marginalized transition models for longitudinal binary data with ignorable and non ignorable drop out we extend the marginalized transition model of heagerty to accommodate non ignorable monotone drop out using a selection model weakly identified drop out parameters are held constant and their effects evaluated through sensitivity analysis for data missing at random mar efficiency of inverse probability of censoring weighted generalized estimating equations ipcw gee is as low as 40 per cent compared to a likelihood based marginalized transition model mtm with comparable modelling burden mtm and ipcw gee regression parameters both display misspecification bias for mar and non ignorable missing data and both reduce bias noticeably by improving model fit

models for longitudinal data with random effects and ar 1 errors abstract for longitudinal data on several individuals linear models that contain both random effects across individuals and autocorrelation in the within individual errors are studied a score test for autocorrelation in the within individual errors for the conditional independence random effects model is first developed an explicit maximum likelihood estimation procedure using the scoring method for the model with random effects and autoregressive ar 1 errors is then derived empirical bayes estimation of the random effects and prediction of future responses of an individual based on this random effects with ar 1 errors model are also considered a numerical example is presented to illustrate these methods

sample size considerations for gee analyses of three level cluster randomized trials cluster randomized trials in health care may involve three instead of two levels for instance in trials where different interventions to improve quality of care are compared in such trials the intervention is implemented in health care units clusters and aims at changing the behavior of health care professionals working in this unit subjects while the effects are measured at the patient level evaluations within the generalized estimating equations approach we derive a sample size formula that accounts for two levels of clustering that of subjects within clusters and that of evaluations within subjects the formula reveals that sample size is inflated relative to a design with completely independent evaluations by a multiplicative term that can be expressed as a product of two variance inflation factors one that quantifies the impact of within subject correlation of evaluations on the variance of subject level means and the other that quantifies the impact of the correlation between subject level means on the variance of the cluster means power levels as predicted by the sample size formula agreed well with the simulated power for more than 10 clusters in total when data were analyzed using bias corrected estimating equations for the correlation parameters in combination with the model based covariance estimator or the sandwich estimator with a finite sample correction

high order finite difference techniques for linear singular perturbation boundary value problems abstract three high order finite difference techniques are developed for the second order singularity perturbed linear boundary value problem in one dimension taylor series expansions and error conversions are used for the development of the techniques convergence and stability conditions of these techniques are proved and some numerical results are given

on errors in variables for binary regression models summary we consider binary regression models when some of the predictors are measured with error for normal measurement errors structural maximum likelihood estimates are considered we show that if the measurement error is large the usual estimate of the probability of the event in question can be substantially in error especially for high risk groups in the situation of large measurement error we investigate a conditional maximum likelihood estimator and its properties

model for the analysis of binary longitudinal pain data subject to informative dropout through remedication abstract we address the problem of accounting for informative dropout in the form of rescue medication when comparing pain relievers with respect to longitudinal binary pain relief outcomes we present a selection model approach for binary longitudinal data that accommodates informative dropout the relationship between dropout or remedication and the binary pain relief response is assumed to be characterized by a random effect that is conditional on this random effect response and dropout are independent unlike previous approaches to this problem which rely on numerical or approximation methods we obtain a closed form expression for the marginal log likelihood of response and dropout by specifying a complementary log log link function for both components and a conjugate log gamma random effect distribution a data analysis supported by simulation results suggest that the model fits reasonably well results are compared to those obtained from conventional but somewhat inappropriate analyses

mixed effects models with bivariate and univariate association parameters for longitudinal bivariate binary response data summary when two binary responses are measured for each study subject across time it may be of interest to model how the bivariate associations and marginal univariate risks involving the two responses change across time to achieve such a goal marginal models with bivariate log odds ratio and univariate logit components are extended to include random effects for all components specifically separate normal random effects are specified on the log odds ratio scale for bivariate responses and on the logit scale for univariate responses assuming conditional independence given the random effects facilitates the modeling of bivariate associations across time with missing at random incomplete data we fit the model to a dataset for which such structures are feasible a longitudinal randomized trial of a cardiovascular educational program where the responses of interest are change in hypertension and hypercholestemia status the proposed model is compared to a naive bivariate model that assumes independence between time points and univariate mixed effects logit models

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

a continuous method for nonlocal functional differential equations with delayed or advanced arguments abstract in the previous works the authors presented the reproducing kernel method rkm for solving various differential equations however to the best of our knowledge there exist no results for functional differential equations the aim of this paper is to extend the application of reproducing kernel theory to nonlocal functional differential equations with delayed or advanced arguments and give the error estimation for the present method some numerical examples are provided to show the validity of the present method

a spline method for second order singularly perturbed boundary value problems we consider a difference scheme based on cubic spline in compression for second order singularly perturbed boundary value problem of the form ey p x y q x y r x y a 0 y b 1 the method is shown to have second and fourth order convergence depending on the choice of parameters 1 and 2 involved in the method the method is tested on an example and the results found to be in agreement with the theory

spline based computational technique for linear singularly perturbed boundary value problems a fourth order difference scheme via cubic spline in compression for singularly perturbed two point boundary value problems of the form ey p x y q x y r x y a a y b bis presented the convergence analysis is given finally computational efficiency of the method is verified through numerical examples

reproducing kernel method for the numerical solution of the 1d swift hohenberg equation abstract the swift hohenberg equation is a nonlinear partial differential equation of fourth order that models the formation and evolution of patterns in a wide range of physical systems we study the 1d swift hohenberg equation in order to demonstrate the utility of the reproducing kernel method the solution is represented in the form of a series in the reproducing kernel space and truncating this series representation we obtain the n term approximate solution in the first approach we aim to explain how to construct a reproducing kernel method without using gram schmidt orthogonalization as orthogonalization is computationally expensive this approach will therefore be most practical for obtaining numerical solutions gram schmidt orthogonalization is later applied in the second approach despite the increased computational time as this approach will prove theoretically useful when we perform a formal convergence analysis of the reproducing kernel method for the swift hohenberg equation we demonstrate the applicability of the method through various test problems for a variety of initial data and parameter values

an approach to the analysis of repeated measurements summary a linear model for repeated measurements is proposed in which the correlation structure within each time sequence of measurements includes parameters for measurement error variation between experimental units and serial correlation within units an approach to data analysis is presented which involves preliminary analysis by ordinary least squares use of the empirical semi variogram of residuals to suggest a suitable correlation structure and formal inference using likelihood based methods applications to two biological data sets are described

a novel method for nonlinear two point boundary value problems combination of adm and rkm abstract in this paper a novel method is proposed for solving nonlinear two point boundary value problems bvps this method is based on a combination of the adomian decomposition method adm and the reproducing kernel method rkm a major advantage of this method over standard adm is that it can avoid unnecessary computation in determining the unknown parameters the proposed method can be applied to singular and nonsingular bvps numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two point boundary value problems

modeling conception as an aggregated bernoulli outcome with latent variables via the em algorithm we describe a general method for analyzing aggregated bernoulli outcomes the research is motivated by an epidemiological reproductive study where the outcome was whether pregnancy was detected in a woman s particular menstrual cycle and the bernoulli trials corresponded to days with intercourse during the cycle each cycle is either viable or not i e is or is not susceptible to conception we develop an em algorithm approach to maximizing the observed data pseudo likelihood based on a set of unobservable latent outcomes linked to the specific days with intercourse this method is flexible in that it allows one to model effect of covariates on the susceptibility factor and on the latent outcomes application of the method to fertility studies enables one to investigate covariates with a long term or transient effect on the daily conception probability a complication is that most couples contribute more than one cycle in a prospective study a generalized estimating equation approach adjusts for the dependency among outcomes within individual couples the method can be applied in any setting where dependency among bernoulli trials is induced by a susceptibility factor and the trial outcomes are only observable in the aggregate

general methods for analysing repeated measures we present an overview of issues and methods for analysing repeated measures of a continuous random variable we discuss modelling the mean vector and covariance structure statistical efficiency regression diagnostics and discrepancies between longitudinal and cross sectional methods we illustrate key points with examples and discuss areas requiring further development

fitted mesh b spline collocation method for solving self adjoint singularly perturbed boundary value problems in this paper we develop b spline collocation method for solving a class of self adjoint singularly perturbed equations given by 0 1 email protected a x y b x y x g x a x a 0 a x 0 b x b 0 y 0 email protected y 1 email protected use the fitted mesh technique to generate piecewise uniform mesh and use b spline method which leads to a tridiagonal linear system the convergence analysis is given and the method is shown to have uniform convergence of second order numerical illustrations are given in the end to demonstrate the efficiency of our method

markov regression models for time series a quasi likelihood approach this paper discusses a quasi likelihood ql approach to regression analysis with time series data we consider a class of markov models referred to by cox 1981 scandinavian journal of statistics 8 93 115 as observation driven models in which the conditional means and variances given the past are explicit functions of past outcomes the class includes autoregressive and markov chain models for continuous and categorical observations as well as models for counts e g poisson and continuous outcomes with constant coefficient of variation e g gamma we focus on poisson and gamma data for illustration analogous to ql for independent observations large sample properties of the regression coefficients depend only on correct specification of the first conditional moment

semiparametric regression analysis for recurrent event interval counts this paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation we consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow up at each visit the patient reports the number of events that occurred since the previous visit or an examination reveals the number of accumulated events such as skin cancers the exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow up times each patient s record thus consists of a sequence of clinic visit dates event counts corresponding to the successive time intervals between clinic visits and baseline covariates we propose a semiparametric regression model extending the fully parametric model of thall 1988 biometrics 44 197 209 to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time varying nature of the underlying event rate covariate effects enter the model parametrically while the underlying time varying event rate is modelled nonparametrically the method of severini and wong 1992 annals of statistics 20 1768 1802 is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution a simulation study and application to a data set are provided

solving a system of linear volterra integral equations using the new reproducing kernel method in this paper we present a new numerical technique to obtain the approximation solution for linear volterra integral equations of the second kind based on reproducing kernel theory the approximation solution is expressed by n term summation of reproducing kernel functions the merit of the new method includes 1 it is easy to implement this method 2 high accuracy the numerical examples compared with other methods show that the new method is more efficient

matching conditional and marginal shapes in binary random intercept models using a bridge distribution function summary random effects logistic regression models are often used to model clustered binary response data regression parameters in these models have a conditional subject specific interpretation in that they quantify regression effects for each cluster very often the logistic functional shape conditional on the random effects does not carry over to the marginal scale thus parameters in these models usually do not have an explicit marginal population averaged interpretation we study a bridge distribution function for the random effect in the random intercept logistic regression model under this distributional assumption the marginal functional shape is still of logistic form and thus regression parameters have an explicit marginal interpretation the main advantage of this approach is that likelihood inference can be obtained for either marginal or conditional regression inference within a single model framework the generality of the results and some properties of the bridge distribution functions are discussed an example is used for illustration

a computational method for solving third order singularly perturbed boundary value problems in this paper a new computational method is presented for solving a class of third order singularly perturbed boundary value problems with a boundary layer at the left of the underlying interval in this method first the given third order singularly perturbed boundary value problem is transformed into a system of two odes subject to suitable initial and boundary conditions and a zeroth order asymptotic expansion for the solution of the given problem is constructed then the reduced terminal value problem is solved analytically in the reproducing kernel space this method is effective and easy to implement a numerical examples is studied to demonstrate the accuracy of the present method results obtained by the method are found to be in good agreement with the exact solution not only in the boundary layer but also away from the layer

approximations of choice probabilities in mixed logit models this paper is concerned with the approximate computation of choice probabilities in mixed logit models the relevant approximations are based on the taylor expansion of the classical logit function and on the high order moments of the random coefficients the approximate choice probabilities and their derivatives are used in conjunction with log likelihood maximization for parameter estimation the resulting method avoids the assumption of an apriori distribution for the random tastes moreover experiments with simulation data show that it compares well with the simulation based methods in terms of computational cost

on solving systems of linear inequalities with artificial neural networks the implementation of the relaxation projection algorithm by artificial neural networks to solve sets of linear inequalities is examined the different versions of this algorithm are described and theoretical convergence results are given the best known analog optimization solvers are shown to use the simultaneous projection version of it neural networks that implement each version are described the results of tests made with simulated realizations of these networks are reported these tests consisted in having all networks solve some sample problems the results obtained help determine good values for the step size parameters and point out the relative merits of the different networks

longitudinal data with serial correlation a state space approach a general linear mixed model first order autoregressive errors state space representations the laird ware model in state space form autoregressive moving average errors nonlinear models multivariate models appendix fortran subroutines

the reproducing kernel method for solving the system of the linear volterra integral equations with variable coefficients in this paper we apply the reproducing kernel method to give the exact solution and approximate solution for the system of the linear volterra integral equations with variable coefficients some examples are given showing its effectiveness and convenience finally the numerical results obtained by the reproducing kernel method are superior to those obtained by other methods in farshid mirzaee 2010 4 tahmasbi and fard 2008 5 saeed and ahmed 2008 8

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 exact solution for solving a class nonlinear operator equations in the reproducing kernel space in this paper the author will introduce the sobolev space w 1 2 w n firstly and then give the reproducing properties of the space w 1 2 w n as these results of those a class of the nonlinear operator equation n i 1 m i j 1 a i ju f is transformed to the n dimensional linear operator equation au f finally we also give the exact solution of this nonlinear operator equation

a computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers singularly perturbed turning point problems tpps for second order ordinary differential equations des exhibiting twin boundary layers are considered in order to obtain numerical solution of these problems a computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods in this method the given internal domain of definition of differential equation is divided into four subintervals and we solve the differential equation in each interval and combine the solution the implementation of the method on parallel architectures is mentioned error estimates are derived and numerical examples are given

a computational method for solving boundary value problems for third order singularly perturbed ordinary differential equations singularly perturbed two point boundary value problems spbvps for third order ordinary differential equations odes with a small parameter multiplying the highest derivative are considered a numerical method is suggested in this paper to solve such problems in this method the given bvp is transformed into a system of two odes subject to suitable initial and boundary conditions then the domain of definition of the differential equation a closed interval is divided into two sub intervals which we call the inner region boundary layer and the outer region then the de is solved in these intervals separately the solutions obtained in these intervals are combined to give the solution in the whole interval to obtain boundary conditions at the transition points boundary values inside this interval we use mostly the zeroth order asymptotic expansion of the solution of the bvp or a suitable asymptotic expansion solution first the linear equations are considered and then the semi linear equations to solve semi linear equations newton s method of quasi linearisation is applied examples are provided to illustrate the method the method is easy to implement and suitable for parallel computing

error estimation for the reproducing kernel method to solve linear boundary value problems in the previous works the authors presented the reproducing kernel method rkm for solving various boundary value problems however an effective error estimation for this method has not yet been discussed the aim of this paper is to fill this gap in this paper we shall give the error estimation for the reproducing kernel method to solve linear boundary value problems

unbalanced repeated measures models with structured covariance matrices the question of how to analyze unbalanced or incomplete repeated measures data is a common problem facing analysts we address this problem through maximum likelihood analysis using a general linear model for expected responses and arbitrary structural models for the within subject covariances models that can be fit include standard univariate and multivariate models with incomplete data random effects models and models with time series and factor analytic error structures we describe newton raphson and fisher scoring algorithms for computing maximum likelihood estimates and generalized em algorithms for computing restricted and unrestricted maximum likelihood estimates an example fitting several models to a set of growth data is included

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

operational characteristics of maximum score estimation abstract this paper reports on the operational characteristics of maximum score estimation of a linear model from binary response data a series of previous articles have shown that in theory the maximum score method makes possible binary response analysis under very weak distributional assumptions here we present evidence on the properties of maximum score estimation in practice after reviewing the known asymptotic theory of maximum score estimation the paper describes an algorithm for maximum score estimation and characterizes its performance then findings from a monte carlo study comparing maximum score and logit maximum likelihood estimation are reported finally the accuracy of bootstrap estimation of maximum score root mean square errors is evaluated

generalization of the mantel haenszel estimating function for sparse clustered binary data we extend the mantel haenszel estimating function to estimate both the intra cluster pairwise correlation and the main effects for sparse clustered binary data we propose both a composite likelihood approach and an estimating function approach for the analysis of such data the proposed estimators are consistent and asymptotically normally distributed simulation results demonstrate that the two approaches are comparable in terms of bias and efficiency however the estimating equation approach is computationally simpler analysis of the georgia high blood pressure survey is used for illustration

estimation filtering and smoothing in state space models with incompletely specified initial conditions on definit la vraisemblance pour un modele d espace d etats avec des conditions initiales incompletement specifiees par transformation des donnees pour eliminer la dependance sur des conditions non specifiees on etend cette approche pour obtenir des estimations sur les vecteurs d etat les predicteurs et les interpolateurs pour des observations manquantes

the maximum capture problem with random utilities problem formulation and algorithms abstract a model for the optimal location of new facilities in a competitive market is introduced under the hypothesis that customers behavior can be modeled by random utility functions it means that the company that wished to locate uses a random utility model to forecast the market share of a location therefore the company cannot forecast the behavior of every customer in a deterministic fashion but is able to embed him by a probability distribution three formulations are proposed to compute upper bounds of the objective function and compared in a numerical simulation a branch and bound method is developed and tested on examples with up to 50 potential locations and a variable neighborhood search heuristic is proposed to solve larger instances

the asymptotic solution of a class of third order boundary value problems arising in the theory of thin film flows this paper studies boundary and interior layer phenomena exhibited by solutions of certain singularly perturbed third order boundary value problems which govern the motion of thin liquid films subject to viscous capillary and gravitational forces precise conditions specifying where and when the third order derivative terms in the differential equations can be neglected are derived and improved estimates for the actual solutions in terms of solutions of the lower order models are constructed the paper also contains a technique for replacing a third order problem with an asymptotically equivalent second order one that may have wider applicability

autoregressive growth curves and kalman filtering the first part of this paper describes how a kalman filter can be used to construct maximum likelihood ml estimates of autoregressive ar and polynomial parameters in polynomial growth curves with ar 1 errors and irregularly spaced data the second part introduces a disturbed highest derivative polynomial dhdp as a model for growth curves this model does not depend on regression coefficients variances of the highest derivative disturbance and the observation error are estimated by ml using a kalman filter the estimated dhdp growth curve is obtained by optimally smoothing the output of the filter equally spaced data is not required the dhdp model and analysis are developed for an individual and extended to a population growth curve using data from many individuals with covariates

projected partial likelihood and its application to longitudinal data summary an estimating equation which we call the projected partial score is introduced for longitudinal data analysis the estimating equation is obtained by projecting the partial likelihood score function onto the vector space spanned by a class of conditionally linear estimating equations we demonstrate that removing certain terms from the projection of the full likelihood score does not alter important inferential properties of the estimating equation and doing so is advantageous in handling missing data and time varying covariates within a prequential frame of reference it is shown that the estimating equation is optimal among the largest collection of estimating equations determined by the conditional moments furthermore the method possesses similar properties to generalised estimating equations in particular the correct conditional variance specification is necessary for efficiency but not for asymptotic consistency and distribution theory

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

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

a uniformly accurate finite element method for a singular perturbation problem in conservative form a petrov galerkin finite element method with exponential basis elements is applied to a nonselfadjoint singularly perturbed two point boundary value problem in conservative form it is shown to be uniformly first order accurate in l infty and is uniformly second order accurate at the nodes i e the error constants are independent of the mesh size and the perturbation parameter

regression models for nonstationary categorical time series asymptotic estimation theory for the analysis of nonstationary categorical time series a parsimonious and flexible class of models is proposed these models are generalizations of regression models for stochastically independent categorical observations consistency asymptotic normality and efficiency of the maximum likelihood estimator are shown under weak and easily verifiable requirements some models for binary time series are discussed in detail to demonstrate asymptotic properties a theorem is given addressing maximum likelihood estimation for general stochastic processes then it is shown that the assumptions of this theorem are consequences of the requirements for categorical time series for this proof some lemmas are used which may be of interest in similar cases

tree structured logistic model for over dispersed binomial data with application to modeling developmental effects this article proposes tree structured logistic regression modeling for over dispersed binomial data recursive partitioning is performed using a combination of statistical tests and residual analysis the splitting criterion in cross validation is based on the deviance function a nested grid algorithm to estimate the bootstrap parameters is developed the regression tree procedure provides a new approach for exploring in detail the relationship between the binomial response and explanatory variables the proposed procedure is used to model the relationship between the incidence of malformation and dose and fetal weight using data from a developmental experiment conducted at the national center for toxicological research a conditional gaussian chain model is used to account for the effect of fetal weight by dose

classification methods for random utility models with i i d disturbances under the most probable alternative rule in this paper random utility maximization based on maximization of correct classification of the choice decisions over a given data set is considered it is shown that if the disturbance vector in the random utility model is independent and identically distributed then preference determination based on the most probable alternative reduces to deterministic utility maximization as a consequence of the above equivalence the form of the error distribution normal weibull uniform etc plays no role in the determination of the preferred alternative parameter estimation under the most probable alternative rule is carried out using two methods the first is based on the solution of an appropriately defined system of linear inequalities and the second one is based on the function optimization of a newly proposed function whose optimum is achieved when the number of correctly classified individuals is maximized the ability to use these algorithms in the framework of pattern recognition and machine learning is pointed out simulations and a real case study involving intercity travel behavior are employed to assess the proposed methods

reproducing kernel method for the numerical solution of the brinkman forchheimer momentum equation we consider two efficient methods for the solution of the brinkman forchheimer momentum equation with boundary conditions on the square physically this model describes the flow of fully developed forced convection in a porous saturated rectangular duct after first demonstrating the existence and symmetry properties of a solution we apply the reproducing kernel method in order to solve the brinkman forchheimer momentum equation we then demonstrate the applicability of the method by considering several specific numerical examples which allow us to understand the variation of the physical solutions as one changes any of the several model parameters the numerical results demonstrate the utility of the reproducing kernel method for solving nonlinear elliptic partial differential equations on compact domains

further examples of the boundary value technique in singular perturbation problems illustration de la technique des valeurs frontieres dans les problemes a perturbations singulieres par des exemples varies

singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations abstract this article shows the existence uniqueness and asymptotic estimates of solutions of the singularly perturbed boundary value problems for a class of the third order nonlinear ordinary differential equations with a small parameter e 0 ey x y y e satisfying the condition y 0 0 y 1 0 y 1 0 or y 0 0 y 1 0 y 1 0

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

a rational spectral collocation method for third order singularly perturbed problems a new numerical method is developed for solving a class of third order singularly perturbed boundary value problems first of all the given problem is transformed into a system of two ordinary differential equations odes subject to suitable initial and boundary conditions then the rational spectral collocation method in barycentric form with sinh transformation is applied to solve the system of odes according to the asymptotic analysis the location and width of boundary layer of the given problem which are chosen as parameters in the sinh transformation can be determined ample numerical experiments are presented to illustrate the computational efficiency and accuracy of the our method

models for longitudinal data a generalized estimating equation approach this article discusses extensions of generalized linear models for the analysis of longitudinal data two approaches are considered subject specific ss models in which heterogeneity in regression parameters is explicitly modelled and population averaged pa models in which the aggregate response for the population is the focus we use a generalized estimating equation approach to fit both classes of models for discrete and continuous outcomes when the subject specific parameters are assumed to follow a gaussian distribution simple relationships between the pa and ss parameters are available the methods are illustrated with an analysis of data on mother s smoking and children s respiratory disease

unequally spaced longitudinal data with ar 1 serial correlation this paper discusses longitudinal data analysis when each subject is observed at different unequally spaced time points observations within subjects are assumed to be either uncorrelated or to have a continuous time first order autoregressive structure possibly with observation error the random coefficients are assumed to have an arbitrary between subject covariance matrix covariates can be included in the fixed effects part of the model exact maximum likelihood estimates of the unknown parameters are computed using the kalman filter to evaluate the likelihood which is then maximized with a nonlinear optimization program an example is presented where a large number of subjects are each observed at a small number of observation times hypothesis tests for selecting the best model are carried out using wald s test on contrasts or likelihood ratio tests based on fitting full and restricted models

an initial value approach for solving singularly perturbed two point boundary value problems in this paper an initial value approach is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end left or right point this approach is based on the boundary layer behavior of the solution the method is distinguished by the following fact the given singularly perturbed two point boundary value problem is replaced by three first order initial value problems several linear and non linear problems are solved to demonstrate the applicability of the method it is observed that the present method approximates the exact solution very well

longitudinal data analysis for linear gaussian models with random disturbed highest derivative polynomial subject effects for linear regression analysis of longitudinal data with gaussian response i propose a new model to generalize the traditional class of random effects models in which the random effects are deterministic polynomials with coefficients randomly distributed over subjects with mean zero the generalization is accomplished by adding zero mean gaussian disturbances to the highest derivative of each random coefficient subject polynomial independently at each observation time the resulting random effects which have mean zero at each observation time are called disturbed highest derivative polynomials dhdps the disturbances induce serial correlation and also allow the subject specific dhdp time trends to be non linear i do not estimate the subject specific dhdp time trends analysis is based on the marginal model that is the fixed effects or population model obtained by integrating the random polynomial coefficients and all disturbances out of the joint distribution of themselves and the response vector this allows a population averaged interpretation one can select the dhdp order by an information criterion when the population time trend is not correctly modelled the optimal dhdp order will be larger than when it is correctly modelled one can make the covariance matrix of the regression coefficients robust to errors in modelling the within subject dependence i describe the relationship of a dhdp to a smoothing polynomial spline and show how to replace the dhdp model with a smoothing polynomial spline model for the within subject dependence in the marginal model

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

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