the heteroscedastic graded response model with a skewed latent trait testing statistical and substantive hypotheses related to skewed item category functions the graded response model grm samejima estimation of ability using a response pattern of graded scores psychometric monograph no 17 richmond va the psychometric society 1969 can be derived by assuming a linear regression of a continuous variable z on the trait to underlie the ordinal item scores takane de leeuw in psychometrika 52 393 408 1987 traditionally a normal distribution is specified for z implying homoscedastic error variances and a normally distributed in this paper we present the heteroscedastic grm with skewed latent trait which extends the traditional grm by incorporation of heteroscedastic error variances and a skew normal latent trait an appealing property of the extended grm is that it includes the traditional grm as a special case this enables specific tests on the normality assumption of z we show how violations of normality in z can lead to asymmetrical category response functions the ability to test this normality assumption is beneficial from both a statistical and substantive perspective in a simulation study we show the viability of the model and investigate the specificity of the effects we apply the model to a dataset on affect and a dataset on alexithymia

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

information processing in complex networks graph entropy and information functionals this paper introduces a general framework for defining the entropy of a graph our definition is based on a local information graph and on information functionals derived from the topological structure of a given graph more precisely an information functional quantifies structural information of a graph based on a derived probability distribution such a probability distribution leads directly to an entropy of a graph then the structural information content of a graph will be is interpreted and defined as the derived graph entropy another major contribution of this paper is the investigation of relationships between graph entropies in addition to this we provide numerical results demonstrating not only the feasibility of our method which has polynomial time complexity but also its usefulness with regard to practical applications aiming to an understanding of information processing in complex networks

recurrence relations based on minimization and maximization abstract explicit and asymptotic solutions are presented to the recurrence m 1 g 1 m n 1 g n 1 min1 t n m t m n 1 t for the cases 1 log 2 log 2 is rational and g n ni 2 1 min 1 log 2 log 2 is rational and a g n n1 b g n 1 the general form of this recurrence was studied extensively by fredman and knuth j math anal appl 48 1974 534 559 who showed without actually solving the recurrence that in the above cases m n n 1 1 where is defined by 1 and that lim n m n n 1 does not exist using similar techniques the recurrence m 1 g 1 m n 1 g n 1 max1 t n m t m n 1 t is also investigated for the special case

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

asymptotic expansions for linear homogeneous divide and conquer recurrences algebraic and analytic approaches collated among all sequences that satisfy a divide and conquer recurrence those which are rational with respect to a numeration system are certainly the most basic and the most essential nevertheless until recently this specific class of sequences has not been systematically studied from the asymptotic standpoint we recall how a mechanical process designed by the author permits to compute their asymptotic expansions the process is based on linear algebra and involves computing jordan normal forms joint spectral radii and solving dilation equations the main contribution of the present article is the comparison between our algebraic method and the classical analytic number theory approach moreover we develop new ways to compute the fourier series of the periodic functions involved in the expansion the article comes with an extended bibliography

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 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

on graph entropy measures based on the number of independent sets and matchings abstract in this paper we consider the graph entropy measures based on the number of independent sets and matchings the reason to study these measures relates to the fact that the independent set and matching problem is computationally demanding however these features can be calculated for smaller networks in case one can establish efficient estimations those measures may be also used for larger graphs so we establish some upper and lower bounds as well as some information inequalities for these information theoretic quantities in order to give further evidence we also generate numerical results to study these measures such as list the extremal graphs for these entropies those results reveal the two entropies possess some new features

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

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

entropy bounds for dendrimers abstract many graph invariants have been used for the construction of entropy based measures to characterize the structure of complex networks when considering shannon entropy based graph measures there has been very little work to find their extremal values a reason for this might be the fact that shannon s entropy represents a multivariate function and all probability values are not equal to zero when considering graph entropies dehmer and kraus proved some extremal results for graph entropies which are based on information functionals and express some conjectures generated by numerical simulations to find extremal values of graph entropies dehmer and kraus discussed the extremal values of entropies for dendrimers in this paper we continue to study the extremal values of graph entropy for dendrimers which has most interesting applications in molecular structure networks and also in the pharmaceutical and biomedical area among all dendrimers with n vertices we obtain the extremal values of graph entropy based on different well known information functionals numerical experiments verifies our results

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

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

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

comparison between the zeroth order randic index and the sum connectivity index the zeroth order randic index and the sum connectivity index are very popular topological indices in mathematical chemistry these two indices are based on vertex degrees of graphs and attracted a lot of attention in recent years recently li and li 2015 studied these two indices for trees of order n in this paper we obtain a relation between the zeroth order randic index and the sum connectivity index for graphs from this we infer an upper bound for the sum connectivity index of graphs moreover we prove that the zeroth order randic index is greater than the sum connectivity index for trees finally we show that r2 g is greater or equal r1 g 1 for any graph and characterize the extremal graphs

bounds for degree based network entropies in this paper we continue studying degree based entropies for networks the quantities represent information theoretic network measures which are based on using information functionals involving vertex degrees we prove bounds for entropies which are based on information functionals using degree powers and come up with interrelations between different measures such interrelations are important to study connections between the measures required to understand the measures in depth

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

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

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

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

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

min max operators in texture analysis a signature is generated for a given picture by operating on it with different masks the operations are gray level generalizations of shrink and expand for binary pictures using serra s morphological methods 10 the signature is a set of numbers each corresponding to an application of an operator at a certain scale and direction and can be used to analyze the discriminate textures it is shown that this family of signatures includes as special cases several currently used texture descriptors

probabilistic inequalities for evaluating structural network measures proving interrelations between structural graph measures analytically has been intricate generally relations between structural graph measures describe the interplay between measures which turned out to be useful for better understanding the properties of such quantities the results which have been achieved so far are restricted to simple measures or special graph classes such as trees in this paper we introduce a probabilistic approach for establishing inequalities between quantitative network measures on random networks those inequalities between different graph measures lead to a deeper understanding of the mathematical apparatus and in particular to a discussion of quality aspects of structural graph measures which is a major contribution of this paper

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

testing the assumptions underlying tetrachoric correlations a method is proposed for empirically testing the appropriateness of using tetrachoric correlations for a set of dichotomous variables trivariate marginal information is used to get a set of one degree of freedom chi square tests of the underlying normality it is argued that such tests should preferrably preceed further modeling of tetrachorics for example modeling by factor analysis the assumptions are tested in some real and simulated data

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

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

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

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

a history of graph entropy measures this survey seeks to describe methods for measuring the entropy of graphs and to demonstrate the wide applicability of entropy measures setting the scene with a review of classical measures for determining the structural information content of graphs we discuss graph entropy measures which play an important role in a variety of problem areas including biology chemistry and sociology in addition we examine relationships between selected entropy measures illustrating differences quantitatively with concrete examples

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

dynamic interpolation search revisited abstract a new dynamic interpolation search is data structure is presented that achieves o log log n search time with high probability on unknown continuous or even discrete input distributions with measurable probability of element collisions including power law and binomial distributions no such previous result holds for is when the probability of element collisions is measurable moreover our data structure exhibits o 1 search time with high probability w h p for a wide class of input distributions that contains all those for which o log log n expected search time was previously known

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

inequalities for entropy based measures of network information content this paper presents a method for establishing relations between entropy based measures applied to graphs a special class of relations called implicit information inequalities or implicit entropy bounds is developed a number of entropy based measures of the structural information content of a graph have been developed over the past several decades but little attention has been paid to relations among these measures the research reported here aims to remedy this deficiency

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

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

divide and conquer heuristics for minimum weighted euclidean matching we consider the following problem given n points in a unit square in the euclidean plane find a matching of the points such that the cost i e the sum of the lengths of the edges between matched points is minimum in particular we present a class of linear time heuristic algorithms for this problem and analyze their worst case performance the worst case performance of an algorithm is defined as the greatest possible cost as a function of n of the matching produced by the algorithm on a set of n points each of the algorithms studied here divides the unit square into a few smaller regions and then is applied recursively to the points in each of these regions

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

information theoretic measures of uhg graphs with low computational complexity we introduce a novel graph class we call universal hierarchical graphs uhg whose topology can be found numerously in problems representing e g temporal spacial or general process structures of systems for this graph class we show that we can naturally assign two probability distributions for nodes and for edges which lead us directly to the definition of the entropy and joint entropy and hence mutual information establishing an information theory for this graph class furthermore we provide some results under which conditions these constraint probability distributions maximize the corresponding entropy also we demonstrate that these entropic measures can be computed efficiently which is a prerequisite for every large scale practical application and show some numerical examples

quantitative graph theory in this paper we describe some highlights of the new branch quantitative graph theory and explain its significant different features compared to classical graph theory the main goal of quantitative graph theory is the structural quantification of information contained in complex networks by employing a measurement approach based on numerical invariants and comparisons furthermore the methods as well as the networks do not need to be deterministic but can be statistic as such this complements the field of classical graph theory which is descriptive and deterministic in nature we provide examples of how quantitative graph theory can be used for novel applications in the context of the overarching concept network science

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

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

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

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