latent variable models with mixed continuous and polytomous data owing to the nature of the problems and the design of questionnaires discrete polytomous data are very common in behavioural medical and social research analysing the relationships between the manifest and the latent variables based on mixed polytomous and continuous data has proven to be difficult a general structural equation model is investigated for these mixed outcomes maximum likelihood ml estimates of the unknown thresholds and the structural parameters in the covariance structure are obtained a monte carlo em algorithm is implemented to produce the ml estimates it is shown that closed form solutions can be obtained for the m step and estimates of the latent variables are produced as a by product of the analysis the method is illustrated with a real example

pairwise fitting of mixed models for the joint modeling of multivariate longitudinal profiles a mixed model is a flexible tool for joint modeling purposes especially when the gathered data are unbalanced however computational problems due to the dimension of the joint covariance matrix of the random effects arise as soon as the number of outcomes and or the number of used random effects per outcome increases we propose a pairwise approach in which all possible bivariate models are fitted and where inference follows from pseudo likelihood arguments the approach is applicable for linear generalized linear and nonlinear mixed models or for combinations of these the methodology will be illustrated for linear mixed models in the analysis of 22 dimensional highly unbalanced longitudinal profiles of hearing thresholds

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

convergence of a stochastic approximation version of the em algorithm the expectation maximization em algorithm is a powerful computational technique for locating maxima of functions it is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models in certain situations however this method is not applicable because the expectation step cannot be performed in closed form to deal with these problems a novel method is introduced the stochastic approximation em saem which replaces the expectation step of the em algorithm by one iteration of a stochastic approximation procedure the convergence of the saem algorithm is established under conditions that are applicable to many practical situations moreover it is proved that under mild additional conditions the attractive stationary points of the saem algorithm correspond to the local maxima of the function presented to support our findings

theory of self similarity of periodic approximants to a quasilattice it is shown that self similarity of a quasilattice has a profound effect on the periodic approximants to the quasilattice the periodic approximants are grouped into series so that i each series is generated from its prototype by a successive application of the deflation and rescaling ii the space group is common among the members of the series and iii the unit cell of the approximant is scaled up by tau with the series number where tau is the scale of self similarity of the relevant quasilattice these results are exemplified with application to the case of the octagonal quasilattice

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

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

a comparison of optimization based approaches for a model computational aerodynamics design problem abstract the objective of this paper is to compare three optimization based methods for solving aerodynamic design problems we use the euler equations for one dimensional duct flow as a model problem the optimization methods are i the black box method with finite difference gradients ii a modification where gradients are found by an algorithm based on the implicit function theorem and iii an all atonce method where the flow and design variables are simultaneously altered the three methods are applied to the model problem and compared for efficiency robustness and implementation difficulty we also show that the black box implicit gradient method is equivalent to applying the variational or optimal control approach to design optimization directly to the discretized analysis problem rather than to the continuous problem as is usually done the black box method with implicit gradients seems to provide a good compromise of features and can be retrofitted to most existing analysis codes to turn them into design codes although the all at once method was found to be less robust than the black box methods when it succeeded it was considerably more efficient

analysis of multivariate probit models summary this paper provides a practical simulation based bayesian and non bayesian analysis of correlated binary data using the multivariate probit model the posterior distribution is simulated by markov chain monte carlo methods and maximum likelihood estimates are obtained by a monte carlo version of the em algorithm a practical approach for the computation of bayes factors from the simulation output is also developed the methods are applied to a dataset with a bivariate binary response to a four year longitudinal dataset from the six cities study of the health effects of air pollution and to a sevenvariate binary response dataset on the labour supply of married women from the panel survey of income dynamics

anisotropic norm oriented mesh adaptation for a poisson problem we present a novel formulation for the mesh adaptation of the approximation of a partial differential equation pde the discussion is restricted to a poisson problem the proposed norm oriented formulation extends the goal oriented formulation since it is equation based and uses an adjoint at the same time the norm oriented formulation somewhat supersedes the goal oriented one since it is basically a solution convergent method indeed goal oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that as mesh size is increased more degrees of freedom only this output is proven to tend to its continuous analog while the solution field itself may not converge a remarkable quality of goal oriented metric based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization in the well identified set of metrics of a well defined functional in the new proposed formulation we amplify this advantage we search in the same well identified set of metrics the minimum of a norm of the approximation error the norm is prescribed by the user and the method allows addressing the case of multi objective adaptation like for example in aerodynamics adaptating the mesh for drag lift and moment in one shot in this work we consider the basic linear finite element approximation and restrict our study to l 2 norm in order to enjoy second order convergence numerical examples for the poisson problem are computed

adjoint sensitivity analysis for time dependent partial differential equations with adaptive mesh refinement a new adjoint sensitivity analysis approach is presented for time dependent partial differential equations with adaptive mesh refinement the new approach called adda combines the best features of both the adjoint of the discretization ad and discretization of the adjoint da approaches it removes the obstacles of applying ad to adaptive methods and in contrast to da requires for its use only a minimal amount of knowledge about the formulation of adjoint pdes and their boundary conditions the effectiveness and efficiency of adda are demonstrated for several numerical examples

space time adaptive solution of inverse problems with the discrete adjoint method this paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent adaptive grid adaptive step models discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation however this approach brings several important challenges the space time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations a reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter grid transfer operators moreover the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations this work shows that several of these potential issues can be avoided through a multi level optimization strategy using discontinuous galerkin dg hp adaptive discretizations paired with runge kutta rk time integration we extend the concept of dual adjoint consistency to space time rk dg discretizations which are then shown to be well suited for the adaptive solution of time dependent inverse problems furthermore we prove that dg mesh transfer operators on general meshes are also dual consistent this allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation ad potentially speeding up development of large scale simulation codes the theoretical analysis is supported by numerical results reported for a two dimensional non stationary inverse problem

global cross ratio models for bivariate discrete ordered responses summary a family of statistical models is presented for bivariate discrete response to a regressor when both components of the response have ordered categories association between components is expressed in terms of global cross ratios cross product ratios of quadrant probabilities for each double dichotomy of the response table of probabilities into quadrants pearson and heron 1913 biometrika 9 159 315 these models are extensions to the work of plackett 1965 journal of the american statistical association 60 516 522 and mantel and brown 1973 biometrics 29 649 665 the marginal cumulative probabilities may satisfy linear logistic or other generalized linear models mccullagh 1980 journal of the royal statistical society series b 42 109 142 an analysis of patients postoperative pain level and medication frequency illustrates these methods

continuous adjoint sensitivities for optimization with general cost functionals on unstructured meshes a continuous adjoint approach is developed to obtain the sensitivity derivatives for the euler equations the completederivationofthecostateequations andtheirtransversality boundary conditionsarepresented both the state and the costate equations are second order e nite volume discretized for unstructured meshes and they are coupled with a constrained optimization algorithm also integrated into the overall methodology are a geometry parameterization method for the shape optimization and a dynamic unstructured mesh method for the shape evolution and the consequent volume mesh adaptations for the proof of concept three transonic airfoil optimization problems are presented this method accepts general cost functionals which are not necessarily functions of pressure only it is also shown that a switch to the natural coordinate system in conjunction with the reduction of the governing state equation to the control surface results in sensitivity integrals that are only a function of the tangential derivativesof the state variables thisapproach eliminates the need fornormal derivativecomputations that can be erroneous

marginal modelling of multivariate categorical data this paper describes likelihood methods of analysis for multivariate categorical data the joint distribution is specified in terms of marginal mean functions and pairwise and higher order association measures for the association the emphasis is on global odds ratios the method allows flexible formulation of a broad class of designs such as repeated measurements longitudinal studies interrater agreement and cross over trials the proposed model can be used for parameter estimation and hypothesis testing simple fitting algorithms are proposed the method is illustrated using a data example

dynamic latent trait models for multidimensional longitudinal data this article presents a new approach for analysis of multidimensional longitudinal data motivated by studies using an item response battery to measure traits of an individual repeatedly over time a general modeling framework is proposed that allows mixtures of count categorical and continuous response variables each response is related to age specific latent traits through a generalized linear model that accommodates item specific measurement errors a transition model allows the latent traits at a given age to depend on observed predictors and on previous latent traits for that individual following a bayesian approach to inference a markov chain monte carlo algorithm is proposed for posterior computation the methods are applied to data from a neurotoxicity study of the pesticide methoxychlor and evidence of a dose dependent increase in motor activity is presented

latent variable models for longitudinal data with bivariate ordinal outcomes we use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes and then extend the model to allow for longitudinal data specifically we relate the observed ordinal outcomes using threshold values to a bivariate latent variable which is then modelled as a linear mixed model random effects terms are used to tie all together repeated observations from the same subject the cross sectional association between the two outcomes is modelled through the correlation coefficient of the bivariate latent variable conditional on random effects assuming conditional independence given random effects the marginal likelihood under the missing data at random assumption is approximated using an adaptive gaussian quadrature for numerical integration the model provides fixed effects parameters that are subject specific but retain the population averaged interpretation when properly scaled this is particularly well suited for the situation in which population comparisons and individual level contrasts are of equal importance data from a psychiatric trial the fluvoxamine an antidepressant drug study are used to illustrate the methodology

maximum likelihood analysis of a general latent variable model with hierarchically mixed data summary a general two level latent variable model is developed to provide a comprehensive framework for model comparison of various submodels nonlinear relationships among the latent variables in the structural equations at both levels as well as the effects of fixed covariates in the measurement and structural equations at both levels can be analyzed within the framework moreover the methodology can be applied to hierarchically mixed continuous dichotomous and polytomous data a monte carlo em algorithm is implemented to produce the maximum likelihood estimate the e step is completed by approximating the conditional expectations through observations that are simulated by markov chain monte carlo methods while the m step is completed by conditional maximization a procedure is proposed for computing the complicated observed data log likelihood and the bic for model comparison the methods are illustrated by using a real data set

contribution to the optimal shape design of two dimensional internal flows with embedded shocks we explore the praticability of optimal shape design for flows modeled by the euler equations we define a functional whose minimum represents the optimality condition the gradient of the functional with respect to the geometry is calculated with the lagrange multipliers which are determined by solving acostateequation the optimization problem is then examined by comparing the performance of several gradient based optimization algorithms in this formulation the flow field can be computed to an arbitrary order of accuracy finally some results for internal flows with embedded shocks are presented including a case for which the solution to the inverse problem does not belong to the design space

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

admitting the inadmissible adjoint formulation for incomplete cost functionals in aerodynamic optimization we derive the adjoint equations for problems in aerodynamic optimization which are improperly considered as inadmissible for example a cost functional which depends on the density rather than on the pressure is considered inadmissible for an optimization problem governed by the euler equations we show that for such problems additional terms should be included in the lagrangian functional when deriving the adjoint equations these terms are obtained from the restriction of the interior pde to the control surface demonstrations of the explicit derivation of the adjoint equations for inadmissible cost functionals are given for the potential euler and navier stokes equations

systematic continuous adjoint approach to viscous aerodynamic design on unstructured grids doi 10 2514 1 24859 a continuous adjoint approach to aerodynamic design for viscous compressible flow on unstructured grids is developed sensitivity gradients arecomputed using tools ofshapedeformation of boundaryintegrals theresulting expressions involve second order derivatives of the flow variables that require numerical solvers with greater than second order accuracy a systematic way of reducing the order of these terms is presented the accuracy of the sensitivity derivatives is assessed by comparison with finite difference computations and the validity of the overall methodology is illustrated with several design examples

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

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

marginal modeling of correlated ordinal data using a multivariate plackett distribution abstract an extension of the bivariate model suggested by dale is proposed for the analysis of dependent ordinal categorical data the so called multivariate dale model is constructed by first generalizing the bivariate plackett distribution to any dimensions because the approach is likelihood based it satisfies properties that are not fulfilled by other popular methods such as the generalized estimating equations approach the proposed method models both the marginal and the association structure in a flexible way the attractiveness of the multivariate dale model is illustrated in three key examples covering areas such as crossover trials longitudinal studies with patients dropping out from the study and discriminant analysis applications the differences and similarities with the generalized estimating approach are highlighted

an a priori anisotropic goal oriented error estimate for viscous compressible flow and application to mesh adaptation abstract we present a goal oriented error analysis for the calculation of low reynolds steady compressible flows with anisotropic mesh adaptation the error analysis is of a priori type its central principle is to express the right hand side of the error equation often referred as the local error as a function of the interpolation error of a collection of fields present in the nonlinear partial differential equations this goal oriented error analysis is the extension of 39 done for inviscid flows to laminar viscous flows by adding viscous terms the main benefits of this approach in comparison to other error estimates in the literature is that the optimal anisotropy of the mesh directly appears in the error analysis and is not obtained from an ad hoc variable nor a local analysis as a consequence an optimum is obtained and the convergence of the mesh adaptive process is very fast i e generally the convergence is obtained after 5 to 10 mesh adaptation cycle then using the continuous mesh framework an optimal metric is analytically obtained from the error estimation applications to mesh adaptive calculations of flows past airfoils are presented

optimal control of flow with discontinuities optimal control of the 1 d riemann problem of euler equations is studied with the initial values for pressure and density as control parameters the least squares type cost functional employs either distributed observations in time or observations calculated at the end of the assimilation window existence of solutions for the optimal control problem is proven smooth and nonsmooth optimization methods employ the numerical gradient respectively a subgradient of the cost functional obtained from the adjoint of the discrete forward model the numerical flow obtained with the optimal initial conditions obtained from the nonsmooth minimization matches very well with the observations the algorithm for smooth minimization converges for the shorter time horizon but fails to perform satisfactorily for the longer time horizon except when the observations corresponding to shocks are detected and removed

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

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