use of the mann whitney u test for clustered data the mann whitney u test is ubiquitous in statistical practice for the comparison of measures of location for two samples where the assumption of normality is questionable frequently one has replicate data for each individual in a group and would like to compare measures of central tendency between groups without assuming normality for this purpose we present a generalization of the mann whitney u test for clustered data the test is performed by computing zc wc mu c sigma c approximately n 0 1 under h0 where wc mu c are the observed and expected mann whitney u statistic based on a comparison of all pairs of replicates in the two groups and sigma c is the standard deviation of wc that is modified to account for clustering effects within a cluster we obtain an explicit variance formula that is a function of four clustering parameters we validate the properties of the test procedure in a simulation study we illustrate the methods with an example comparing the baseline humphrey visual field between two treatment groups in a randomized clinical trial of patients with retinitis pigmentosa rp

practical global optimization for multiview geometry this paper presents a practical method for finding the provably globally optimal solution to numerous problems in projective geometry including multiview triangulation camera resectioning and homography estimation unlike traditional methods which may get trapped in local minima due to the non convex nature of these problems this approach provides a theoretical guarantee of global optimality the formulation relies on recent developments in fractional programming and the theory of convex underestimators and allows a unified framework for minimizing the standard l 2 norm of reprojection errors which is optimal under gaussian noise as well as the more robust l 1 norm which is less sensitive to outliers even though the worst case complexity of our algorithm is exponential the practical efficacy is empirically demonstrated by good performance on experiments for both synthetic and real data an open source matlab toolbox that implements the algorithm is also made available to facilitate further research

estimating kappa from binocular data a common error in statistical analysis of ophthalmic data is the lack of accounting for the positive correlation generally present between observations made in fellow eyes the alternative of data analysis from only one eye in each patient may lead to loss of power and unrealistically large confidence intervals this paper discusses a method to estimate kappa a measure of agreement between two graders when both graders rate the same set of pairs of eyes the method assumes that the true left eye and right eye kappa values are equal and makes use of the correlated binocular data to estimate confidence intervals for the common kappa simulations show that the new estimators are better than the estimator based on only one eye new confidence intervals had the correct coverage probability but were usually only about 70 per cent as wide as single eye intervals the general methodology described here applies to analysis of grader agreement in rating other paired body structures

branch and bound methods for euclidean registration problems in this paper we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object we present a framework that allows us to use point to point point to line and point to plane correspondences for solving various types of pose and registration problems involving euclidean or similarity transformations traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem our approach of solving the mathematical optimization problems guarantees global optimality the optimization scheme is based on ideas from global optimization theory in particular convex underestimators in combination with branch and bound methods we provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data we also give examples of where traditional methods fail due to the local minima problem

go icp a globally optimal solution to 3d icp point set registration the iterative closest point icp algorithm is one of the most widely used methods for point set registration however being based on local iterative optimization icp is known to be susceptible to local minima its performance critically relies on the quality of the initialization and only local optimality is guaranteed this paper presents the first globally optimal algorithm named go icp for euclidean rigid registration of two 3d point sets under the l 2 error metric defined in icp the go icp method is based on a branch and bound scheme that searches the entire 3d motion space se 3 by exploiting the special structure of se 3 geometry we derive novel upper and lower bounds for the registration error function local icp is integrated into the bnb scheme which speeds up the new method while guaranteeing global optimality we also discuss extensions addressing the issue of outlier robustness the evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization go icp can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available

estimating equations for kappa statistics kappa statistics are often used for measuring agreement or association the original measure suggested by cohen for use with nominal data has since been generalized in a number of ways including the incorporation of weights adaptation for use with more than one rater and the application to bivariate data each modification requires a new approximation to the standard error and these have usually been derived by the delta method this paper illustrates the use of estimating equations for kappa which offer a unified approach to many previously considered situations and which is also applicable to more complex designs

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

a branch and bound approach to correspondence and grouping problems data correspondence grouping under an unknown parametric model is a fundamental topic in computer vision finding feature correspondences between two images is probably the most popular application of this research field and is the main motivation of our work it is a key ingredient for a wide range of vision tasks including three dimensional reconstruction and object recognition existing feature correspondence methods are based on either local appearance similarity or global geometric consistency or a combination of both in some heuristic manner none of these methods is fully satisfactory especially in the presence of repetitive image textures or mismatches in this paper we present a new algorithm that combines the benefits of both appearance based and geometry based methods and mathematically guarantees a global optimization our algorithm accepts the two sets of features extracted from two images as input and outputs the feature correspondences with the largest number of inliers which verify both the appearance similarity and geometric constraints specifically we formulate the problem as a mixed integer program and solve it efficiently by a series of linear programs via a branch and bound procedure we subsequently generalize our framework in the context of data correspondence grouping under an unknown parametric model and show it can be applied to certain classes of computer vision problems our algorithm has been validated successfully on synthesized data and challenging real images

a note on the kappa statistic for clustered dichotomous data the kappa statistic is widely used to assess the agreement between two raters motivated by a simulation based cluster bootstrap method to calculate the variance of the kappa statistic for clustered physician patients dichotomous data we investigate its special correlation structure and develop a new simple and efficient data generation algorithm for the clustered physician patients dichotomous data based on the delta method and its special covariance structure we propose a semi parametric variance estimator for the kappa statistic an extensive monte carlo simulation study is performed to evaluate the performance of the new proposal and five existing methods with respect to the empirical coverage probability root mean square error and average width of the 95 confidence interval for the kappa statistic the variance estimator ignoring the dependence within a cluster is generally inappropriate and the variance estimators from the new proposal bootstrap based methods and the sampling based delta method perform reasonably well for at least a moderately large number of clusters e g the number of clusters k 50 the new proposal and sampling based delta method provide convenient tools for efficient computations and non simulation based alternatives to the existing bootstrap based methods moreover the new proposal has acceptable performance even when the number of clusters is as small as k 25 to illustrate the practical application of all the methods one psychiatric research data and two simulated clustered physician patients dichotomous data are analyzed

kappa statistic for clustered matched pair data kappa statistic is widely used to assess the agreement between two procedures in the independent matched pair data for matched pair data collected in clusters on the basis of the delta method and sampling techniques we propose a nonparametric variance estimator for the kappa statistic without within cluster correlation structure or distributional assumptions the results of an extensive monte carlo simulation study demonstrate that the proposed kappa statistic provides consistent estimation and the proposed variance estimator behaves reasonably well for at least a moderately large number of clusters e g k 50 compared with the variance estimator ignoring dependence within a cluster the proposed variance estimator performs better in maintaining the nominal coverage probability when the intra cluster correlation is fair 0 3 with more pronounced improvement when is further increased to illustrate the practical application of the proposed estimator we analyze two real data examples of clustered matched pair data copyright 2014 john wiley sons ltd

likelihood inference for exchangeable binary data with varying cluster sizes ce papier etudie l estimation au maximum de vraisemblance dans des modeles satures et insatures pour des donnees binaires correlees echangeables lorsqu on dispose d un echantillon de clusters independants de tailles variables nous discutons plusieurs parametrisations de ces modeles et nous proposons l utilisation de l algorithme em pour obtenir des estimations du maximum de vraisemblance la methodologie est illustree par des applications a une etude d agregation familiale de maladie et a la construction d un essai randomise par groupe pour la prevention du cancer

fast rotation search with stereographic projections for 3d registration registering two 3d point clouds involves estimating the rigid transform that brings the two point clouds into alignment recently there has been a surge of interest in using branch and bound bnb optimisation for point cloud registration while bnb guarantees globally optimal solutions it is usually too slow to be practical a fundamental source of difficulty lies in the search for the rotational parameters in this work first by assuming that the translation is known we focus on constructing a fast rotation search algorithm with respect to an inherently robust geometric matching criterion we propose a novel bounding function for bnb that is provably tighter than previously proposed bounds further we also propose a fast algorithm to evaluate our bounding function our idea is based on using stereographic projections to precompute and index all possible point matches in spatial r trees for rapid evaluations the result is a fast and globally optimal rotation search algorithm to conduct full 3d registration we co optimise the translation by embedding our rotation search kernel in a nested bnb algorithm since the inner rotation search is very efficient the overall 6dof optimisation is speeded up significantly without losing global optimality on various challenging point clouds including those taken out of lab settings our approach demonstrates superior efficiency

a simple frailty model for family studies with covariates a simple easily analysed frailty model based on logistic regression and employing only binary frailties is developed and analysed methods for testing for frailty and estimates of frailty parameters and covariate effects are presented the effects of ignoring or mis specifying frailty are examined in detail and shown to downwardly bias the estimates of covariate effects in a variety of situations even when frailty is overestimated when the true frailty is large it can be difficult to estimate accurately because of the flatness of the likelihood however it is shown that this does not have a large influence on the estimates of the effects of the observed covariates methods for dealing with multiple frailties for example sibships and spouse pairs are also developed the results are illustrated on a large data set examining the risk factors associated with palmar keratoses

geometry and convergence analysis of algorithms for registration of 3d shapes the computation of a rigid body transformation which optimally aligns a set of measurement points with a surface and related registration problems are studied from the viewpoint of geometry and optimization we provide a convergence analysis for widely used registration algorithms such as icp using either closest points besl and mckay 1992 or tangent planes at closest points chen and medioni 1991 and for a recently developed approach based on quadratic approximants of the squared distance function pottmann et al 2004 icp based on closest points exhibits local linear convergence only its counterpart which minimizes squared distances to the tangent planes at closest points is a gauss newton iteration it achieves local quadratic convergence for a zero residual problem and if enhanced by regularization and step size control comes close to quadratic convergence in many realistic scenarios quadratically convergent algorithms are based on the approach in pottmann et al 2004 the theoretical results are supported by a number of experiments there we also compare the algorithms with respect to global convergence behavior stability and running time

global optimization through rotation space search this paper introduces a new algorithmic technique for solving certain problems in geometric computer vision the main novelty of the method is a branch and bound search over rotation space which is used in this paper to determine camera orientation by searching over all possible rotations problems can be reduced to known fixed rotation problems for which optimal solutions have been previously given in particular a method is developed for the estimation of the essential matrix giving the first guaranteed optimal algorithm for estimating the relative pose using a cost function based on reprojection errors recently convex optimization techniques have been shown to provide optimal solutions to many of the common problems in structure from motion however they do not apply to problems involving rotations the search method described in this paper allows such problems to be solved optimally apart from the essential matrix the algorithm is applied to the camera pose problem providing an optimal algorithm the approach has been implemented and tested on a number of both synthetically generated and real data sets with good performance

tests of homogeneity for generalized linear models abstract we propose two tests for testing homogeneity among clustered data adjusting for the effects of covariates the first is a score test for a generalized linear model with random effect in which the distribution of the response variable given the random effect is entirely defined in contrast to the likelihood ratio test however the score test does not require estimation of the parameters of a mixed effects model nor specification of the mixing distribution the second test is proposed in the framework of the generalized estimating equation gee approach in deriving this test we need only the specification of the marginal expectation and variance of the response variable and the fourth moment for the overdispersion term whereas for deriving the score test for mixed effects models the entire conditional distribution must be specified we demonstrate that the two tests are identical when the covariance matrix assumed in the gee approach is that of the random effects model in both approaches

an efficient globally optimal algorithm for asymmetric point matching although the robust point matching algorithm has been demonstrated to be effective for non rigid registration there are several issues with the adopted deterministic annealing optimization technique first it is not globally optimal and regularization on the spatial transformation is needed for good matching results second it tends to align the mass centers of two point sets to address these issues we propose a globally optimal algorithm for the robust point matching problem in the case that each model point has a counterpart in scene set by eliminating the transformation variables we show that the original matching problem is reduced to a concave quadratic assignment problem where the objective function has a low rank hessian matrix this facilitates the use of large scale global optimization techniques we propose a modified normal rectangular branch and bound algorithm to solve the resulting problem where multiple rectangles are simultaneously subdivided to increase the chance of shrinking the rectangle containing the global optimal solution in addition we present an efficient lower bounding scheme which has a linear assignment formulation and can be efficiently solved extensive experiments on synthetic and real datasets demonstrate the proposed algorithm performs favorably against the state of the art methods in terms of robustness to outliers matching accuracy and run time

maximum likelihood estimation of intraclass correlation in the analysis of familial data estimating equation approach summary we introduce a generalized model for estimating intraclass correlation in the analysis of familial data this model incorporates the models of donner koval 1980 donner bull 1983 rosner 1984 and miunoz rosner carey 1986 as special cases we then obtain the maximum likelihood estimates of the parameters of the model in particular we obtain a single estimating equation to be solved iteratively for the estimation of the intraclass correlation p and discuss all the special cases asymptotic variance for the estimate of the intraclass correlation is obtained for all the models and some examples are given

a bivariate cumulative probit regression model for ordered categorical data this paper proposes a latent variable regression model for bivariate ordered categorical data and develops the necessary numerical procedure for parameter estimation the proposed model is an extension of the standard bivariate probit model for dichotomous data to ordered categorical data with more than two categories for each margin in addition the proposed model allows for different covariates for the margins which is characteristic of data from typical ophthalmological studies it utilizes the stochastic ordering implicit in the data and the correlation coefficient of the bivariate normal distribution in expressing intra subject dependency illustration of the proposed model uses data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors for diabetic retinopathy among younger onset diabetics the proposed regression model also applies to other clinical or epidemiological studies that involve paired organs

linear n point camera pose determination the determination of camera position and orientation from known correspondences of 3d reference points and their images is known as pose estimation in computer vision and space resection in photogrammetry it is well known that from three corresponding points there are at most four algebraic solutions less appears to be known about the cases of four and five corresponding points we propose a family of linear methods that yield a unique solution to 4 and 5 point pose determination for generic reference points we first review the 3 point algebraic method then we present our two step 4 point and one step 5 point linear algorithms the 5 point method can also be extended to handle more than five points finally we demonstrate our methods on both simulated and real images we show that they do not degenerate for coplanar configurations and even outperform the special linear algorithm for coplanar configurations in practice

comparison of alternative regression models for paired binary data we used simulated data derived from real ophthalmologic examples to evaluate the performance of alternative logistic regression approaches for paired binary data approaches considered were standard logistic regression ignoring the correlation between fellow eyes treating individuals classified on the basis of their more impaired eye as the unit of analysis or considering only right eyes marginal logistic regression models fitted by the maximum likelihood approach of lipsitz laird and harrington or the estimating equation approach of liang and zeger and conditional logistic regression models fitted by the maximum likelihood approach of rosner or the estimating equation approach of connolly and liang taylor series approximations were used to compare conditional and marginal parameter estimates consideration of type i and ii error rates found application of standard logistic regression to be inferior to methods that treated the eye as the unit of analysis and accounted for the correlation between fellow eyes among these latter approaches none was uniformly superior to the others across the range of condition considered

functional association models for multivariate survival processes we consider multivariate temporal processes that are continuously observed within overlapping time windows the intended application is in censored multistate and multivariate survival settings where point processes are continuously observed these data differ from other functional data like longitudinal data which are discretely observed at irregular times existing functional approaches to survival processes use intensity models which require smoothing and depend critically on the choice of smoothing parameters similarly to discretely observed data in this article we study functional mean and association regression models for the point processes with unspecified time varying coefficients the continuous observation scheme is exploited the coefficients may be estimated nonparametrically by extending generalized estimating equations to continuously observed data the estimators automatically converge at the parametric rate without smoothing unlike with discretely observed data uniform consistenc

globally optimal algorithms for stratified autocalibration we present practical algorithms for stratified autocalibration with theoretical guarantees of global optimality given a projective reconstruction we first upgrade it to affine by estimating the position of the plane at infinity the plane at infinity is computed by globally minimizing a least squares formulation of the modulus constraints in the second stage this affine reconstruction is upgraded to a metric one by globally minimizing the infinite homography relation to compute the dual image of the absolute conic diac the positive semidefiniteness of the diac is explicitly enforced as part of the optimization process rather than as a post processing step for each stage we construct and minimize tight convex relaxations of the highly non convex objective functions in a branch and bound optimization framework we exploit the inherent problem structure to restrict the search space for the diac and the plane at infinity to a small fixed number of branching dimensions independent of the number of views chirality constraints are incorporated into our convex relaxations to automatically select an initial region which is guaranteed to contain the global minimum experimental evidence of the accuracy speed and scalability of our algorithm is presented on synthetic and real data

estimating logistic regression parameters for bivariate binary data summary consider bivariate binary data with possibly different covariates for each marginal binary observation suppose that the correlation between paired observations is a nuisance and the interest lies in estimating logistic regression parameters associated with the covariates we consider the estimator obtained by using the independence estimating equation with corrected variance this estimator can be very efficient and robust compared with maximum likelihood or the estimator of liang and zeger some comments are made concerning higher dimensional multivariate data

estimating kappa from binocular data and comparing marginal probabilities suppose that two graders classify all eyes in a sample of patients for the presence or absence of a specified abnormality in the statistical analysis of the data possible correlation between the observations in the right and left eyes should be taken into account recently general methods have been developed to analyse grader agreement in rating paired body structures in the present paper an alternative procedure is proposed that utilizes existing formulae for the computation of weighted kappa and its standard error in addition the mcnemar test is generalized to compare the probabilities of a positive judgement by the two graders

a class of logistic regression models for multivariate binary time series abstract a logistic model for multivariate binary time series is proposed first we establish the equivalence between a log linear model for the marginal distribution of a multivariate binary random vector and logistic models for the conditional distributions of each component given the others the logistic formulation is used to describe a markov chain for each series which implies a markov model for the vector of time series a pseudolikelihood estimation procedure is presented the methods are illustrated with data on psychosomatic and psychological diagnoses for families in a health maintenance plan

regression analysis in the presence of heterogeneous intraclass correlations summary in the statistical analysis of twinship and familial data one often encounters the need for regression methods that control for the possibly different aggregation of the twins and the members of the families according to their type e g monozygotic dizygotic for twinship data we present the maximum likelihood solution for the regression analysis of data in the presence of heterogeneous intraclass correlations this work extends previous results for the case of a homogeneous intraclass correlation an application of the methods for the analysis of twinship data is included

testing the equality of two dependent kappa statistics procedures are developed and compared for testing the equality of two dependent kappa statistics in the case of two raters and a dichotomous outcome variable such problems may arise when each of a sample of subjects are rated under two distinct settings and it is of interest to compare the observed levels of inter observer and intra observer agreement the procedures compared are extensions of previously developed procedures for comparing kappa statistics computed from independent samples the results of a monte carlo simulation show that adjusting for the dependency between samples tends to be worthwhile only if the between setting correlation is comparable in magnitude to the within setting correlations in this case a goodness of fit procedure that takes into account the dependency between samples is recommended

exchangeability in multivariate markov chain models time homogeneous markov chain models with state space 0 1 k are useful in analysis of binary follow up data on k individuals that interact the number of parameters increases exponentially with k so more restrictive models are imperative for statistical inference the hypothesis that the matrix of transition probabilities is invariant under permutation of individuals is discussed it is shown that if individuals are exchangeable then the process counting the number of individuals occupying a given state is a markov chain this reduction of data is sufficient if either at most a single individual may change state between two consecutive time points or if a state is absorbing similar results are obtained for exchangeability within two subgroups inference in the multivariate process reduces to a univariate problem if individuals are independent given the group s previous response it is shown how conditional independence could be tested assuming exchangeability the different hypotheses re examined in an analysis of the occurrence of bacteria in milk samples of danish dairy cattle

incorporation of clustering effects for the wilcoxon rank sum test a large sample approach the wilcoxon rank sum test is frequently used in statistical practice for the comparison of measures of location when the underlying distributions are far from normal or not known in advance an assumption of the ordinary rank sum test is that individual sampling units are independent in many ophthalmologic clinical trials the early treatment for diabetic retinopathy scale etdrs is a principal endpoint used for measuring the level of diabetic retinopathy this is an ordinal scale and it is natural to consider the wilcoxon rank sum test for the comparison of the level of diabetic retinopathy between treatment groups however under this design unlike the usual wilcoxon rank sum test the subject is the unit of randomization but the eye is the unit of analysis furthermore a person will tend to have different but correlated etdrs scores for fellow eyes thus we propose a correction to the variance of the wilcoxon rank sum statistic that accounts for clustering effects and that can be used for both balanced same number of subunits per cluster or unbalanced different number of subunits per cluster data both in the presence or absence of ties with p value adjusted accordingly in this article we present large sample theory and simulation results for this test procedure and apply it to diabetic retinopathy data from type i diabetics in the sorbinil retinopathy trial

unbiased estimation and statistical analysis of 3 d rigid motion from two views the problem of estimating 3d rigid motion from point correspondences over two views is formulated as nonlinear least squares ls optimization and the statistical behaviors of the errors in the solution are analyzed by introducing a realistic model of noise described in terms of the covariance matrices of n vectors it is shown that the ls solution based on the epipolar constraint is statistically biased the geometry of this bias is described in both quantitative and qualitative terms finally an unbiased estimation scheme is presented and random number simulations are conducted to observe its effectiveness

analyzing bivariate ordinal data using a global odds ratio abstract a moment method is proposed for regression analysis of bivariate ordered categorical data using the global odds ratio as the measure of association for modeling the margins this method utilizes the stochastic ordering implicit in the data this method allows for covariate effects in modeling the association between responses an application of the proposed model is illustrated using the ophthalmological data from the wisconsin epidemiologic study of diabetic retinopathy for identifying risk factors among younger onset diabetics this model is also extended to a longitudinal data setting with more than two repeated measures

latent variables measurement error and methods for analysing longitudinal binary and ordinal data we explore structural equations with latent variables for modelling between individual variability and measurement error in the analysis of longitudinal binary and ordinal data the structural equation formulation provides insight into the assumptions and differences in interpretation of methods that are popular for longitudinal data analysis introducing the concept of continuous latent variables makes it clear that marginal and cluster specific models differ because their predicted variables are scaled to different standard deviations and that adjustment for measurement error in the outcome involves a change in scale as well we apply both structural equation modelling and common longitudinal modelling approaches to data from a study of sleep disorders in the process we compare results from marginal modelling using an sas gee routine karim and zeger 1988 qu s gauss program qu 1992 for generalized mixed models using gee the mixor package for cluster specific mixed effects models hedeker and gibbons 1994 and liscomp for structural models muthen 1988

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

distribution free fitting of logit models with random effects for repeated categorical responses this article discusses random effects models for within subject comparisons of repeated responses on the same categorical scale the models account for the correlation that normally occurs between repeated responses the standard way of fitting such models maximizes the marginal likelihood after integrating with respect to a distribution for the random effect an alternative non parametric approach does not assume a distributional form for the random effects recent literature shows that for certain simple logit models this approach yields essentially the same model parameter estimates as conditional maximum likelihood moreover these estimates also result from fitting corresponding quasi symmetric log linear models for simple data sets in which primary interest relates to subject specific comparisons of the repeated responses one can easily obtain the estimates with standard software for log linear models examples include data from crossover designs and from comparisons of treatment and control groups regarding the change between baseline and follow up observations

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

directed sets and cofinal types we show that 1 s 1 x x xl and l are the only cofinal types of directed sets of size sl but that there exist many cofinal types of directed sets of size continuum a partially ordered set d is directed if every two elements of d have an upper bound in d in this note we consider some basic problems concerning directed sets which have their origin in the theory of moore smith convergence in topology 12 3 19 9 one such problem is to determine all essential kind of directed sets needed for defining the closure operator in a given class of spaces 3 p 47 concerning this problem the following important notion was introduced by j tukey 19 two directed sets d and e are cofinally similar if there is a partially ordered set c in which both can be embedded as cofinal subsets he showed that this is an equivalence relation and that d and e are cofinally similar iff there is a convergent map from d into e and also a convergent map from e into d the equivalence classes of this relation are called cofinal types this concept has been extensively studied since then by various authors 4 13 7 8 already from the first introduction of this concept it has been known that 1 1 x x 1 and x1 represent different cofinal types of directed sets of size btl but no more than five such types were known the main result of this paper shows that 1 1 x x 1 and x1 are the only cofinal types of convergence in spaces of character 81 which can be constructed without additional set theoretic assumptions on the other hand we shall construct many different cofinal types of directed sets of size continuum this gives a solution to problem 1 of j isbell 7 the paper also contains several results about the structure of the class of all cofinal types as well as a result about decomposing arbitrary partially ordered sets into directed sets the results of this note were proved in february march 1982 and presented to the asl in january 1983 1 a decomposition theorem in this section we show that an arbitrary partially ordered set can be decomposed into a number of its directed subsets depending on the sizes of its antichains this result is connected with an unpublished problem of f galvin concerning the dilworth decomposition theorem 6 and it generalizes a similar result of e milner and k prikry 11 the transitivity condition of a partial ordering is not used in our proof so we state our result so as to apply to an arbitrary received by the editors december 3 1984 1980 mathpmaties subjeet classification primary 03e05 03e35 secondary 06a10 18b35 54a15 c1985 american mathematical society 0002 9947 85 1 00 25 per page

a parametric model for cluster correlated categorical data summary a fully parametric copula model for symmetric dependent clustered categorical data is discussed the model accommodates any marginal regression models of interest and admits a broad range of within cluster association the form of the distribution is independent of cluster size and may be used to model data with varying cluster sizes the model contains an association parameter that is estimated from the data to give a measure of the strength of the within cluster association and also a test of independence two examples are given to illustrate the methods

some comments on rosner s multiple logistic model for clustered data rosner 1984 biometrics 41 1025 1035 proposed a binary regression model for analyzing binary response data gathered in clusters or groups this model is useful for understanding the degree of intracluster correlation among responses adjusted for the potential confounding effects of other covariates however estimates of the effects of covariates on the binary outcome obtained using rosner s model can be misleading for example we show that the covariate effects given by rosner s model do not correspond to those measured by either of the two standard approaches for correlated binary data we present an example that compares the regression coefficients arising from fits of rosner s model to other logistic models for clustered observations using data from a study of breast disease

multivariate methods for binary longitudinal data with heterogeneous correlation over time clustered binary data occur frequently in biostatistical work one particular application is in binary longitudinal data where several visits are available for the same individual several approaches have been proposed for the analysis of clustered binary data in rosner a polychotomous logistic regression model was proposed which is a generalization of the beta binomial distribution and allows for person and visit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of visits within an individual are equally correlated which may be inappropriate if several visits are available over a long follow up period in this paper this approach is extended to allow for heterogeneous correlation over time the total time period is divided into subintervals and a beta binomial mixture model is introduced to estimate odds ratios relating outcomes for pairs of visits both within a subinterval as well as in different subintervals to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of person subinterval and visit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston ma in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

a minimal solution for the extrinsic calibration of a camera and a laser rangefinder this paper presents a new algorithm for the extrinsic calibration of a perspective camera and an invisible 2d laser rangefinder lrf the calibration is achieved by freely moving a checkerboard pattern in order to obtain plane poses in camera coordinates and depth readings in the lrf reference frame the problem of estimating the rigid displacement between the two sensors is formulated as one of registering a set of planes and lines in the 3d space it is proven for the first time that the alignment of three plane line correspondences has at most eight solutions that can be determined by solving a standard p3p problem and a linear system of equations this leads to a minimal closed form solution for the extrinsic calibration that can be used as hypothesis generator in a ransac paradigm our calibration approach is validated through simulation and real experiments that show the superiority with respect to the current state of the art method requiring a minimum of five input planes

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

multivariate methods for clustered binary data with multiple subclasses with application to binary longitudinal data clustered binary data occur frequently in biostatistical work several approaches have been proposed for the analysis of clustered binary data in rosner 1984 biometrics 40 1025 1035 a polychotomous logistic regression model was proposed that is a generalization of the beta binomial distribution and allows for unit and subunit specific covariates while controlling for clustering effects one assumption of this model is that all pairs of subunits within a cluster are equally correlated this is appropriate for ophthalmologic work where clusters are generally of size 2 but may be inappropriate for larger cluster sizes a beta binomial mixture model is introduced to allow for multiple subclasses within a cluster and to estimate odds ratios relating outcomes for pairs of subunits within a subclass as well as in different subclasses to include covariates an extension of the polychotomous logistic regression model is proposed which allows one to estimate effects of unit class and subunit specific covariates while controlling for clustering using the beta binomial mixture model this model is applied to the analysis of respiratory symptom data in children collected over a 14 year period in east boston massachusetts in relation to maternal and child smoking where the unit is the child and symptom history is divided into early adolescent and late adolescent symptom experience

constrained monte carlo maximum likelihood for dependent data maximum likelihood estimates mles in autologistic models and other exponential family models for dependent data can be calculated with markov chain monte carlo methods the metropolis algorithm or the gibbs sampler which simulate ergodic markov chains having equilibrium distributions in the model from one realization of such a markov chain a monte carlo approximant to the whole likelihood function can be constructed the parameter value if any maximizing this function approximates the mle

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

review and analysis of solutions of the three point perspective pose estimation problem in this paper the major direct solutions to the three point perspective pose estimation problems are reviewed from a unified perspective beginning with the first solution which was published in 1841 by a german mathematician continuing through the solutions published in the german and then american photogrammetry literature and most recently in the current computer vision literature the numerical stability of these three point perspective solutions are also discussed we show that even in case where the solution is not near the geometric unstable region considerable care must be exercised in the calculation depending on the order of the substitutions utilized the relative error can change over a thousand to one this difference is due entirely to the way the calculations are performed and not due to any geometric structural instability of any problem instance we present an analysis method which produces a numerically stable calculation

a comparison of methods for testing homogeneity of proportions in teratologic studies summary we consider teratologic studies in which the aim is to compare the survival rate of animals in a treatment group to the corresponding rate in a control group the design of such studies often involves the allocation of intact litters of animals to treatment invalidating the application of standard statistical methods we review the strengths and weaknesses of several approaches for dealing with this problem including methodology recently developed for the analysis of clustered binary data a simulation study is conducted in which litter sizes are generated from a distribution having specified mean and degree of imbalance it is recommended on the basis of this study and on theoretical considerations that the choice of method should depend on whether the comparison of interest is experimental or observational for experimental comparisons involving the random assignment of litters to different treatment groups methods based on the adjustment of standard chi square statistics are recommended unless the number of litters in each group is very large

a note on the unbiased estimation of the intraclass correlation the intraclass correlation is a parameter featured in much psychological research two commonly used estimators of the maximum likelihood and least squares estimators are known to be negatively biased olkin and pratt 1958 derived the minimum variance unbiased estimator of the intraclass correlation but use of this estimator has apparently been impeded by the lack of a closed form solution this note briefly reviews the unbiased estimator and gives a fortran 77 subroutine to calculate it