an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

structural modeling and psychometrika an historical perspective on growth and achievements the field of linear structural equation modeling with continuous variables is reviewed trends in psychometric theory and data analysis across the five decades of publication ofpsychometrika are discussed especially the clarification of concepts of population and sample explication of the parametric structure of models delineation of concepts of exploratory and confirmatory data analysis expansion of statistical theory in psychometrics estimation via optimization of an explicit objective function and implementation of general function minimization methods developments in the ideas of factor analysis latent variables as well as structural and causal modeling are noted some major conceptual achievements involving general covariance structure representations multiple population models and moment structures are reviewed the major statistical achievements of normal theory generalized least squares estimation elliptical and distribution free estimation and higher moment estimation are discussed computer programs that implement some of the theoretical developments are described

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

building an identifiable latent class model with covariate effects on underlying and measured variables in recent years latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest such models summarize shared features of the multiple indicators as an underlying categorical variable and the indicators substantive associations with predictors are built directly and indirectly in unique model parameters in this paper we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership but that also allow direct effects of secondary covariates on the indicators themselves theory for model identification is developed we detail an expectation maximization algorithm for parameter estimation standard error calculation and convergent properties comparison of the proposed model with models underlying existing latent class modeling software is provided a detailed analysis of how visual impairments affect older persons functioning requiring distance vision is used for illustration

adjustment for non differential misclassification error in the generalized linear model it is well known that estimates of association between an outcome variable and a set of categorical covariates some of which are measured with misclassification tend to be biased upon application of the usual methods of estimation that ignore the classification error we propose a method to adjust for misclassification in covariates when one applies the generalized linear model in the case where one can observe some true covariates only through surrogates we combine a latent class analysis with the approach to incorporate multiple surrogates into the model we include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution we provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework

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

solution of the implicitly discretised reacting flow equations by operator splitting abstract a non iterative method for handling the coupling of the implicitly discretised time dependent fluid flow equations is described the method is based on the use of pressure and velocity as dependent variables and is hence applicable to both the compressible and incompressible versions of the transport equations the main feature of the technique is the splitting of the solution process into a series of steps whereby operations on pressure are decoupled from those on velocity at each step with the split sets of equations being amenable to solution by standard techniques at each time step the procedure yields solutions which approximate the exact solution of the difference equations the accuracy of this splitting procedure is assessed for a linearised form of the discretised equations and the analysis indicates that the solution yielded by it differs from the exact solution of the difference equations by terms proportional to the powers of the time step size by virtue of this it is possible to dispense with iteration thus resulting in an efficient implicit scheme while retaining simplicity of implementation relative to contemporary block simultaneous methods this is verified in a companion paper which presents results of computations carried out using the method

continuous and discrete latent structure models for item response data relations are examined between latent trait and latent class models for item response data conditions are given for the two latent class and two parameter normal ogive models to agree and relations between their item parameters are presented generalizationss are then made to continuous models with more than one latent trait and discrete models with more than two latent classes and methods are presented for relating latent class models to factor models for dichotomized variables results are illustrated using data from the law school admission test previously analyzed by several authors

a bayesian modeling approach for generalized semiparametric structural equation models in behavioral biomedical and psychological studies structural equation models sems have been widely used for assessing relationships between latent variables regression type structural models based on parametric functions are often used for such purposes in many applications however parametric sems are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable a different but equally important limitation of traditional parametric sems is that they are not designed to handle mixed data types continuous count ordered and unordered categorical this paper develops a generalized semiparametric sem that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables a structural equation of the proposed sem is formulated using a series of unspecified smooth functions the bayesian p splines approach and markov chain monte carlo methods are developed to estimate the smooth functions and the unknown parameters moreover we examine the relative benefits of semiparametric modeling over parametric modeling using a bayesian model comparison statistic called the complete deviance information criterion dic the performance of the developed methodology is evaluated using a simulation study to illustrate the method we used a data set derived from the national longitudinal survey of youth

strong and weak constraint variational assimilations for reduced order fluid flow modeling in this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a galerkin projection of the navier stokes equation the techniques proposed differ in the control variables they involve the first one introduces a weak dynamical model defined only up to an additional uncertainty time dependent function whereas the second one handles a strong dynamical constraint in which the dynamical system s coefficients constitute the control variables both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction the techniques have been assessed on numerical data and for real experimental conditions with noisy particle image velocimetry data

a latent variable transformation model approach for exploring dysphagia multiple outcomes are often collected in applications where the quantity of interest cannot be measured directly or is difficult or expensive to measure in a head and neck cancer study conducted at dana farber cancer institute the investigators wanted to determine the effect of clinical and treatment factors on unobservable dysphagia through collected multiple outcomes of mixed types latent variable models are commonly adopted in this setting these models stipulate that multiple collected outcomes are conditionally independent given the latent factor mixed types of outcomes e g continuous vs ordinal and censored outcomes present statistical challenges however as a natural analog of the multivariate normal distribution does not exist for mixed data recently lin et al proposed a semiparametric latent variable transformation model for mixed outcome data however it may not readily accommodate event time outcomes where censoring is present in this paper we extend the work of lin et al by proposing both semiparametric and parametric latent variable models that allow for the estimation of the latent factor in the presence of measurable outcomes of mixed types including censored outcomes both approaches allow for a direct estimate of the treatment or other covariate effect on the unobserved latent variable greatly enhancing the interpretability of the models the semiparametric approach has the added advantage of allowing the relationship between the measurable outcomes and latent variables to be unspecified rendering more robust inference the parametric and semiparametric models can also be used together providing a comprehensive modeling strategy for complicated latent variable problems copyright 2014 john wiley sons ltd

reducing measurement error in student achievement estimation the achievement level is a variable measured with error that can be estimated by means of the rasch model teacher grades also measure the achievement level but they are expressed on a different scale this paper proposes a method for combining these two scores to obtain a synthetic measure of the achievement level based on the theory developed for regression with covariate measurement error in particular the focus is on ordinal scaled grades using the simex method for measurement error correction the result is a measure comparable across subjects with smaller measurement error variance an empirical application illustrates the method

bivariate latent variable models for clustered discrete and continuous outcomes abstract we use the concept of a latent variable to derive the joint distribution of a continuous and a discrete outcome and then extend the model to allow for clustered data the model can be parameterized in a way that allows one to write the joint distribution as a product of a standard random effects model for the continuous variable and a correlated probit model for the discrete variable this factorization suggests a convenient approach to parameter estimation using quasi likelihood techniques our approach is motivated by the analysis of developmental toxicity experiments for which a number of discrete and continuous outcomes are measured on offspring clustered within litters fetal weight and malformation data illustrate the results

an estimating equations approach for the liscomp model maximum likelihood estimation is computationally infeasible for latent variable models involving multivariate categorical responses in particular for the liscomp model a three stage generalized least squares approach introduced by muthen 1983 1984 can experience problems of instability bias non convergence and non positive definiteness of weight matrices in situations of low prevalence small sample size and large numbers of observed indicator variables we propose a quadratic estimating equations approach that only requires specification of the first two moments by performing simultaneous estimation of parameters this method does not encounter the problems mentioned above and experiences gains in efficiency methods are compared through a numerical study and an application to a study of life events and neurotic illness

on structural equation modeling with data that are not missing completely at random a general latent variable model is given which includes the specification of a missing data mechanism this framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data here missing completely at random is not a prerequisite for unbiased estimation in large samples as when using the traditional listwise or pairwise present data approaches the theory is connected with old and new results in the area of selection and factorial invariance it is pointed out that in many applications maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software such as lisrel and liscomp several sets of artifical data are generated within the general model framework the proposed estimator is compared to the two traditional ones and found superior

rich families and projectional skeletons in asplund wcg spaces abstract we show a way of constructing projectional skeletons using the concept of rich families in banach spaces which admit a projectional generator our next result is that a banach space x is asplund and weakly compactly generated if and only if there exists a commutative 1 projectional skeleton q on x such that q is a commutative 1 projectional skeleton on x we consider both real and also complex banach spaces

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

an analysis of numerical errors in large eddy simulations of turbulence the reliability of numerical simulations of turbulence depend on our ability to quantify and control discretization errors in the classical literature on error analysis typically simple linear equations are studied estimates of errors derived from such analyses depend on the assumption that each dependent variable can be characterized by a unique amplitude and scale of spatial variation that can be normalized to unity this assumption is not valid for strongly nonlinear problems such as turbulence where nonlinear interactions rapidly redistribute energy resulting in the appearance of a broad continuous spectrum of amplitudes in such situations the numerical error as well as the subgrid model can change with grid spacing in a complicated manner that cannot be inferred from the results of classical error analysis in this paper a formalism for analyzing errors in such nonlinear problems is developed in the context of finite difference approximations for the navier stokes equations when the flow is fully turbulent analytical expressions for the power spectra of these errors are derived by exploiting the joint normal approximation for turbulent velocity fields these results are applied to large eddy simulation of turbulence to obtain quantitative bounds on the magnitude of numerical errors an assessment of the significance of these errors in made by comparing their magnitudes with that of the nonlinear and subgrid terms one method of controlling the errors is suggested and its effectiveness evaluated through quantitative measures although explicit evaluations are presented only for large eddy simulation the expressions derived for the power spectra of errors are applicable to direct numerical simulation as well

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

multivariate thurstonian models the recent development of probabilistic thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter and intra individual difference the multidimensional nature of choice objects and the effects of similarity and comparability among choice objects a common feature of these models is that they focus on asingle preference judgment it is customary however to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes this paper proposes a generalization of thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships the approach is illustrated by modeling data from two multivariate preference experiments

a polychoric instrumental variable piv estimator for structural equation models with categorical variables this paper presents a new polychoric instrumental variable piv estimator to use in structural equation models sems with categorical observed variables the piv estimator is a generalization of bollen s psychometrika 61 109 121 1996 2sls iv estimator for continuous variables to categorical endogenous variables we derive the piv estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models we also provide an estimator of the variance and covariance parameters of the model asymptotic standard errors for these and test statistics of overall model fit we examine this estimator via an empirical study and also via a small simulation study our results illustrate the greater robustness of the piv estimator to structural misspecifications than the system wide estimators that are commonly applied in sems

on local influence analysis of full information item factor models the full information item factor fiif model is very useful for analyzing relations of dichotomous variables in this article we present a feasible procedure to assess local influence of minor perturbations for identifying influence aspects of the fiif model the development is based on a q displacement function which is closely related with the monte carlo em algorithm in the ml estimation in the e step of this algorithm the conditional expectations are approximated by sample means of observations simulated by the gibbs sampler from the appropriate conditional distributions it turns out that these observations can be utilized for computing the building blocks of the proposed diagnostic measures the diagnoses are based on the conformal normal curvature that can be computed easily a number of interesting perturbation schemes are considered the methodology is illustrated with two real examples

generating multivariate ordinal data via entropy principles when conducting robustness research where the focus of attention is on the impact of non normality the marginal skewness and kurtosis are often used to set the degree of non normality monte carlo methods are commonly applied to conduct this type of research by simulating data from distributions with skewness and kurtosis constrained to pre specified values although several procedures have been proposed to simulate data from distributions with these constraints no corresponding procedures have been applied for discrete distributions in this paper we present two procedures based on the principles of maximum entropy and minimum cross entropy to estimate the multivariate observed ordinal distributions with constraints on skewness and kurtosis for these procedures the correlation matrix of the observed variables is not specified but depends on the relationships between the latent response variables with the estimated distributions researchers can study robustness not only focusing on the levels of non normality but also on the variations in the distribution shapes a simulation study demonstrates that these procedures yield excellent agreement between specified parameters and those of estimated distributions a robustness study concerning the effect of distribution shape in the context of confirmatory factor analysis shows that shape can affect the robust chi 2 and robust fit indices especially when the sample size is small the data are severely non normal and the fitted model is complex

the polyserial correlation coefficient the polyserial and point polyserial correlations are discussed as generalizations of the biserial and point biserial correlations the relationship between the polyserial and point polyserial correlation is derived the maximum likelihood estimator of the polyserial correlation is compared with a two step estimator and with a computationally convenient ad hoc estimator all three estimators perform reasonably well in a monte carlo simulation some practical applications of the polyserial correlation are described

paradoxical results in multidimensional item response theory in multidimensional item response theory mirt it is possible for the estimate of a subject s ability in some dimension to decrease after they have answered a question correctly this paper investigates how and when this type of paradoxical result can occur we demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of linearly compensatory models maximum likelihood estimates are guaranteed to do so in light of these findings the appropriateness of multidimensional item response methods for assigning scores in high stakes testing is called into question

tracking switched dynamic network topologies from information cascades contagions such as the spread of popular news stories or infectious diseases propagate in cascades over dynamic networks with unobservable topologies however social signals such as product purchase time or blog entry timestamps are measurable and implicitly depend on the underlying topology making it possible to track it over time interestingly network topologies often jump between discrete states that may account for sudden changes in the observed signals the present paper advocates a switched dynamic structural equation model to capture the topology dependent cascade evolution as well as the discrete states driving the underlying topologies conditions under which the proposed switched model is identifiable are established leveraging the edge sparsity inherent to social networks a recursive ell 1 norm regularized least squares estimator is put forth to jointly track the states and network topologies an efficient first order proximal gradient algorithm is developed to solve the resulting optimization problem numerical experiments on both synthetic data and real cascades measured over the span of one year are conducted and test results corroborate the efficacy of the advocated approach

alpha dimension free and model based internal consistency reliability as pointed out by sijtsma in press coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score better estimators of internal consistency are available in addition to those mentioned by sijtsma an old dimension free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency the various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items

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

reconstruction of unsteady viscous flows using data assimilation schemes this paper investigates the use of various data assimilation da approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts variational ensemble kalman filter based and ensemble based variational da techniques are deployed along with a 2d compressible navier stokes flow solver which is also used to generate synthetic observations of a reference flow the performance of these da schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2d flow field moreover different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale da problems with up to 105 control variables in particular we show how an iterative procedure can be used within the framework of ensemble based methods to deal with both non uniform unsteady boundary conditions and initial field reconstruction the different methodologies developed and assessed in this work give a review of what can be done with da schemes in computational fluid dynamics cfd paradigm in the same time this work also provides useful information which can also turn out to be rational arguments in the da scheme choice dedicated to a specific cfd application

identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes this article considers the identification conditions of confirmatory factor analysis cfa models for ordered categorical outcomes with invariance of different types of parameters across groups the current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model this approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways once an invariance condition is imposed on a parameter these identification conditions may become restrictions and define statistically non equivalent models leading to different conclusions by analyzing the transformation that leaves the model implied probabilities of response patterns unchanged we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model

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

on the link between cognitive diagnostic models and knowledge space theory the present work explores the connections between cognitive diagnostic models cdm and knowledge space theory kst and shows that these two quite distinct approaches overlap it is proved that in fact the multiple strategy dina deterministic input noisy and gate model and the cblim a competence based extension of the basic local independence model blim are equivalent to demonstrate the benefits that arise from integrating the two theoretical perspectives it is shown that a fairly complete picture on the identifiability of these models emerges by combining results from both camps the impact of the results is illustrated by an empirical example and topics for further research are pointed out

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

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

numerical dissipation vs subgrid scale modelling for large eddy simulation this study presents an alternative way to perform large eddy simulation based on a targeted numerical dissipation introduced by the discretization of the viscous term it is shown that this regularisation technique is equivalent to the use of spectral vanishing viscosity the flexibility of the method ensures high order accuracy while controlling the level and spectral features of this purely numerical viscosity a pao like spectral closure based on physical arguments is used to scale this numerical viscosity a priori it is shown that this way of approaching large eddy simulation is more efficient and accurate than the use of the very popular smagorinsky model in standard as well as in dynamic version the main strength of being able to correctly calibrate numerical dissipation is the possibility to regularise the solution at the mesh scale thanks to this property it is shown that the solution can be seen as numerically converged conversely the two versions of the smagorinsky model are found unable to ensure regularisation while showing a strong sensitivity to numerical errors the originality of the present approach is that it can be viewed as implicit large eddy simulation in the sense that the numerical error is the source of artificial dissipation but also as explicit subgrid scale modelling because of the equivalence with spectral viscosity prescribed on a physical basis

a note on exploratory item factor analysis by singular value decomposition we revisit a singular value decomposition svd algorithm given in chen et al psychometrika 84 124 146 2019b for exploratory item factor analysis ifa this algorithm estimates a multidimensional ifa model by svd and was used to obtain a starting point for joint maximum likelihood estimation in chen et al 2019b thanks to the analytic and computational properties of svd this algorithm guarantees a unique solution and has computational advantage over other exploratory ifa methods its computational advantage becomes significant when the numbers of respondents items and factors are all large this algorithm can be viewed as a generalization of principal component analysis to binary data in this note we provide the statistical underpinning of the algorithm in particular we show its statistical consistency under the same double asymptotic setting as in chen et al 2019b we also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory further extensions of the algorithm are discussed finally simulation studies suggest that the algorithm has good finite sample performance

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

pairwise likelihood ratio tests and model selection criteria for structural equation models with ordinal variables correlated multivariate ordinal data can be analysed with structural equation models parameter estimation has been tackled in the literature using limited information methods including three stage least squares and pseudo likelihood estimation methods such as pairwise maximum likelihood estimation in this paper two likelihood ratio test statistics and their asymptotic distributions are derived for testing overall goodness of fit and nested models respectively under the estimation framework of pairwise maximum likelihood estimation simulation results show a satisfactory performance of type i error and power for the proposed test statistics and also suggest that the performance of the proposed test statistics is similar to that of the test statistics derived under the three stage diagonally weighted and unweighted least squares furthermore the corresponding under the pairwise framework model selection criteria aic and bic show satisfactory results in selecting the right model in our simulation examples the derivation of the likelihood ratio test statistics and model selection criteria under the pairwise framework together with pairwise estimation provide a flexible framework for fitting and testing structural equation models for ordinal as well as for other types of data the test statistics derived and the model selection criteria are used on data on trust in the police selected from the 2010 european social survey the proposed test statistics and the model selection criteria have been implemented in the r package lavaan

structural equation models with continuous and polytomous variables a two stage procedure is developed for analyzing structural equation models with continuous and polytomous variables at the first stage the maximum likelihood estimates of the thresholds polychoric covariances and variances and polyserial covariances are simultaneously obtained with the help of an appropriate transformation that significantly simplifies the computation an asymptotic covariance matrix of the estiates is also computed at the second stage the parameters in the structural covariance model are obtained via the generalized least squares approach basic statistical properties of the estimates are derived and some illustrative examples and a small simulation study are reported

asplund spaces characterized by rich families and separable reduction of frechet subdifferentiability abstract asplund property of a banach space x is characterized by the existence of a rich family in the product x x consisting of some carefully chosen separable subspaces this structural result is then used to add a lot of precision and simplicity to the known separable reductions of frechet subdifferentials

a problem with discretizing vale maurelli in simulation studies previous influential simulation studies investigate the effect of underlying non normality in ordinal data using the vale maurelli vm simulation method we show that discretized data stemming from the vm method with a prescribed target covariance matrix are usually numerically equal to data stemming from discretizing a multivariate normal vector this normal vector has however a different covariance matrix than the target it follows that these simulation studies have in fact studied data stemming from normal data with a possibly misspecified covariance structure this observation affects the interpretation of previous simulation studies

a model based approach to simultaneous clustering and dimensional reduction of ordinal data the literature on clustering for continuous data is rich and wide differently that one developed for categorical data is still limited in some cases the clustering problem is made more difficult by the presence of noise variables dimensions that do not contain information about the clustering structure and could mask it the aim of this paper is to propose a model for simultaneous clustering and dimensionality reduction of ordered categorical data able to detect the discriminative dimensions discarding the noise ones following the underlying response variable approach the observed variables are considered as a discretization of underlying first order latent continuous variables distributed as a gaussian mixture to recognize discriminative and noise dimensions these variables are considered to be linear combinations of two independent sets of second order latent variables where only one contains the information about the cluster structure while the other one contains noise dimensions the model specification involves multidimensional integrals that make the maximum likelihood estimation cumbersome and in some cases infeasible to overcome this issue the parameter estimation is carried out through an em like algorithm maximizing a composite log likelihood based on low dimensional margins examples of application of the proposal on real and simulated data are performed to show the effectiveness of the proposal

statistical assessment of mediational effects for logistic mediational models the concept of mediation has broad applications in medical health studies although the statistical assessment of a mediational effect under the normal assumption has been well established in linear structural equation models sem it has not been extended to the general case where normality is not a usual assumption in this paper we propose to extend the definition of mediational effects through causal inference the new definition is consistent with that in linear sem and does not rely on the assumption of normality here we focus our attention on the logistic mediation model where all variables involved are binary three approaches to the estimation of mediational effects delta method bootstrap and bayesian modelling via monte carlo simulation are investigated simulation studies are used to examine the behaviour of the three approaches measured by 95 per cent confidence interval ci coverage rate and root mean square error rmse criteria it was found that the bayesian method using a non informative prior outperformed both bootstrap and the delta methods particularly for small sample sizes case studies are presented to demonstrate the application of the proposed method to public health research using a nationally representative database extending the proposed method to other types of mediational model and to multiple mediators are also discussed

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

covariance structure models and influence diagrams statisticians use covariance structure modeling as a versatile tool for modeling and testing theory the models that result provide explicit and detailed descriptions of stochastic systems we show how covariance structure models are related mathematically conceptually philosophically and practically to gaussian influence diagrams as described by shachter and kenley 1989 this relationship suggests ways in which covariance structure modeling can be used to advantage in the prescriptive domain of decision analysis the paper includes an example concerning the management of hazardous materials in which a covariance structure model is converted to an influence diagram for use in a prescriptive analysis

a reduced order model based on kalman filtering for sequential data assimilation of turbulent flows abstract a kalman filter based sequential estimator is presented in this work the estimator is integrated in the structure of segregated solvers for the analysis of incompressible flows this technique provides an augmented flow state integrating available observation in the cfd model naturally preserving a zero divergence condition for the velocity field because of the prohibitive costs associated with a complete kalman filter application two model reduction strategies have been proposed and assessed these strategies dramatically reduce the increase in computational costs of the model which can be quantified in an augmentation of 10 15 with respect to the classical numerical simulation in addition an extended analysis of the behavior of the numerical model covariance q has been performed optimized values are strongly linked to the truncation error of the discretization procedure the estimator has been applied to the analysis of a number of test cases exhibiting increasing complexity including turbulent flow configurations the results show that the augmented flow successfully improves the prediction of the physical quantities investigated even when the observation is provided in a limited region of the physical domain in addition the present work suggests that these data assimilation techniques which are at an embryonic stage of development in cfd may have the potential to be pushed even further using the augmented prediction as a powerful tool for the optimization of the free parameters in the numerical simulation

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

a short note on the estimation of the asymptotic covariance matrix for polychoric correlations by using a taylor expansion of the equations that define the two step estimator for polychoric correlations the asymptotic covariance matrix for the estimated correlations can be derived in a simple and straightforward way

assessing the size of model misfit in structural equation models when a statistically significant mean difference is found the magnitude of the difference is judged qualitatively using an effect size such as cohen s d in contrast in a structural equation model sem the result of the statistical test of model fit is often disregarded if significant and inferences are drawn using close models retained based on point estimates of sample statistics goodness of fit indices however when a sem cannot be retained using a test of exact fit all substantive inferences drawn from it are suspect it is therefore important to determine the size of the model misfit standardized residual covariances and residual correlations provide standardized effect sizes of the misfit of sem models they can be summarized using the standardized root mean squared residual srmsr and the correlation root mean squared residual crmsr which can be used as overall effect sizes of the misfit statistical theory is provided that allows the construction of confidence intervals and tests of close fit based on the srmsr and crmsr it is hoped that the use of standardized effect sizes of misfit will help reconcile current practices in sem and elsewhere in statistics

an instrumental variable estimator for mixed indicators analytic derivatives and alternative parameterizations methodological development of the model implied instrumental variable miiv estimation framework has proved fruitful over the last three decades major milestones include bollen s psychometrika 61 1 109 121 1996 original development of the miiv estimator and its robustness properties for continuous endogenous variable sems the extension of the miiv estimator to ordered categorical endogenous variables bollen and maydeu olivares in psychometrika 72 3 309 2007 and the introduction of a generalized method of moments estimator bollen et al in psychometrika 79 1 20 50 2014 this paper furthers these developments by making several unique contributions not present in the prior literature 1 we use matrix calculus to derive the analytic derivatives of the piv estimator 2 we extend the piv estimator to apply to any mixture of binary ordinal and continuous variables 3 we generalize the piv model to include intercepts and means 4 we devise a method to input known threshold values for ordinal observed variables and 5 we enable a general parameterization that permits the estimation of means variances and covariances of the underlying variables to use as input into a sem analysis with piv an empirical example illustrates a mixture of continuous variables and ordinal variables with fixed thresholds we also include a simulation study to compare the performance of this novel estimator to wlsmv

immersed boundary methods for general finite difference and finite volume navier stokes solvers we present an immersed boundary algorithm for incompressible flows with complex boundaries suitable for cartesian or curvilinear grid system the key stages of any immersed boundary technique are the interpolation of a velocity field given on a mesh onto a general boundary a line in 2d a surface in 3d and the spreading of a force field from the immersed boundary to the neighboring mesh points to enforce the desired boundary conditions on the immersed boundary points we propose a technique that uses the reproducing kernel particle method w k liu s jun y f zhang reproducing kernel particle methods int j numer methods fluids 20 8 1995 1081 1106 for the interpolation and spreading unlike other methods presented in the literature the one proposed here has the property that the integrals of the force field and of its moment on the grid are conserved independent of the grid topology uniform or non uniform cartesian or curvilinear the technique is easy to implement and is able to maintain the order of the original underlying spatial discretization applications to two and three dimensional flows in cartesian and non cartesian grid system with uniform and non uniform meshes are presented

multivariate analysis with linearizable regressions we study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables this class seems more realistic than the multivariate normal or the elliptical distributions and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis in particular a two stage procedure which first scales the variables optimally and then fits a simultaneous equations model is studied in detail and is shown to have some desirable properties

simultaneous factor analysis of dichotomous variables in several groups a new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals the method makes it possible to compare factor loading pattern factor variances and covariances and factor means over groups the method uses information from first and second order proportions and estimates the model by generalized least squares hypotheses regarding different degrees of invariance over groups may be evaluated by a large sample chi square test

inflow and initial conditions for direct numerical simulation based on adjoint data assimilation a method for generating inflow conditions for direct numerical simulations dns of spatially developing flows is presented the proposed method is based on variational data assimilation and adjoint based optimization the estimation is conducted through an iterative process involving a forward integration of a given dynamical model followed by a backward integration of an adjoint system defined by the adjoint of the discrete scheme associated to the dynamical system the approach s robustness is evaluated on two synthetic velocity field sequences provided by numerical simulation of a mixing layer and a wake flow behind a cylinder the performance of the technique is also illustrated in a real world application by using noisy large scale piv measurements this method denoises experimental velocity fields and reconstructs a continuous trajectory of motion fields from discrete and unstable measurements

bayesian estimation and testing of structural equation models the gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model sem given covariance data and a prior distribution over the parameters point estimates standard deviations and interval estimates for the parameters can be computed from these samples if the prior distribution over the parameters is uninformative the posterior is proportional to the likelihood and asymptotically the inferences based on the gibbs sample are the same as those based on the maximum likelihood solution for example output from lisrel or eqs in small samples however the likelihood surface is not gaussian and in some cases contains local maxima nevertheless the gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface with an informative prior distribution over the parameters the posterior can be used to make inferences about the parameters of underidentified models as we illustrate on a simple errors in variables model

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

bayesian non parametric models for spatially indexed data of mixed type we develop bayesian nonparametric models for spatially indexed data of mixed type our work is motivated by challenges that occur in environmental epidemiology where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and under stand the effects of risk factors on health outcomes of interest the modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables and uses mul tivariate gaussians to jointly model these responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific obtained as probit transformations of gaussian markov random fields con founding variables and spatial configuration have a similar role in the model in that they only in uence along with the responses the allocation probabilities of the areas into the mixture components thereby allowing for exible adjustment of the effects of observed confounders while allowing for the possibility of residual spatial structure possibly occurring due to unmeasured or undiscovered spatially varying factors aspects of the model are illustrated in simulation studies and an application to a real data set

kernel based structural equation models for topology identification of directed networks structural equation models sems have been widely adopted for inference of causal interactions in complex networks recent examples include unveiling topologies of hidden causal networks over which processes such as spreading diseases or rumors propagate the appeal of sems in these settings stems from their simplicity and tractability since they typically assume linear dependencies among observable variables acknowledging the limitations inherent to adopting linear models the present paper put forth nonlinear sems which account for possible nonlinear dependencies among network nodes the advocated approach leverages kernels as a powerful encompassing framework for nonlinear modeling and an efficient estimator with affordable tradeoffs is put forth interestingly pursuit of the novel kernel based approach yields a convex regularized estimator that promotes edge sparsity a property exhibited by most real world networks and the resulting optimization problem is amenable to proximal splitting optimization methods to this end solvers with complementary merits are developed by leveraging the alternating direction method of multipliers and proximal gradient iterations experiments conducted on simulated data demonstrate that the novel approach outperforms linear sems with respect to edge detection errors furthermore tests on a real gene expression dataset unveil interesting new edges that were not revealed by linear sems which could shed more light on regulatory behavior of human genes

generalized latent trait models in this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model a unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented we discuss in addition the scoring of individuals on the latent dimensions the general framework presented allows not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions the approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly

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

partial identification of latent correlations with binary data the tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector however when the underlying vector is not normal the tetrachoric correlation will be different from the underlying correlation since assuming underlying normality is often done on pragmatic and not substantial grounds the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling this motivates studying the range of latent correlations that are compatible with given binary data when the distribution of the latent vector is partly or completely unknown we show that nothing can be said about the latent correlations unless we know more than what can be derived from the data we identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known also we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations implications for tests of underlying normality are briefly discussed

inner characterizations of weakly compactly generated banach spaces and their relatives we give characterizations of weakly compactly generated spaces their subspaces vasak spaces weakly lindelof determined spaces as well as several other classes of banach spaces related to uniform g teaux smoothness in terms of the presence of a total subset of the space with some additional properties in addition we describe geometrically when possible these classes by means of suitable smoothness or rotundity of the norm as a consequence we get new functional analytic proofs of several theorems on uniform eberlein gul ko and talagrand compacta

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

a comparison of latent trait and latent class analyses of likert type data this paper brings together and compares two developments in the analysis of likert attitude scales the first is the generalization of latent class models to ordered response categories the second is the introduction of latent trait models with multiplicative parameter structures for the analysis of rating scales key similarities and differences between these two methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of life satisfaction data the way in which the latent trait model defines a unit of measurement takes into account the order of the response categories and scales the latent classes is discussed while the latent class model provides better fit to these data this is achieved at the cost of a logically inconsistent assignment of individuals to latent classes

thurstonian modeling of ranking data via mean and covariance structure analysis although thurstonian models provide an attractive representation of choice behavior they have not been extensively used in ranking applications since only recently efficient estimation methods for these models have been developed these however require the use of special purpose estimation programs which limits their applicability here we introduce a formulation of thurstonian ranking models that turns an idiosyncratic estimation problem into an estimation problem involving mean and covariance structures with dichotomous indicators well known standard solutions for the latter can be readily applied to this specific problem and as a result any thurstonian model for ranking data can be fitted using existing general purpose software for mean and covariance structure analysis although the most popular programs for covariance structure analysis e g lisrel and eqs cannot be presently used to estimate thurstonian ranking models other programs such as mecosa already exist that can be straightforwardly used to estimate these models

on the estimation of polychoric correlations and their asymptotic covariance matrix a general theory for parametric inference in contingency tables is outlined estimation of polychoric correlations is seen as a special case of this theory the asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds computational aspects are also discussed

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

banach spaces with projectional skeletons a projectional skeleton in a banach space is a directed family of projections onto separable subspaces covering the entire space the class of banach spaces with projectional skeletons is strictly larger than the class of plichko spaces i e banach spaces with a countably norming markushevich basis we show that every space with a projectional skeleton has a projectional resolution of the identity and has a norming space with similar properties to spaces we characterize the existence of a projectional skeleton in terms of elementary substructures providing simple proofs of known results concerning weakly compactly generated spaces and plichko spaces we prove a preservation result for plichko banach spaces involving transfinite sequences of projections as a corollary we show that a banach space is plichko if and only if it has a commutative projectional skeleton

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

limited information estimation and testing of thurstonian models for paired comparison data under multiple judgment sampling we relate thurstonian models for paired comparisons data to thurstonian models for ranking data which assign zero probabilities to all intransitive patterns we also propose an intermediate model for paired comparisons data that assigns nonzero probabilities to all transitive patterns and to some but not all intransitive patterns

fast moment estimation for generalized latent dirichlet models we develop a generalized method of moments gmm approach for fast parameter estimation in a new class of dirichlet latent variable models with mixed data types parameter estimation via gmm has co

factor analysis with mixed observed and latent variables in the exponential family we develop a general approach to factor analysis that involves observed and latent variables that are assumed to be distributed in the exponential family this gives rise to a number of factor models not considered previously and enables the study of latent variables in an integrated methodological framework rather than as a collection of seemingly unrelated special cases the framework accommodates a great variety of different measurement scales and accommodates cases where different latent variables have different distributions the models are estimated with the method of simulated likelihood which allows for higher dimensional factor solutions to be estimated than heretofore the models are illustrated on synthetic data we investigate their performance when the distribution of the latent variables is mis specified and when part of the observations are missing we study the properties of the simulation estimators relative to maximum likelihood estimation with numerical integration we provide an empirical application to the analysis of attitudes

an approximate marginal logistic distribution for the analysis of longitudinal ordinal data subject specific and marginal models have been developed for the analysis of longitudinal ordinal data subject specific models often lack a population average interpretation of the model parameters due to the conditional formulation of random intercepts and slopes marginal models frequently lack an underlying distribution for ordinal data in particular when generalized estimating equations are applied to overcome these issues latent variable models underneath the ordinal outcomes with a multivariate logistic distribution can be applied in this article we extend the work of o brien and dunson 2004 who studied the multivariate t distribution with marginal logistic distributions we use maximum likelihood instead of a bayesian approach and incorporated covariates in the correlation structure in addition to the mean model we compared our method with gee and demonstrated that it performs better than gee with respect to the fixed effect parameter estimation when the latent variables have an approximately elliptical distribution and at least as good as gee for other types of latent variable distributions