modelling neuromotor ratings with floor effects associated movements ams are a classical diagnostic tool to assess differences between normal children and children with some motor dysfunction this paper presents a methodology to produce age and gender dependent reference curves for ams of normal children for various tasks of a test battery data available consist of separate ratings of duration and extent of ams which are ordinal quantities with few levels other problems are severe age and gender dependent floor effects as well as some ceiling effects leaving little information for analysis at older ages to get a better scale we combined the two ordinal ratings into one meaningful and quasi continuous quantity referred to as intensity of ams in order to solve problems due to floor effects ceiling effects and discreteness we assumed left right and interval censored values respectively we considered a censored regression problem and postulated a truncated normal distribution for the non censored values after an appropriate transformation of the data using wei and tanner s poor man s data augmentation algorithm together with the technique of linear mixed effects modelling useful reference curves could be produced in contrast to the cumulative probabilities approach for ordinal data our methodology allows the calculation of individual age and gender standardized values which puts us in a position to investigate numerous scientific questions

the simulation of aerial movement i the determination of orientation angles from film data abstract quantitative mechanical analyses of human movement require the time histories of the angles which specify body configuration and orientation when these angles are obtained from a filmed performance they may be used to evaluate the accuracy of a simulation model this paper presents a method of determining orientation angles and their rates of change from film data the stages used comprise the synchronization of data obtained from two camera views the determination of three dimensional coordinates of joint centres the calculation of an angle from a sequence of sine and cosine values and the curve fitting of angles using quintic splines for each state other possible approaches are discussed original procedures are presented for obtaining individual error estimates of both the film data and the calculated angles to permit the automatic fitting of quintic splines for interpolation and differentiation and for deriving the time history of an angle as a continuous function from a sequence of sine and cosine values the method is applied to a forward somersault with 1 1 2 twists and the average error estimate of 17 orientation angles is obtained as 2 1 degrees

approximate bayesian analysis of censored survival data summary the bayesian analysis of data arising from a location scale regression model and which may include a number of right censored observations is considered the posterior distributions of the suitably normalized precision parameter and regression coefficient vector are shown to be well approximated by x2 and multivariate t distributions respectively the ideas are illustrated using some clinical survival data

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

traveling wave front for a two component lattice dynamical system arising in competition models abstract we study traveling front solutions for a two component system on a one dimensional lattice this system arises in the study of the competition between two species with diffusion or migration if we divide the habitat into discrete regions or niches we consider the case when the nonlinear source terms are of lotka volterra type and of monostable case we first show that there is a positive constant the minimal wave speed such that a traveling front exists if and only if its speed is above this minimal wave speed then we show that any wave profile is strictly monotone moreover under some conditions we show that the wave profile is unique up to translations for a given wave speed finally we characterize the minimal wave speed by the parameters in the system

linear regression analysis of censored survival data based on rank tests summary recently linear rank statistics with censored data have been used as the estimating functions for the regression parameters in the linear model with an unspecified error distribution the resulting rank estimators are consistent and asymptotically normal however the asymptotic variances of these estimators are complicated and are difficult to estimate well with censored data in this paper we propose some simple methods for making inference about a subset of the regression coefficients while regarding others as nuisance parameters a lack of fit test for the linear model is also presented the proposed procedures are illustrated with an example

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

determination of subject specific model parameters for visco elastic elements the determination of subject specific model parameter values is necessary in order for a computer simulation model of human motion to be evaluated quantitatively this study used an optimisation procedure along with a kinematically driven simulation model of the contact phase in running jumps to determine the elastic parameters of segmental wobbling masses and the foot ground interface kinetic and kinematic data were obtained on running jumps for height and distance performed by an elite male high jumper stiffness and damping coefficients of the visco elastic elements in the model were varied until the difference between simulation and performance was minimised percentage differences of 6 and 9 between the simulated and recorded performances were obtained in the jumps for height and distance respectively when the parameters obtained from the jump for height were used in a simulation of the jump for distance and vice versa there was poor agreement with the recorded jump on the other hand a common set of visco elastic parameters were obtained using the data from both recorded jumps resulting in a mean difference of only 8 made up of 7 and 10 between simulation and performance that was almost as good as the individual matches simulations were not overly sensitive to perturbations of the common set of visco elastic parameters it is concluded that subject specific elastic parameters should be calculated from more than a single jump in order to provide a robust set of values that can be used in different simulations

applications of multiple imputation to the analysis of censored regression data the first part of the article reviews the data augmentation algorithm and presents two approximations to the data augmentation algorithm for the analysis of missing data problems the poor man s data augmentation algorithm and the asymptotic data augmentation algorithm these two algorithms are then implemented in the context of censored regression data to obtain semiparametric methodology the performances of the censored regression algorithms are examined in a simulation study it is found up to the precision of the study that the bias of both the poor man s and asymptotic data augmentation estimators as well as the buckley james estimator does not appear to differ from zero however with regard to mean squared error over a wide range of settings examined in this simulation study the two data augmentation estimators have a smaller mean squared error than does the buckley james estimator in addition associated with the two data augmentation estimators is a natural device for estimating the standard error of the estimated regression parameters it is shown how this device can be used to estimate the standard error of either data augmentation estimate of any parameter e g the correlation coefficient associated with the model in the simulation study the estimated standard error of the asymptotic data augmentation estimate of the regression parameter is found to be congruent with the monte carlo standard deviation of the corresponding parameter estimate the algorithms are illustrated using the updated stanford heart transplant data set

regression analysis with randomly right censored data this paper proposes a new estimator of the parameter vector in a linear regression model when the observations are randomly censored on the right and when the error distribution is unknown this estimator is explicitly defined and easily computable the paper contains sufficient conditions under which this estimator is mean square consistent and asymptotically normal a numerical example is given

the simulation of aerial movement iv a computer simulation model a computer simulation model of human airborne movement is described the body is modelled as 11 rigid linked segments with 17 degrees of freedom which are chosen with a view to modelling twisting somersaults the accuracy of the model is evaluated by comparing the simulation values of the angles describing somersault tilt and twist with the corresponding values obtained from film data of nine twisting somersaults the maximum deviations between simulation and film are found to be 0 04 revolutions for somersault seven degrees for tilt and 0 12 revolutions for twist it is shown that anthropometric measurement errors from which segmental inertia parameters are calculated have a small effect on a simulation whereas film digitization errors can account for a substantial part of the deviation between simulation and film values

an application of imputation to an estimation problem in grouped lifetime analysis tanner and wang in press have introduced the data augmentation algorithm for the analysis of parametric missing data problems in this article this paradigm is used to develop an algorithm for the nonparametric estimation of the hazard function from grouped and censored lifetime data this algorithm makes use of the notions of cross validation and multiple imputation to prescribe the appropriate degree of smoothing for the nonparametric hazard estimate a procedure for estimating the variance of the estimator is also proposed the nonparametric hazard estimate and corresponding variance formula are shown to perform well in a simulation study the algorithm is illustrated with a numerical example

bayesian analysis of binary and polychotomous response data abstract a vast literature in statistics biometrics and econometrics is concerned with the analysis of binary and polychotomous response data the classical approach fits a categorical response regression model using maximum likelihood and inferences about the model are based on the associated asymptotic theory the accuracy of classical confidence statements is questionable for small sample sizes in this article exact bayesian methods for modeling categorical response data are developed using the idea of data augmentation the general approach can be summarized as follows the probit regression model for binary outcomes is seen to have an underlying normal regression structure on latent continuous data values of the latent data can be simulated from suitable truncated normal distributions if the latent data are known then the posterior distribution of the parameters can be computed using standard results for normal linear models draws from this posterior are used to sample new latent data and t

speed selection for the wavefronts of the lattice lotka volterra competition system abstract in this paper we study speed selection for traveling wavefronts of the lattice lotka volterra competition model for the linear speed selection by constructing new types of upper solutions to the system we widely extend the results in the literature we prove that for the nonlinear speed selection the wavefront of the first species decays with a faster rate at the far end this enables us to construct novel lower solutions to establish the existence of pushed wavefronts a topic that has been understudied we raise a new conjecture related to the classical hosono s version of the diffusive system and our numerical simulations help to confirm it while our rigorous results only provide a partial answer

minimal speed selection of traveling waves to the lotka volterra competition model abstract in this paper the minimal speed determinacy of traveling wave fronts of a two species competition model of diffusive lotka volterra type is investigated first a cooperative system is obtained from the classical lotka volterra competition model then we apply the upper lower solution technique on the cooperative system to study the traveling waves as well as its minimal speed selection mechanisms linear or nonlinear new types of upper and lower solutions are established previous results for the linear speed selection are extended and novel results on both linear and nonlinear selections are derived

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

linear models random censoring and synthetic data summary estimators for the linear model in the presence of censoring are available a new extension of the least squares estimator to censored data is equivalent to applying the ordinary least squares estimator to synthetic times time constructed by magnifying the gaps between successive order statistics under suitable regularity conditions the synthetic data estimator is fisher consistent and asymptotically normal examples facilitate com parison of the synthetic data estimator with estimators proposed by buckley james 1979 and by koul susarla van ryzin 1981 the entire lifetime of a person a machine a plant or an animal is not always observable some lifetimes may be censored in that only a lower bound for the lifetime is recorded statisticians are often interested in modelling the distribution of the true lifetimes as a function of covariates when censoring is present a proportional hazards model is often used when there is no censoring linear models are often used for ad hoc modelling of dependent variables miller halpern 1982 survey the methods that have been proposed for the linear model in the presence of censoring this paper describes a closed form method which is consistent and asymptotically normal this method incorporates censor ing in a natural way section 2 formulates classical least squares estimation in a manner that generalizes to accommodate random right censoring section 3 gives some theoretical results for the simplest nontrivial linear model the two sample case section 4 contains examples and the final section discusses the role of this estimator the covariate vector of the ith person will be denoted by xi and usually includes one as the first component the true lifetime yi follows a linear model if its conditional distribution given xi is

a mixed model procedure for analyzing ordered categorical data a mixed model procedure is developed for predicting the value of an ordered categorical response from knowledge of various predictor variables this procedure resembles the best linear unbiased procedure of henderson 1975 biometrics 31 423 447 for predicting the value of a quantitative response the approach is based on a mixed model version of the threshold model in which it is assumed that the observed category is determined by the value of an underlying unobservable continuous response that follows a mixed linear model the results are illustrated by an application to the problem of predicting the degree of difficulty that will be experienced by a dairy cow in the birth of her calf

random effects in censored ordinal regression latent structure and bayesian approach this paper discusses random effects in censored ordinal regression and presents a gibbs sampling approach to fit the regression model a latent structure and its corresponding bayesian formulation are introduced to effectively deal with heterogeneous and censored ordinal observations this work is motivated by the need to analyze interval censored ordinal data from multiple studies in toxicological risk assessment application of our methodology to the data offers further support to the conclusions developed earlier using gee methods yet provides additional insight into the uncertainty levels of the risk estimates

the simulation of aerial movement ii a mathematical inertia model of the human body a mathematical inertia model which permits the determination of personalized segmental inertia parameter values from anthropometric measurements is described the human body is modelled using 40 geometric solids which are specified by 95 anthropometric measurements a stadium solid is introduced for modelling the torso segments using perimeter and width measurements this procedure is more accurate than the use of elliptical discs of given width and depth and permits a smaller number of such solids to be used inertia parameter values may be obtained for body models of up to 20 segments errors in total body mass estimates from this and other models are discussed with reference to the unknown lung volumes

maximising somersault rotation in tumbling performing complex somersaulting skills during the flight phase of tumbling requires the generation of linear and angular momenta during the approach and takeoff phases this paper investigates how approach characteristics and takeoff technique affect performance with a view to maximising somersault rotation in tumbling a five segment planar simulation model customised to an elite gymnast was used to produce a simulation which closely matched a recorded performance of a double layout somersault by the elite gymnast three optimisations were carried out to maximise somersault rotation with different sets of initial conditions using the same initial linear and angular momentum as the double layout somersault and varying the joint torque activation timings allowed a double straight somersault to be performed with 19 more rotation potential than the actual performance increasing the approach velocity to a realistic maximum of 7 ms 1 resulted in a 42 reduction in rotation potential when the activation timings were unchanged but allowed a triple layout somersault to be performed with an increase of 31 in rotation potential when activation timings were re optimised increasing also the initial angular momentum to a realistic maximum resulted in a 4 reduction in rotation potential when the activation timings were unchanged but allowed a triple straight somersault to be performed with a further increase of 9 in rotation potential when activation timings were re optimised it is concluded that the limiting factor to maximising somersault rotation is the ability to generate high linear and angular velocities during the approach phase coupled with the ability to adopt consonant activation timings during the takeoff phase

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea