of the variance are presented

parabolic problems with nonlinear boundary conditions and critical nonlinearities we prove existence uniqueness and regularity of solutions for heat equations with nonlinear boundary conditions we study these problems with initial data in l q omega w 1 w q omega 1 q infinity or measures and with critically growing non linearities

modelling transitional and joint marginal distributions in repeated categorical data when a repeated measures endpoint classifies people into several categories marginal and transitional models provide two distinct approaches for data analysis marginal models estimate the probabilities of being in different categories over time transitional models estimate the probability of changing between any two given states during follow up visits this paper develops transitional and marginal models and applies them to a clinical trial of treatments of opiate addiction the primary outcome was the presence or absence of opiates in a thrice weekly urine test administered for 17 weeks subjects frequently miss visits however and in effect respond in one of three ways to a visit missing opiates present or opiates absent thus we have three possible states our transitional model conditions on the current state and models the transition from state k to one of the other 0 k 1 states using a mutinomial logit model this model generalizes previous work of muenz and rubinstein significant covariates in this model are predictive of state changes our marginal model views the state at each time point rather than the transitions as the primary response here we model the probability of being in state k with a multinomial logit model correlation within individuals over visits can be handled by applying the approach of zeger and liang or the bootstrap significant covariates in this model can include more global summaries of a person such as extent of previous opiate use both marginal and transitional models are needed to provide a complete description of an individual s behaviour over time since global summaries might not affect transitions of particular substantive interest is how the opiate treatments affect both the marginal and transition probabilities

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

a review of some statistical methods for covariance analysis of categorical data three general methods for covariance analysis of categorical data are reviewed and applied to an example from a clinical trial in rheumatoid arthritis the three methods considered are randomization model nonparametric procedures maximum likelihood logistic regression and weighted least squares analysis of correlated marginal functions a fourth heuristic approach the unweighted linear model analysis is an approximate procedure but it is easy to implement the assumptions and statistical issues for each method are discussed so as to emphasize philosophical differences between their rationales attention is given to computational differences but it is shown that the methods lead to similar results for analogous problems it is argued that the essential differences between the methods lie in their underlying assumptions and the generality of the conclusions which may be drawn

randomization model methods for evaluating treatment efficacy in multicenter clinical trials summary this paper studies randomization model methods for analyzing data from a multicenter study comparing the effectiveness of two treatments the mantel haenszel mean score statistic which can be used for continuous or ordered categorical response variables is shown to be a useful nonparametric alternative to standard linear model methods for testing the significance of the average treatment difference in an extensive simulation study the mean score test performs nearly as well as the optimal linear model methods when the normal theory assumptions are satisfied a related estimator of the average treatment difference is also studied this estimator which is a weighted average of the center specific mean differences is analogous to the commonly used mantel haenszel estimator of the average odds ratio in stratified 2 x 2 contingency tables the proposed estimator is equivalent to the fixed effects analysis of variance estimator from the main effects model and valid estimation of its variance is feasible under very general assumptions a frequently occurring problem in medical research is evaluation of the effectiveness of a new treatment in patients with a specified disease or condition one commonly used design involves selection of eligible patients randomization to one of two groups new therapy standard treatment measurement of an appropriate outcome variable following treatment and statistical comparison of the distribution of the outcome in the two groups since the number of eligible patients at any one center may be relatively small such clinical trials often involve the participation of multiple investigators in this case patients are randomized within each center the objectives of the data analysis are to test if there is a statistically significant difference between the two treatments and to estimate the magnitude of the average treatment difference for both objectives it is important to control for the fact that the data are from multiple centers if the outcome variable is normally distributed standard linear model methods are often used to test and estimate the treatment difference one issue that arises in such an analysis however concerns whether the center effect should be treated as fixed or random in the fixed effects model both treatment group and center are considered to be fixed effects and the assumption is made that subjects are randomly selected from the center specific patient populations this model permits statistical inferences to the patient populations associated with the participating centers the mixed model approach treats the treatment group as a fixed effect and the center as a random effect although statistical inferences to a larger population of centers are permitted it makes the strong assumption that centers are selected at random in practice very few if any study protocols incorporate either random selection of centers or random selection of patients within centers thus neither the mixed model nor the fixed effects linear model can be strictly justified in addition although the fixed effects two way analysis of variance anova model with effects for center and treatment is commonly used there is no consensus among statisticians as to whether the model should include the center by treatment interaction this is partially due to the fact that patient enrollment often varies considerably among centers whereas the estimator of the average treatment difference from the main effects model

semigroups and nonlinear evolution equations abstract in the main part of this paper we survey some recent results on a semigroup approach to parabolic equations under nonlinear boundary conditions in particular we give a detailed motivation and a heuristic derivation of a generalized variation of constant formula which is the basis for the whole method in the appendix we prove some new results about semigroups in interpolation and extrapolation spaces

a comparison of likelihood based and marginal estimating equation methods for analysing repeated ordered categorical responses with missing data application to an intervention trial of vitamin prophylaxis for oesophageal dysplasia the purpose of this research was to develop appropriate methods for analysing repeated ordinal categorical data that arose in an intervention trial to prevent oesophageal cancer the measured response was the degree of oesophageal dysplasia at 2 5 and 6 years after randomization an important feature was that some response measurements were missing and the missingness was not completely at random mcar we show that standard likelihood based methods and standard methods based on marginal estimating equations yield biased results and we propose adaptations to both these approaches that yield valid inference under the weaker missing at random mar assumption on the basis of efficiency calculations simulation studies of finite sample properties ease of computation and flexibility for testing and exploring a range of treatment models we recommend the adapted likelihood based approach for problems of this type in which there are abundant data for estimating parameters

analysis of repeated ordered categorical outcomes with possibly missing observations and time dependent covariates abstract this article describes a method for comparing responses in two groups of subjects observed repeatedly at a common set of observation times when the response is an ordered categorical outcome the method which allows both time dependent covariates and missing observations consists of two analytic steps in the first step the data are analyzed separately at each occasion using a regression model chosen from the class of models for ordinal data proposed by mccullagh 1980 the joint asymptotic distribution of the estimates of these occasion specific regression coefficients and a consistent estimator of their asymptotic covariance matrix are obtained without imposing any parametric model of dependence on the repeated observations in the second step this asymptotic distribution together with appropriate simultaneous inference procedures is used to characterize the overall difference between groups and the variation in group differences over time the missing data process may differ between gro

some general methods for the analysis of categorical data in longitudinal studies this paper is concerned with the analysis of multivariate categorical data from epidemiologic and clinical studies with longitudinal designs an expository discussion of pertinent hypotheses for such situations is provided within the context of two relevant data sets appropriate large sample tests of these hypotheses are developed through the application of weighted least squares to generate wald statistics these procedures are illustrated with extensive analyses of one of these data sets in some situations the resulting cross classification of the response variables leads to extremely sparse frequency data especially when the number of subjects is not large for such repeated measurement designs in which a single variable is measured repeatedly over time this paper considers the use of a generalized mantel haenszel strategy for tests of marginal homogeneity symmetry these randomization model methods are illustrated for data in which the repeated measurement variable is reported on an ordinal scale this paper also focuses on the available computing software to implement these methods within the version 5 release of the sas system the randomization model approach can be implemented within the freq procedure and a broad range of models and hypotheses can be investigated within the catmod procedure

some large sample distribution free estimators and tests for multivariate partially incomplete data from two populations the most common instance of multivariate observations is the case of repeated measures over time the two most widely used methods for the analysis of k repeated measures for two groups are the k degrees of freedom d f t2 manova f test and the within subjects 1 degree of freedom anova f test both require complete samples from normally distributed populations in this paper i describe alternative k and 1 d f distribution free procedures which allow for randomly missing observations these include a large sample analysis of means the wei and lachin multivariate wilcoxon test with estimates of the mann whitney parameter and a multivariate hodges lehmann location shift estimator based on the multivariate u statistic of wei and johnson each of these methods provides a distribution free k variate estimate of the magnitude of group differences which can be used as the basis for an overall test of group differences these tests include the k d f omnibus t2 like test 1 d f tests of restricted hypotheses such as the wei lachin multivariate one sided test of stochastic ordering and the test of general association based on a minimum variance generalized least squares gls estimate of the average group difference i then describe covariate stratified adjusted gls estimates and tests of group differences this approach also provides tests of homogeneity interaction for within subjects and between subjects effects i illustrate these analyses with an analysis of repeated cholesterol measurements in two groups of patients stratified by sex such analyses provide an overall distribution free summary estimate and test of the treatment effect obtained by combining the group differences over both time repeated measures and strata

large sample properties of matching estimators for average treatment effects matching estimators for average treatment effects are widely used in evaluation research despite the fact that their large sample properties have not been established in many cases the absence of formal results in this area may be partly due to the fact that standard asymptotic expansions do not apply to matching estimators with a fixed number of matches because such estimators are highly nonsmooth functionals of the data in this article we develop new methods for analyzing the large sample properties of matching estimators and establish a number of new results we focus on matching with replacement with a fixed number of matches first we show that matching estimators are not n 1 2 consistent in general and describe conditions under which matching estimators do attain n 1 2 consistency second we show that even in settings where matching estimators are n 1 2 consistent simple matching estimators with a fixed number of matches do not attain the semiparametric efficiency bound third we provide a consistent estimator for the large sample variance that does not require consistent nonparametric estimation of unknown functions software for implementing these methods is available in matlab stata and r

nonparametric analysis of covariance by matching the basic problem under consideration is the comparison of treatments with respect to a response y when a covariable x is taken into account various methods involving matching may be regarded as compromises between the standard analysis of covariance and the standard analysis of independent matched pairs first there is no need to restrict attention to independent matched pairs but rather all matched pairs may be incorporated then if x is concomitant that is if its distribution is the same regardless of treatment methods may be used which are based ultimately on randomization although in practice they are based on analysis of variance when x is not concomitant methods related to partial correlation between y and treatment given x are applicable all methods considered may use either the actual magnitudes of y or analogues of their ranks

on pure acyclic complexes abstract in this paper we study the pure acyclic complexes of modules we obtain several characterizations of these complexes extending results that are known for the pure acyclic complexes of flat modules in particular we extend neeman s characterization 18 of the pure acyclic complexes of flat modules in terms of complexes of projective modules by considering more generally complexes of pure projective modules as a consequence we obtain simson s result 22 on the pure projectivity of pure periodic modules

a repeated measures concordance correlation coefficient the concordance correlation coefficient is commonly used to assess agreement between two raters or two methods of measuring a response when the data are measured on a continuous scale however the situation may arise in which repeated measurements are taken for each rater or method e g longitudinal studies in clinical trials or bioassay data with subsamples this paper proposes a coefficient for measuring agreement between two raters or two methods of measuring a response in the presence of repeated measurements we illustrate the methodology with examples comparing 1 1 hr versus 2 hr blood draws for measuring cortisol in an asthma clinical trial and 2 two measurements of percentage body fat from skinfold calipers and dual energy x ray absorptiometry

goodman and kruskal s gamma coefficient for ordinalized bivariate normal distributions we consider a bivariate normal distribution with linear correlation formula see text whose random components are discretized according to two assigned sets of thresholds on the resulting bivariate ordinal random variable one can compute goodman and kruskal s gamma coefficient formula see text which is a common measure of ordinal association given the known analytical monotonic relationship between pearson s formula see text and kendall s rank correlation formula see text for the bivariate normal distribution and since in the continuous case kendall s formula see text coincides with goodman and kruskal s formula see text the change of this association measure before and after discretization is worth studying we consider several experimental settings obtained by varying the two sets of thresholds or equivalently the marginal distributions of the final ordinal variables this study confirming previous findings shows how the gamma coefficient is always larger in absolute value than kendall s rank correlation this discrepancy lessens when the number of categories increases or given the same number of categories when using equally probable categories based on these results a proposal is suggested to build a bivariate ordinal variable with assigned margins and goodman and kruskal s formula see text by ordinalizing a bivariate normal distribution illustrative examples employing artificial and real data are provided

a new nonparametric approach for baseline covariate adjustment for two group comparative studies we consider two armed clinical trials in which the response and or the covariates are observed on either a binary ordinal or continuous scale a new general nonparametric np approach for covariate adjustment is presented using the notion of a relative effect to describe treatment effects the relative effect is defined by the probability of observing a higher response in the experimental than in the control arm the notion is invariant under monotone transformations of the data and is therefore especially suitable for ordinal data for a normal or binary distributed response the relative effect is the transformed effect size or the difference of response probability respectively an unbiased and consistent np estimator for the relative effect is presented further we suggest a np procedure for correcting the relative effect for covariate imbalance and random covariate imbalance yielding a consistent estimator for the adjusted relative effect asymptotic theory has been developed to derive test statistics and confidence intervals the test statistic is based on the joint behavior of the estimated relative effect for the response and the covariates it is shown that the test statistic can be used to evaluate the treatment effect in the presence of random covariate imbalance approximations for small sample sizes are considered as well the sampling behavior of the estimator of the adjusted relative effect is examined we also compare the probability of a type i error and the power of our approach to standard covariate adjustment methods by means of a simulation study finally our approach is illustrated on three studies involving ordinal responses and covariates

the analysis of binary longitudinal data with time independent covariates summary this paper considers extensions of logistic regression to the case where the binary outcome variable is observed repeatedly for each subject we propose two working models that lead to consistent estimates of the regression parameters and of their variances under mild assumptions about the time dependence within each subject s data the efficiency of the proposed estimators is examined an analysis of stress in mothers with infants is presented to illustrate the proposed method

simultaneously modeling joint and marginal distributions of multivariate categorical responses abstract we discuss model fitting methods for analyzing simultaneously the joint and marginal distributions of multivariate categorical responses the models are members of a broad class of generalized logit and loglinear models we fit them by improving a maximum likelihood algorithm that uses lagrange s method of undetermined multipliers and a newton raphson iterative scheme we also discuss goodness of fit tests and adjusted residuals and give asymptotic distributions of model parameter estimators for this class of models inferences are equivalent for poisson and multinomial sampling assumptions simultaneous models for joint and marginal distributions may be useful in a variety of applications including studies dealing with longitudinal data multiple indicators in opinion research cross over designs social mobility and inter rater agreement the models are illustrated for one such application using data from a recent general social survey regarding opinions about various types of government s

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

regularity and asymptotic behavior for the second order parabolic equation with nonlinear boundary conditions in lp abstract the equation lu x u on b 0 b bounded smooth domain in r n with nonlinear boundary conditions u v g x u on b 0 is studied l being the uniformly parabolic operator with time independent coefficients under suitable conditions on the nonlinearities that do not involve monotonicity global existence uniqueness compactness of the orbits and certain regularizing effects of the semigroup are established in the case that l is in divergence form it is shown that under generic conditions orbits tend as t to some equilibrium and that the stable equilibria attract essentially baire category the whole space l2 b

a test of the missing data mechanism for repeated categorical data due to the occurrence of missing observations longitudinal data are rarely balanced and complete weighted least squares analyses described by grizzle starmer and koch 1969 biometrics 25 489 504 have been developed for the analysis of incomplete longitudinal categorical data stanish gillings and koch 1978 biometrics 34 305 317 woolson and clarke 1984 journal of the royal statistical society series a 147 87 99 however all these analyses have assumed that missing observations are missing completely at random in the sense of rubin 1976 biometrika 63 581 592 when the occurrence of missing observations is related to the unobserved response values these analyses may result in biased results in this paper we develop a simple and practical test of the missing mechanism in incomplete repeated categorical data the proposed test is an extension of the test of little 1988 journal of the american statistical association 83 1198 1202 and uses a test criterion given in general form by wald the test is illustrated using data from a longitudinal investigation of obesity in school age children

markov models for covariate dependence of binary sequences suppose that a heterogeneous group of individuals is followed over time and that each individual can be in state 0 or state 1 at each time point the sequence of states is assumed to follow a binary markov chain in this paper we model the transition probabilities for the 0 to 0 and 1 to 0 transitions by two logistic regressions thus showing how the covariates relate to changes in state with p covariates there are 2 p 1 parameters including intercepts which we estimate by maximum likelihood we show how to use transition probability estimates to test hypotheses about the probability of occupying state 0 at time i i 2 t and the equilibrium probability of state 0 these probabilities depend on the covariates a recursive algorithm is suggested to estimate regression coefficients when some responses are missing extensions of the basic model which allow time dependent covariates and nonstationary or second order markov chains are presented an example shows the model applied to a study of the psychological impact of breast cancer in which women did or did not manifest distress at four time points in the year following surgery

existence and regularity for a nonlinear boundary flow problem of population genetics abstract in this paper we consider a heat equation with nonlinear boundary condition occurring in population genetics the selection migration problem for alleles in a region considering flow of genes throughout the boundary such a problem determines a gradient flow in a convenient phase space and then the dynamics for large times depends heavily on the knowledge of the equilibrium solutions we address the questions of the existence of a nontrivial equilibrium solution and its regularity

the homotopy category of flat modules and grothendieck duality let r be a ring we prove that the homotopy category k r proj is always aleph 1 compactly generated and depending on the ring r it may or may not be compactly generated we use this to give a description of k r proj as a quotient of k r flat the remarkable fact is that this new description of k r proj generalizes to non affine schemes this will appear in murfet s thesis

an equality test across nonparametric regressions abstract we propose a procedure for testing the equality of several nonparametric multivariate regressions we allow the regressors designs and the number of observations to differ across subsamples the division into subsamples is defined through a variable c which can be either fixed or random for a random c our procedure is a general test of significance for qualitative variables in a nonparametric regression for a fixed c our procedure provides a nonparametric analysis of covariance which is valid for cross section or panel data in both cases the test is a one sided normal test and is consistent against all alternatives

semi parametric and non parametric methods for the analysis of repeated measurements with applications to clinical trials techniques applicable for the analysis of longitudinal data when the response variable is non normal are not nearly as comprehensive as for normally distributed outcomes however there have been several recent developments semi parametric and non parametric methodology for the analysis of repeated measurements is reviewed the commonly encountered design in which for each subject one assesses a univariate response variable at multiple fixed time points is considered the types of outcomes considered include binary ordered categorical and continuous but extremely non normal response variables all of the methods considered allow for incomplete data due to the occurrence of missing observations in addition discrete and or continuous covariates which may be time dependent are accommodated by some of the approaches the methods are demonstrated using data from three clinical trials

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