multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

measurement error in dietary assessment an investigation using covariance structure models part i in part i we presented a covariance structure model for analysing measurement error in the assessment of nitrogen intake in this paper we include data on urine nitrogen excretion which allows a critical assessment of the model proposed inclusion of urine nitrogen data produces more pessimistic estimates of the quality of dietary intake measurements and shows that previous assumptions about independence of measurement error were wrong this underscores the need for well founded assumptions in the analysis of measurement error

latent variable modeling in heterogeneous populations common applications of latent variable analysis fail to recognize that data may be obtained from several populations with different sets of parameter values this article describes the problem and gives an overview of methodology that can address heterogeneity artificial examples of mixtures are given where if the mixture is not recognized strongly distorted results occur mimic structural modeling is shown to be a useful method for detecting and describing heterogeneity that cannot be handled in regular multiple group analysis other useful methods instead take a random effects approach describing heterogeneity in terms of random parameter variation across groups these random effects models connect with emerging methodology for multilevel structural equation modeling of hierarchical data examples are drawn from educational achievement testing psychopathology and sociology of education estimation is carried out by the liscomp program

efficient estimation for semiparametric structural equation models with censored data abstractstructural equation modeling is commonly used to capture complex structures of relationships among multiple variables both latent and observed we propose a general class of structural equation models with a semiparametric component for potentially censored survival times we consider nonparametric maximum likelihood estimation and devise a combined expectation maximization and newton raphson algorithm for its implementation we establish conditions for model identifiability and prove the consistency asymptotic normality and semiparametric efficiency of the estimators finally we demonstrate the satisfactory performance of the proposed methods through simulation studies and provide an application to a motivating cancer study that contains a variety of genomic variables supplementary materials for this article are available online

nearly h1 optimal finite element methods abstract we examine the problem of finding the h 1 projection onto a finite element space of an unknown field satisfying a specified boundary value problem solving the projection problem typically requires knowing the exact solution we circumvent this issue and obtain a petrov galerkin formulation which achieves h 1 optimality requiring weighting functions to be defined locally on the element level permits only approximate h 1 optimality in multi dimensional configurations we investigate the relation between our formulation and other stabilized fem formulations we show in particular that our formulation leads to a derivation of the supg method in special cases the present formulation reduces to that of residual free bubbles finally we present guidelines for obtaining the petrov weight functions and include a numerical example for the helmholtz equation

automatically stable discontinuous petrov galerkin methods for stationary transport problems quasi optimal test space norm we investigate the application of the discontinuous petrov galerkin dpg finite element framework to stationary convection diffusion problems in particular we demonstrate how the quasi optimal test space norm improves the robustness of the dpg method with respect to vanishing diffusion we numerically compare coarse mesh accuracy of the approximation when using the quasi optimal norm the standard norm and the weighted norm our results show that the quasi optimal norm leads to more accurate results on three benchmark problems in two spatial dimensions we address the problems associated to the resolution of the optimal test functions with respect to the quasi optimal norm by studying their convergence numerically in order to facilitate understanding of the method we also include a detailed explanation of the methodology from the algorithmic point of view

efficient bootstrap simulation on donne deux idees pour renforcer une simulation la premiere est d equilibrer les echantillons simules la seconde est de faire un usage explicite des approximations qui ne demandent pas de simulation

the characteristic based split cbs scheme a unified approach to fluid dynamics this paper presents a comprehensive overview of the characteristic based methods and characteristic based split cbs scheme the practical difficulties of employing the original characteristic schemes are discussed the important features of the cbs scheme are brought out by studying several problems of compressible and incompressible flows all special consideration necessary for solving these problems are thoroughly discussed the cbs scheme is presented in such a way that any interested researcher should be able to develop a code using the information provided several invicid and viscous flow examples are also provided to demonstrate the unified cbs approach for sample two dimensional codes input files and instructions the readers are referred to www nithiarasu co uk copyright 2006 john wiley sons ltd

on using linear elements in incompressible plane strain problems a simple edge based approach for triangles in this paper a simple iterative method is presented for finite element solution of incompressible plane strain problems using linear elements instead of using a mixed formulation approach we use an equivalent displacement velocity approach in an iterative manner control volumes are taken for regions which are to exhibit incompressible behaviour for triangular elements the control volume is chosen as the area built on the parts of each pair of elements at the sides of an edge in this case elements are let to exchange volume it is shown that the proposed edge based approach removes the deficiency of the linear triangular elements i e locking effect similar edge based approach is applied to the linear quadrilateral elements however if the control volume is chosen as the element volume the formulation gives similar results as the discontinuous mixed formulation using one pressure point without exhibiting instability behaviour the formulation is based on decomposition of the displacement velocity field into deviatoric and volumetric parts the volumetric part is iteratively eliminated without confronting locking or instability phenomenon the iterative procedure is very cheap and simple to be implemented in any fem code several examples are given to demonstrate the performance of the procedure copyright 2004 john wiley sons ltd

structural modeling of measurement error in generalized linear models with rasch measures as covariates this paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables the focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models latent variable estimates are then treated as observed measures of the true variables this leads to a two stage estimation procedure which constitutes an alternative to a joint model for the outcome variable and the responses given to the questionnaire simulation studies explore the effect of ignoring the true error structure and the performance of the proposed method two illustrative examples concern achievement data of university students particular attention is given to the rasch model

bayesian factor analysis for multilevel binary observations multilevel covariance structure models have become increasingly popular in the psychometric literature in the past few years to account for population heterogeneity and complex study designs we develop practical simulation based procedures for bayesian inference of multilevel binary factor analysis models we illustrate how markov chain monte carlo procedures such as gibbs sampling and metropolis hastings methods can be used to perform bayesian inference model checking and model comparison without the need for multidimensional numerical integration we illustrate the proposed estimation methods using three simulation studies and an application involving student s achievement results in different areas of mathematics

parameterization of multivariate random effects models for categorical data alternative parameterizations and problems of identification and estimation of multivariate random effects models for categorical responses are investigated the issues are illustrated in the context of the multivariate binomial logit normal bln model introduced by coull and agresti 2000 biometrics 56 73 80 we demonstrate that the bln model is poorly identified unless proper restrictions are imposed on the parameters moreover estimation of bln models is unduly computationally complex in the first application considered by coull and agresti an identification problem results in highly unstable highly correlated parameter estimates and large standard errors a probit normal version of the specified bln model is demonstrated to be underidentified whereas the bln model is empirically underidentified identification can be achieved by constraining one of the parameters we show that a one factor probit model is equivalent to the probit version of the specified bln model and that a one factor logit model is empirically equivalent to the bln model estimation is greatly simplified by using a factor model

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

high dimensional maximum marginal likelihood item factor analysis by adaptive quadrature although the bock aitkin likelihood based estimation method for factor analysis of dichotomous item response data has important advantages over classical analysis of item tetrachoric correlations a serious limitation of the method is its reliance on fixed point gauss hermite g h quadrature in the solution of the likelihood equations and likelihood ratio tests when the number of latent dimensions is large computational considerations require that the number of quadrature points per dimension be few but with large numbers of items the dispersion of the likelihood given the response pattern becomes so small that the likelihood cannot be accurately evaluated with the sparse fixed points in the latent space in this paper we demonstrate that substantial improvement in accuracy can be obtained by adapting the quadrature points to the location and dispersion of the likelihood surfaces corresponding to each distinct pattern in the data in particular we show that adaptive g h quadrature combined with mean and covariance adjustments at each iteration of an em algorithm produces an accurate fast converging solution with as few as two points per dimension evaluations of this method with simulated data are shown to yield accurate recovery of the generating factor loadings for models of upto eight dimensions unlike an earlier application of adaptive gibbs sampling to this problem by meng and schilling the simulations also confirm the validity of the present method in calculating likelihood ratio chi square statistics for determining the number of factors required in the model finally we apply the method to a sample of real data from a test of teacher qualifications

a combined fic tdg finite element approach for the numerical solution of coupled advection diffusion reaction equations with application to a bioregulatory model for bone fracture healing summary numerical schemes for the approximative solution of advection diffusion reaction equations are often flawed because of spurious oscillations caused by steep gradients or dominant advection or reaction in addition for strong coupled nonlinear processes which may be described by a set of hyperbolic pdes established time stepping schemes lack either accuracy or stability to provide a reliable solution in this contribution an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques namely the finite calculus fic fem scheme introduced by onate et al with time discontinuous galerkin tdg methods whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection dominated problems the latter ensures reliable solutions with regard to the temporal evolution a brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests the performance of the suggested fic tdg finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by geris et al which consists of at least 12 coupled hyperbolic evolution equations copyright 2012 john wiley sons ltd

latent class models for diary method data parameter estimation by local computations the increasing use of diary methods calls for the development of appropriate statistical methods for the resulting panel data latent markov models can be used to model both individual differences and temporal dynamics the computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model this is done by associating a probabilistic model with a directed acyclic graph and applying transformations to the graph the structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables which is the basis of a modified and more efficient e step of the em algorithm the usefulness of the approach is illustrated by estimating a latent markov model involving a large number of measurement occasions and subsequently a hierarchical extension of the latent markov model that allows for transitions at different levels furthermore logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates throughout models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients

stabilized mixed finite element formulations for materially nonlinear partially saturated two phase media standard and enhanced bbar or eas low order finite elements applied to the problem of consolidation of two phase nonlinear continua do not satisfy the lbb condition when the same interpolation functions are used for both displacement and pore pressure fields strong spatial pressure oscillations are the main consequence of the lbb condition violation the class of direct stabilized methods widely used in the field of fluid mechanics is a powerful tool to circumvent violation of the aforementioned condition three stabilized formulations designed for the problem of consolidation of fully or partially saturated media are presented galerkin least squares gls with the least squares term construction based on the residuum of the local fluid mass conservation equation the pressure stabilized formulation fpl in which the rate of the pore pressure laplacian residual free in the incompressibility limit is added to the fluid mass conservation equation and finally a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation an h convergence study and test problems for the three stabilized schemes are discussed

a generalized galerkin method for steady convection diffusion problems with application to quadratic shape function elements abstract a generalization of the standard galerkin finite element method is considered to enable it to deal successfully with steady convection diffusion problems the proposed method employs a generalized governing equation which is obtained by subtracting from the original differential equation the scalar product of its gradient by a vector of free parameters associated with each of the coordinate directions the generalized equation is successively discretized by the standard bubnov galerkin finite element method the effectiveness of the method is illustrated for the case of quadratic local interpolations in one and two space dimensions

multilevel mixed linear model analysis using iterative generalized least squares summary models for the analysis of hierarchically structured data are discussed an iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case there is a discussion of applications to complex surveys longitudinal data and estimation in multivariate models with missing responses an example is given using educational data

stabilized finite element methods for steady advection diffusion with production abstract finite element methods for solving equations of steady advection diffusion with production are constructed employing a linear source to model production the galerkin method requires relatively fine meshes to retain an acceptable degree of accuracy for wide ranges of values of the physical coefficients numerous criteria for improved accuracy via galerkin least squares are proposed and examined in the entire parameter space of these several provide the lowest error in nodal amplification factors each in a certain range of ratios of physical coefficients guidelines for required mesh resolutions are presented for galerkin and galerkin least squares showing that in large parts of the parameter space substantial savings may be obtained by employing galerkin least squares galerkin least squares gradient least squares a new variation of the galerkin method is designed to provide exact nodal amplification factors offering accurate solutions at any resolution numerical tests validate these conclusions

bayesian semiparametric analysis of structural equation models with mixed continuous and unordered categorical variables recently structural equation models sems have been applied for analyzing interrelationships among observed and latent variables in biological and medical research latent variables in these models are typically assumed to have a normal distribution this article considers a bayesian semparametric sem with covariates and mixed continuous and unordered categorical variables in which the explanatory latent variables in the structural equation are modeled via an appropriate truncated dirichlet process with a stick breaking procedure results obtained from a simulation study and an analysis of a real medical data set are presented to illustrate the methodology

on the stabilization parameter in the subgrid scale approximation of scalar convection diffusion reaction equations on distorted meshes abstract in this paper we revisit the definition of the stabilization parameter in the finite element approximation of the convection diffusion reaction equation the starting point is the decomposition of the unknown into its finite element component and a subgrid scale that needs to be approximated in order to incorporate the distortion of the mesh into this approximation we transform the equation for the subgrid scale within each element to the shape regular reference domain the expression for the subgrid scale arises from an approximate fourier analysis and the identification of the wave number direction where instabilities are most likely to occur the final outcome is an expression for the stabilization parameter that accounts for anisotropy and the dominance of either convection or reaction terms in the equation

a high resolution petrov galerkin method for the 1d convection diffusion reaction problem abstract we present the design of a high resolution petrov galerkin hrpg method using linear finite elements for the problem defined by the residual r t u x k 2 x 2 s f where k s 0 the structure of the method in 1d is identical to the consistent approximate upwind petrov galerkin cau pg method a c galeao e g dutra do carmo a consistent approximate upwind petrov galerkin method for the convection dominated problems comput methods appl mech engrg 68 1988 83 95 except for the definitions of the stabilization parameters such a structure may also be attained via the finite calculus fic procedure e onate derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems comput methods appl mech engrg 151 1998 233 265 e onate j miquel g hauke stabilized formulation for the advection diffusion absorption equation using finite calculus and linear finite elements comput methods appl mech engrg 195 2006 3926 3946 by an appropriate definition of the characteristic length the prefix high resolution is used here in the sense popularized by harten i e second order accuracy for smooth regular regimes and good shock capturing in nonregular regimes the design procedure embarks on the problem of circumventing the gibbs phenomenon observed in l 2 projections next we study the conditions on the stabilization parameters to circumvent the global oscillations due to the convective term a conjuncture of the two results is made to deal with the problem at hand that is usually plagued by gibbs global and dispersive oscillations in the numerical solution it is shown that the method indeed reproduces stabilized high resolution numerical solutions for a wide range of values of u k s and f finally some remarks are made on the extension of the hrpg method to multidimensions

a positivity preserving variational method for multi dimensional convectiondiffusionreaction equation a new positivity preserving variational ppv procedure is proposed to solve the convectiondiffusionreaction cdr equation through the generalization of stabilized finite element methods the present variational procedure offers minimal phase and amplitude errors for different regimes associated with convection diffusion and reaction effects by means of fourier analysis we first review the shortcomings of the galerkin least squares gls and the subgrid scale sgs methods during the change in sign of the reaction coefficient that motivates us for the present linear stabilization as a combined gls sgs methodology discrete upwind operator with a solution dependent nonlinear term is then introduced in high gradient regions which enables the positivity preserving property in the variational formulation direct extension to multi dimensions is carried out by considering the principle streamline and crosswind directions the efficacy of the method is demonstrated by the systematic accuracy and stability analyses in one and two dimensions results show the reduction of oscillations in the solution in one and two dimensional cases and a remarkable reduction in the phase error is observed for the cases with negative reaction coefficient the proposed formulation provides a superior solution in the reaction dominated as well as the convection dominated regimes due to the minimization of spurious oscillations and accurate capturing of the high gradient regions

simple modifications for stabilization of the finite point method a stabilized version of the finite point method fpm is presented a source of instability due to the evaluation of the base function using a least square procedure is discussed a suitable mapping is proposed and employed to eliminate the ill conditioning effect due to directional arrangement of the points a step by step algorithm is given for finding the local rotated axes and the dimensions of the cloud using local average spacing and inertia moments of the points distribution it is shown that the conventional version of fpm may lead to wrong results when the proposed mapping algorithm is not used it is shown that another source for instability and non monotonic convergence rate in collocation methods lies in the treatment of neumann boundary conditions unlike the conventional fpm in this work the neumann boundary conditions and the equilibrium equations appear simultaneously in a weight equation similar to that of weighted residual methods the stabilization procedure may be considered as an interpretation of the finite calculus fic method the main difference between the two stabilization procedures lies in choosing the characteristic length in fic and the weight of the boundary residual in the proposed method the new approach also provides a unique definition for the sign of the stabilization terms the reasons for using stabilization terms only at the boundaries is discussed and the two methods are compared several numerical examples are presented to demonstrate the performance and convergence of the proposed methods copyright 2005 john wiley sons ltd

regression among factor scores structural equation models with latent variables are sometimes estimated using an intuitive three step approach here denoted factor score regression consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest in this simple example estimation of the structural parameter proceeds as follows first common factor models areseparately estimated for each latent variable second factor scores areseparately assigned to each latent variable based on the estimates third ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter we investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables it is demonstrated that the conventional approach to factor score regression performs very badly revised factor score regression using regression factor scores for the explanatory latent variables and bartlett scores for the response latent variables produces consistent estimators for all parameters

improved regression calibration the likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form which makes maximum likelihood estimation taxing a popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation we propose an improved regression calibration approach a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood it is both consistent and computationally efficient and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood simulations suggest that improved regression calibration which is easy to implement in standard software works well in a range of situations

generalized multilevel structural equation modeling a unifying framework for generalized multilevel structural equation modeling is introduced the models in the framework called generalized linear latent and mixed models gllamm combine features of generalized linear mixed models glmm and structural equation models sem and consist of a response model and a structural model for the latent variables the response model generalizes glmms to incorporate factor structures in addition to random intercepts and coefficients as in glmms the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower level units in the higher level units and missing data a wide range of response processes can be modeled including ordered and unordered categorical responses counts and responses of mixed types the structural model is similar to the structural part of a sem except that it may include latent and observed variables varying at different levels for example unit level latent variables factors or random coefficients can be regressed on cluster level latent variables special cases of this framework are explored and data from the british social attitudes survey are used for illustration maximum likelihood estimation and empirical bayes latent score prediction within the gllamm framework can be performed using adaptive quadrature in gllamm a freely available program running in stata

a locally extended finite element method for the simulation of multi fluid flows using the particle level set method abstract the simulation of immiscible two phase flows on eulerian meshes requires the use of special techniques to guarantee a sharp definition of the evolving fluid interface this work describes the combination of two distinct technologies with the goal of improving the accuracy of the target simulations first of all a spatial enrichment is employed to improve the approximation properties of the eulerian mesh this is done by injecting into the solution space new features to make it able to correctly resolve the solution in the vicinity of the moving interface then the lagrangian particle level set pls method is employed to keep trace of the evolving solution and to improve the mass conservation properties of the resulting method while the local enrichment can be understood in the general context of the xfem we employ an element local variant which allows preserving the matrix graph and hence highly improving the computational efficiency

maximum likelihood estimation of multilevel structural equation models with random slopes for latent covariates a maximum likelihood estimation routine for two level structural equation models with random slopes for latent covariates is presented because the likelihood function does not typically have a closed form solution numerical integration over the random effects is required the routine relies upon a method proposed by du toit and cudeck psychometrika 74 1 65 82 2009 for reformulating the likelihood function so that an often large subset of the random effects can be integrated analytically reducing the computational burden of high dimensional numerical integration the method is demonstrated and assessed using a small scale simulation study and an empirical example

derivation of stabilized equations for numerical solution of advective diffusive transport and fluid flow problems abstract the concept of the so called artificial or balancing diffusion used to stabilize the numerical solution of advective diffusive transport and fluid flow problems is revised in this paper it is shown that the standard forms of the balancing diffusion terms usually chosen in a heuristic manner can be naturally found by introducing higher order approximations in the derivation of the governing differential equations via standard conservation or equilibrium principles this allows us to reinterpret many stabilization algorithms and concepts used in every day practice by numerical analysts and also provides an expression for computing the stabilization parameter

a variational maximization maximization algorithm for generalized linear mixed models with crossed random effects we present a variational maximization maximization algorithm for approximate maximum likelihood estimation of generalized linear mixed models with crossed random effects e g item response models with random items random raters or random occasion specific effects the method is based on a factorized variational approximation of the latent variable distribution given observed variables which creates a lower bound of the log marginal likelihood the lower bound is maximized with respect to the factorized distributions as well as model parameters with the proposed algorithm a high dimensional intractable integration is translated into a two dimensional integration problem we incorporate an adaptive gauss hermite quadrature method in conjunction with the variational method in order to increase computational efficiency numerical studies show that under the small sample size conditions that are considered the proposed algorithm outperforms the laplace approximation

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

using phantom and imaginary latent variables to parameterize constraints in linear structural models the most widely used computer programs for structural equation models analysis are the lisrel series of joreskog and sorbom the only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal rindskopf 1983 showed how these simple properties could be used to represent models with more complicated constraints namely inequality constraints on unique variances in this paper two new concepts are introduced which enable a much wider variety of constraints to be made the concepts phantom and imaginary latent variables allow fairly general equality and inequality constraints on factor loadings and structural model coefficients

latent curve analysis as a method for representing development latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth maximum likelihood parameter estimates and associated asymptotic tests follow directly these procedures may be viewed as an alternative to standard repeated measures anova and to first order auto regressive methods as formulated the model encompasses cohort sequential designs and allow for period or practice effects a numerical illustration using data initially collected by nesselroade and baltes is presented

a two level structural equation model approach for analyzing multivariate longitudinal responses the analysis of longitudinal data to study changes in variables measured repeatedly over time has received considerable attention in many fields this paper proposes a two level structural equation model for analyzing multivariate longitudinal responses that are mixed continuous and ordered categorical variables the first level model is defined for measures taken at each time point nested within individuals for investigating their characteristics that are changed with time the second level is defined for individuals to assess their characteristics that are invariant with time the proposed model accommodates fixed covariates nonlinear terms of the latent variables and missing data a maximum likelihood ml approach is developed for the estimation of parameters and model comparison results of a simulation study indicate that the performance of the ml estimation is satisfactory the proposed methodology is applied to a longitudinal study concerning cocaine use

a general structural equation model with dichotomous ordered categorical and continuous latent variable indicators a structural equation model is proposed with a generalized measurement part allowing for dichotomous and ordered categorical variables indicators in addition to continuous ones a computationally feasible three stage estimator is proposed for any combination of observed variable types this approach provides large sample chi square tests of fit and standard errors of estimates for situations not previously covered two multiple indicator modeling examples are given one is a simultaneous analysis of two groups with a structural equation model underlying skewed likert variables the second is a longitudinal model with a structural model for multivariate probit regressions

constrained maximum likelihood estimation of two level covariance structure model via em type algorithms in this paper the constrained maximum likelihood estimation of a two level covariance structure model with unbalanced designs is considered the two level model is reformulated as a single level model by treating the group level latent random vectors as hypothetical missing data then the popular em algorithm is extended to obtain the constrained maximum likelihood estimates for general nonlinear constraints the multiplier method is used at them step to find the constrained minimum of the conditional expectation an accelerated em gradient procedure is derived to handle linear constraints the empirical performance of the proposed em type algorithms is illustrated by some artifical and real examples

the superconvergent patch recovery spr and adaptive finite element refinement abstract the error estimation processes which have been developed by the authors depend on the accuracy with which stresses gradients can be recovered the recovery methods available currently such as the l 2 projection and averaging are inaccurate and an improved process is needed this paper presents a very much improved recovery process yielding superconvergent values throughout the domain details of this method named the superconvergent patch recovery are presented with test results showing its efficiency examples of adaptive h based refinement are given showing high local and overall efficiency indices for error estimation

oddls a new unstructured mesh finite element method for the analysis of free surface flow problems this paper introduces a new stabilized finite element method based on the finite calculus comput methods appl mech eng 1998 151 233 267 and arbitrary lagrangian eulerian techniques comput methods appl mech eng 1998 155 235 249 for the solution to free surface problems the main innovation of this method is the application of an overlapping domain decomposition concept in the statement of the problem the aim is to increase the accuracy in the capture of the free surface as well as in the resolution of the governing equations in the interface between the two fluids free surface capturing is based on the solution to a level set equation the navier stokes equations are solved using an iterative monolithic predictor corrector algorithm encyclopedia of computational mechanics wiley new york 2004 where the correction step is based on imposing the divergence free condition in the velocity field by means of the solution to a scalar equation for the pressure examples of application of the oddls formulation for overlapping domain decomposition level set to the analysis of different free surface flow problems are presented copyright 2008 john wiley sons ltd

a taylor galerkin method for convective transport problems a method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions to produce accurate temporal differencing the method employs forward time taylor series expansions including time derivatives of second and third order which are evaluated from the governing partial differential equation this yields a generalized time discretized equation which is successively discretized in space by means of the standard bubnov galerkin finite element method the technique is illustrated first in one space dimension with linear elements and euler leap frog and crank nicolson time stepping several interesting relations with standard galerkin and recently developed petrov galerkin methods emerge and the new taylor galerkin schemes are found to exhibit particularly high phase accuracy with minimal numerical damping the method is successively extended to deal with variable coefficient problems and multi dimensional situations

a finite element method for fluid structure interaction with surface waves using a finite calculus formulation abstract a stabilized semi implicit fractional step finite element method fem for solving coupled fluid structure interaction problems involving free surface waves is presented the stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus fic procedure a mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described examples of the efficiency of the stabilized semi implicit algorithm for the analysis of fluid structure interaction problems in totally or partially submerged bodies is presented

modeling incompressible flows at low and high reynolds numbers via a finite calculus finite element approach we present a formulation for incompressible flows analysis using the finite element method fem the necessary stabilization for dealing with convective effects and the incompressibility condition is modeled via the finite calculus fic method the stabilization terms introduced by the fic formulation allow to solve a wide range of fluid flow problems for low and high reynolds numbers flows without the need for a turbulence model examples of application of the fic fem formulation to the analysis of 2d and 3d incompressible flows with moderate and large reynolds numbers are presented

finite volumes and finite elements two good friends in this paper a comparison between the finite element and the finite volume methods is presented in the context of elliptic convective diffusion and fluid flow problems the paper shows that both procedures share a number of features like mesh discretization and approximation moreover it is shown that in many cases both techniques are completely equivalent

pseudo maximum likelihood estimation of mean and covariance structures with missing data abstract a nonlinear mean and covariance structure model for one or more groups is constructed the model subsumes the usual linear model considered in the literature it is then shown how to estimate the parameters of the model and the asymptotic covariance matrix of the parameter estimates using pseudo maximum likelihood pml estimation the resulting estimates are strongly consistent under general regularity conditions provided only that the model for the first two moments is correctly specified nevertheless because the data are not necessarily drawn from a multivariate normal distribution the usual likelihood ratio tests for model comparisons in mean and covariance structure models do not apply wald tests and lagrange multiplier tests may be used to implement such comparisons next the standard results on ml estimation with missing data are extended to the case of pml estimation with missing data and the results are applied to the model the approach to the missing data problem adopted whic

fluid structure interaction using the particle finite element method abstract in the present work a new approach to solve fluid structure interaction problems is described both the equations of motion for fluids and for solids have been approximated using a material lagrangian formulation to approximate the partial differential equations representing the fluid motion the shape functions introduced by the meshless finite element method mfem have been used thus the continuum is discretized into particles that move under body forces gravity and surface forces due to the interaction with neighboring particles all the physical properties such as density viscosity conductivity etc as well as the variables that define the temporal state such as velocity and position and also other variables like temperature are assigned to the particles and are transported with the particle motion the so called particle finite element method pfem provides a very advantageous and efficient way for solving contact and free surface problems highly simplifying the treatment of fluid structure interactions

a posteriori optimization of parameters in stabilized methods for convection diffusion problems part i abstract stabilized finite element methods for convection dominated problems require the choice of appropriate stabilization parameters from numerical analysis often only their asymptotic values are known this paper presents a general framework for optimizing stabilization parameters with respect to the minimization of a target functional exemplarily this framework is applied to the supg finite element method and the minimization of a residual based error estimator an error indicator and a functional including the crosswind derivative of the computed solution benefits of the basic approach are demonstrated by means of numerical results

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

generalized sample size determination formulas for investigating contextual effects by a three level random intercept model behavioral and psychological researchers have shown strong interests in investigating contextual effects i e the influences of combinations of individual and group level predictors on individual level outcomes the present research provides generalized formulas for determining the sample size needed in investigating contextual effects according to the desired level of statistical power as well as width of confidence interval these formulas are derived within a three level random intercept model that includes one predictor contextual variable at each level to simultaneously cover various kinds of contextual effects that researchers can show interest the relative influences of indices included in the formulas on the standard errors of contextual effects estimates are investigated with the aim of further simplifying sample size determination procedures in addition simulation studies are performed to investigate finite sample behavior of calculated statistical power showing that estimated sample sizes based on derived formulas can be both positively and negatively biased due to complex effects of unreliability of contextual variables multicollinearity and violation of assumption regarding the known variances thus it is advisable to compare estimated sample sizes under various specifications of indices and to evaluate its potential bias as illustrated in the example

multiscale computational analysis in mechanics using finite calculus an introduction abstract the paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus fic formulation the fic approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size this introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters the discrete nodal values obtained with the fic formulation and the finite element method fem can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched fem typical multiscale problems in mechanics which can be solved with the fic method include convection diffusion reaction problems with high localized gradients incompressible problems in solid and fluid mechanics localization problems such as prediction of shear bands in solids and shock waves in compressible fluids turbulence etc the paper presents an introduction of the treatment of multiscale problems using the fic approach in conjunction with the fem examples of application of the fic fem formulation to the solution of simple multiscale convection diffusion problems are given

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

multi fluid flows with the particle finite element method abstract particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied on it in this paper the particle finite element method based on finite element shape functions is used to solve the continuous fluid mechanics equations in the case of heterogeneous density to evaluate the external applied forces to each particle the incompressible navier stokes equations are solved at each time step using a lagrangian formulation all the information in the fluid is transmitted via the particles all kinds of density heterogeneous fluids and multiphase flows with internal interfaces including or not free surfaces breaking waves and fluid separations may be easily solved with this methodology

a finite point method in computational mechanics applications to convective transport and fluid flow the paper presents a fully meshless procedure fo solving partial differential equations the approach termed generically the finite point method is based on a weighted least square interpolation of point data and point collocation for evaluating the approximation integrals some examples showing the accuracy of the method for solution of adjoint and non self adjoint equations typical of convective diffusive transport and also to the analysis of compressible fluid mechanics problem are presented

on spurious oscillations at layers diminishing sold methods for convection diffusion equations part i a review abstract an unwelcome feature of the popular streamline upwind petrov galerkin supg stabilization of convection dominated convection diffusion equations is the presence of spurious oscillations at layers since the mid of the 1980s a number of methods have been proposed to remove or at least to diminish these oscillations without leading to excessive smearing of the layers the paper gives a review and state of the art of these methods discusses their derivation proposes some alternative choices of parameters in the methods and categorizes them some numerical studies which supplement this review provide a first insight into the advantages and drawbacks of the methods

accurate fic fem formulation for the multidimensional steady state advection diffusion absorption equation abstract in this paper we present an accurate stabilized fic fem formulation for the multidimensional steady state advection diffusion absorption equation the stabilized formulation is based on the galerkin fem solution of the governing differential equations derived via the finite increment calculus fic method using two stabilization parameters the value of the two stabilization parameters ensuring an accurate nodal fem solution using uniform meshes of linear elements is obtained from the optimal values for the 1d problem the accuracy of the new fic fem formulation is demonstrated in the solution of 2d steady state advection diffusion absorption problems for a range of physical parameters and boundary conditions

a fic based stabilized finite element formulation for turbulent flows abstract we present a new stabilized finite element fem formulation for incompressible flows based on the finite increment calculus fic framework onate 1998 in comparison to existing fic approaches for fluids this formulation involves a new term in the momentum equation which introduces non isotropic dissipation in the direction of velocity gradients we also follow a new approach to the derivation of the stabilized mass equation inspired by recent developments for quasi incompressible flows onate et al 2014 the presented fic fem formulation is used to simulate turbulent flows using the dissipation introduced by the method to account for turbulent dissipation in the style of implicit large eddy simulation

on the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids the purpose of this paper is to study the effect of the bulk modulus on the iterative solution of free surface quasi incompressible fluids using a mixed partitioned scheme a practical rule to set up the value of a pseudo bulk modulus a priori in the tangent bulk stiffness matrix for improving the conditioning of the linear system of algebraic equations is also given the efficiency of the proposed strategy is tested in several problems analyzing the advantage of the modified bulk tangent matrix with regard to the stability of the pressure field the convergence rate and the computational speed of the analyses the technique has been tested on a finite calculus particle finite element method lagrangian formulation but it can be easily extended to other quasi incompressible stabilized finite element formulations copyright c 2014 john wiley sons ltd

comparison of some finite element methods for solving the diffusion convection reaction equation abstract in this paper we describe several finite element methods for solving the diffusion convection reaction equation none of them is new although the presentation is non standard in an effort to emphasize the similarities and differences between them in particular it is shown that the classical supg method is very similar to an explicit version of the characteristic galerkin method whereas the taylor galerkin method has a stabilization effect similar to a sub grid scale model which is in turn related to the introduction of bubble functions

multilevel logistic regression for polytomous data and rankings we propose a unifying framework for multilevel modeling of polytomous data and rankings accommodating dependence induced by factor and or random coefficient structures at different levels the framework subsumes a wide range of models proposed in disparate methodological literatures partial and tied rankings alternative specific explanatory variables and alternative sets varying across units are handled the problem of identification is addressed we develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software the methodology is applied to party choice and rankings from the 1987 1992 panel of the british election study three levels are considered elections voters and constituencies

an em algorithm for fitting two level structural equation models maximum likelihood is an important approach to analysis of two level structural equation models different algorithms for this purpose have been available in the literature in this paper we present a new formulation of two level structural equation models and develop an em algorithm for fitting this formulation this new formulation covers a variety of two level structural equation models as a result the proposed em algorithm is widely applicable in practice a practical example illustrates the performance of the em algorithm and the maximum likelihood statistic

factor analysis for clustered observations classical factor analysis assumes a random sample of vectors of observations for clustered vectors of observations such as data for students from colleges or individuals within households it may be necessary to consider different within group and between group factor structures such a two level model for factor analysis is defined and formulas for a scoring algorithm for estimation with this model are derived a simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed this method provides a suitable starting solution for the iterative algorithm but it is also a very good approximation to the maximum likelihood solution extensions for higher levels of nesting are indicated with judicious application of quasi newton methods the amount of computation involved in the scoring algorithm is moderate even for complex problems in particular no inversion of matrices with large dimensions is involved the methods are illustrated on two examples

maximum likelihood estimation of two level latent variable models with mixed continuous and polytomous data summary two level data with hierarchical structure and mixed continuous and polytomous data are very common in biomedical research in this article we propose a maximum likelihood approach for analyzing a latent variable model with these data the maximum likelihood estimates are obtained by a monte carlo em algorithm that involves the gibbs sampler for approximating the e step and the m step and the bridge sampling for monitoring the convergence the approach is illustrated by a two level data set concerning the development and preliminary findings from an aids preventative intervention for filipina commercial sex workers where the relationship between some latent quantities is investigated

bayesian modeling of measurement error in predictor variables using item response theory it is shown that measurement error in predictor variables can be modeled using item response theory irt the predictor variables that may be defined at any level of an hierarchical regression model are treated as latent variables the normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables which may be responses to tests or questionnaires it will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a bayesian framework using gibbs sampling in this article handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model examples using real data are given

a general model for the analysis of multilevel data a general model is developed for the analysis of multivariate multilevel data structures special cases of the model include repeated measures designs multiple matrix samples multilevel latent variable models multiple time series and variance and covariance component models

additive multilevel item structure models with random residuals item modeling for explanation and item generation an additive multilevel item structure amis model with random residuals is proposed the model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels the amis model is useful for explanation purposes and also for prediction purposes as in an item generation context the parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature and the performance of this algorithm is evaluated in a simulation study

the particle finite element method a powerful tool to solve incompressible flows with free surfaces and breaking waves summary particle methods are those in which the problem is represented by a discrete number of particles each particle moves accordingly with its own mass and the external internal forces applied to it particle methods may be used for both discrete and continuous problems in this paper a particle method is used to solve the continuous fluid mechanics equations to evaluate the external applied forces on each particle the incompressible navier stokes equations using a lagrangian formulation are solved at each time step the interpolation functions are those used in the meshless finite element method and the time integration is introduced by an implicit fractional step method in this manner classical stabilization terms used in the momentum equations are unnecessary due to lack of convective terms in the lagrangian formulation once the forces are evaluated the particles move independently of the mesh all the information is transmitted by the particles fluid structure interaction problems including free fluid surfaces breaking waves and fluid particle separation may be easily solved with this methodology copyright 2004 john wiley sons ltd

the discontinuous enrichment method we propose a finite element based discretization method in which the standard polynomial field is enriched within each element by a nonconforming field that is added to it the enrichment contains free space solutions of the homogeneous differential equation that are not represented by the underlying polynomial field continuity of the enrichment across element interfaces is enforced weakly by lagrange multipliers in this manner we expect to attain high coarse mesh accuracy without significant degradation of conditioning assuring good performance of the computation at any mesh resolution examples of application to acoustics and advection diffusion are presented

possibilities of finite calculus in computational mechanics abstract the expression finite calculus refers to the derivation of the governing differential equations in mechanics by invoking balance of fluxes forces etc in a domain of finite size the governing equations resulting from this approach are different from those of infinitessimal calculus theory and they incorporate new terms depending on the dimensions of the balance domain the new modified equations allow to derive naturally stabilized numerical schemes using finite element finite difference finite volume or meshless methods the paper briefly discusses the possibilities of the modified governing equations derived via the finite calculus technique for the numerical solution of convection diffusion problems incompressible flow and incompressible solid mechanic problems and strain localization problems

high dimensional exploratory item factor analysis by a metropolis hastings robbins monro algorithm a metropolis hastings robbins monro mh rm algorithm for high dimensional maximum marginal likelihood exploratory item factor analysis is proposed the sequence of estimates from the mh rm algorithm converges with probability one to the maximum likelihood solution details on the computer implementation of this algorithm are provided the accuracy of the proposed algorithm is demonstrated with simulations as an illustration the proposed algorithm is applied to explore the factor structure underlying a new quality of life scale for children it is shown that when the dimensionality is high mh rm has advantages over existing methods such as numerical quadrature based em algorithm extensions of the algorithm to other modeling frameworks are discussed

unified lagrangian formulation for elastic solids and incompressible fluids application to fluid structure interaction problems via the pfem abstract we present a general lagrangian formulation for treating elastic solids and quasi fully incompressible fluids in a unified form the formulation allows to treat solid and fluid subdomains in a unified manner in fluid structure interaction fsi situations in our work the fsi problem is solved via the particle finite element method pfem the pfem is an effective technique for modeling complex interactions between floating and submerged bodies and free surface flows accounting for splashing of waves large motions of the bodies and frictional contact conditions applications of the unified lagrangian formulation to a number of fsi problems are given

multilevel and latent variable modeling with composite links and exploded likelihoods composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models applications considered include survival or duration models models for rankings small area estimation with census information models for ordinal responses item response models with guessing randomized response models unfolding models latent class models with random effects multilevel latent class models models with log normal latent variables and zero inflated poisson models with random effects some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation

a stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation abstract a stabilized finite element formulation for incompressible viscous flows is derived the starting point are the modified navier stokes equations incorporating naturally the necessary stabilization terms via a finite increment calculus fic procedure application of the standard finite element galerkin method to the modified differential equations leads to a stabilized discrete system of equations overcoming the numerical instabilities emanating from the advective terms and those due to the lack of compatibility between approximate velocity and pressure fields the fic method also provides a natural explanation for the stabilization terms appearing in all equations for both the navier stokes and the simpler stokes equations transient solution schemes with enhanced stabilization properties are also proposed finally a procedure for computing the stabilization parameters is presented

maximum likelihood estimation of limited and discrete dependent variable models with nested random effects abstract gauss hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models unfortunately the estimates are biased for large cluster sizes and or intraclass correlations we show that adaptive quadrature largely overcomes these problems we then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependent variables the models can include several nested random effects intercepts and coefficients representing unobserved heterogeneity at different levels of a hierarchical dataset the required multivariate integrals are evaluated efficiently using spherical quadrature rules simulations show that adaptive quadrature performs well in a wide range of situations

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100