tensors of nonnegative rank two abstract a nonnegative tensor has nonnegative rank at most 2 if and only if it is supermodular and has flattening rank at most 2 we prove this result then explore the semialgebraic geometry of the general markov model on phylogenetic trees with binary states and comment on possible extensions to tensors of higher rank

the foundations of factor analysis summary a new approach to factor analysis and related latent variable methods is proposed which is based on data reduction using the idea of bayesian sufficiency considerations of symmetry invariance and independence are used to determine an appropriate family of models the results are expressed in terms of linear functions of the manifest variables after the manner of principal components analysis the approach justifies some of the practices based on the normal theory factor model and lays a foundation for the treatment of nonnormal including categorical variables 1 background factor analysis is a widely used statistical technique but its theoretical foundations are somewhat obscure and subject to dispute it is one of a family of multivariate methods which also includes latent structure and latent trait analysis the common feature of the models underlying these methods is that the observed random variables are assumed to depend on latent that is unobserved random variables there is sometimes debate about whether these latent variables are real in any sense but they can be viewed simply as constructs designed to simplify and summarize the complex web of interrelated variables with which nature confronts us by expressing these relationships in terms of a small number of latent variables or factors the models effect a reduction in dimensionality which aids comprehension an early theoretical account of the subject is by anderson rubin 1956 and more recent and comprehensive treatments are provided by lawley maxwell 1971 and harman 1968 the present paper is an attempt to provide a coherent framework within which existing methodology can be evaluated and a base from which new methods can be developed our approach is to start from a very general statement of the problem in terms of the distributions of the random variables involved and then to invoke ideas of symmetry invariance and conditional independence to determine the class of models that it is reasonable to consider this not only exhibits the unity of the various models already in existence but resolves many of the ambiguities and obscurities with which the subject has been bedevilled an early approach on these lines is given by anderson 1959 and was recognized by birnbaum in his contribution to lord novick 1968 the same line was followed by bartholomew 1980 in spite of this the practical implications do not seem to have been made fully explicit or generally recognized

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

untwisting a projective reconstruction a method for upgrading a projective reconstruction to metric is presented the method compares favourably to state of the art algorithms and has been found extremely reliable for both large and small reconstructions in a large number of experiments on real data the notion of a twisted pair is generalized to the uncalibrated case the reconstruction is first transformed by considering cheirality so that it does not contain any twisted pairs it is argued that this is essential since the method then proceeds by local perturbation as is preferrable we utilize a cost function that reflects the prior likelihood of calibration matrices well it is shown that with any such cost function there is little hope of untwisting a twisted pair by local perturbation the results show that in practice it is most often sufficient to start with a reconstruction that is free from twisted pairs provided that the minimized objective function is a geometrically meaningful quantity when subjected to the common degeneracy of little or no rotation between the views the proposed method still yields a very reasonable member of the family of possible solutions furthermore the method is very fast and therefore suitable for the purpose of viewing reconstructions

latent class analysis of two way contingency tables by bayesian methods summary latent class analysis in two way contingency tables usually suffers from unidentifiability problems these can be overcome by using bayesian techniques in which prior distributions are assumed on the latent parameters application of these techniques however involves some unusual computational difficulties bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper

stochastic ordering using the latent trait and the sum score in polytomous irt models in a restricted class of item response theory irt models for polytomous items the unweighted total score has monotone likelihood ratio mlr in the latent trait mlr implies two stochastic ordering so properties denoted som and sol which are both weaker than mlr but very useful for measurement with irt models therefore these so properties are investigated for a broader class of irt models for which the mlr property does not hold

a rasch model for partial credit scoring a unidimensional latent trait model for responses scored in two or more ordered categories is developed this partial credit model is a member of the family of latent trait models which share the property of parameter separability and so permit specifically objective comparisons of persons and items the model can be viewed as an extension of andrich s rating scale model to situations in which ordered response alternatives are free to vary in number and structure from item to item the difference between the parameters in this model and the category boundaries in samejima s graded response model is demonstrated an unconditional maximum likelihood procedure for estimating the model parameters is developed

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

limits on log odds ratios for unidimensional item response theory models bounds are established for log odds ratios log cross product ratios involving pairs of items for item response models first expressions for bounds on log odds ratios are provided for one dimensional item response models in general then explicit bounds are obtained for the rasch model and the two parameter logistic 2pl model results are also illustrated through an example from a study of model checking procedures the bounds obtained can provide an elementary basis for assessment of goodness of fit of these models

essential independence and likelihood based ability estimation for polytomous items a definition ofessential independence is proposed for sequences of polytomous items for items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability we develop a theory ofessential unidimensionality which closely parallels that of stout essentially unidimensional item sequences can be shown to have a unique up to change of scale dominant underlying trait which can be consistently estimated by a monotone transformation of the sum of the item scores in more general polytomous response latent trait models with or without ordered responses anm estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity identifiability conditions a rigorous proof of this fact is given and the standard error of the estimator is explored these results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence but standard errors may vary greatly from what is usually expected depending on the degree of departure from local independence an index of departure from local independence is also proposed

likelihood inference on the underlying structure of irt models the assumptions underlying item response theory irt models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model it is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which however are necessary but not sufficient in this paper we describe how the theory for likelihood based inference under equality and inequality constraints may be used to test the underlying assumptions of irt models it turns out that the analysis based directly on the latent structure is simpler and more flexible in particular we indicate how several interesting extensions of the rasch model may be obtained by partial relaxation of the basic constraints an application to a data set provided by educational testing service is used to illustrate the approach

time varying formation control for general linear multi agent systems with switching directed topologies time varying formation analysis and design problems for multi agent systems with general linear dynamics and switching directed interaction topologies are investigated different from the previous results the formation in this paper can be defined by specified piecewise continuously differentiable vectors and the switching topologies are directed firstly necessary and sufficient conditions for general linear multi agent systems with switching directed topologies to achieve time varying formations are proposed where a description of the feasible time varying formation set and approaches to expand the feasible formation set are given then an explicit expression of the time varying formation reference function is derived to describe the macroscopic movement of the whole formation an approach to assign the motion modes of the formation reference is provided moreover an algorithm consisting of four steps to design the formation protocol is presented in the case where the given time varying formation belongs to the feasible formation set it is proven that by designing the formation protocol using the proposed algorithm time varying formation can be achieved by multi agent systems with general linear dynamics and switching directed topologies if the dwell time is larger than a positive threshold finally numerical simulations are presented to demonstrate the effectiveness of the theoretical results

psychometrics from practice to theory and back the paper surveys 15 years of progress in three psychometric research areas latent dimensionality structure test fairness and skills diagnosis of educational tests it is proposed that one effective model for selecting and carrying out research is to chose one s research questions from practical challenges facing educational testing then bring to bear sophisticated probability modeling and statistical analyses to solve these questions and finally to make effectiveness of the research answers in meeting the educational testing challenges be the ultimate criterion for judging the value of the research the problem solving power and the joy of working with a dedicated focused and collegial group of colleagues is emphasized finally it is suggested that the summative assessment testing paradigm that has driven test measurement research for over half a century is giving way to a new paradigm that in addition embraces skills level formative assessment opening up a plethora of challenging exciting and societally important research problems for psychometricians

independence via uncorrelatedness under certain dependence structures a characterization of independence via uncorrelatedness is shown to hold for the families satisfying positive and negative dependence conditions for the associated random variables the bounds on covariance functions obtained by lebowitz comm math phys 28 1972 313 321 readily yield such a characterization an elementary proof for the same characterization is also given for a condition weaker than association labeled as strong positive negative orthant dependence this condition is compared with the linear positive dependence under which newman and wright ann probab 9 1981 671 675 obtained the characterization

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

unified cooperative control of multiple agents on a sphere for different spherical patterns in this technical note we consider the cooperative control of multiple agents on a sphere provide the appropriate attraction repulsion interactions between agents with introduction of the state dependent repulsive coefficients and design the unified control laws for agents to achieve three fundamental spherical configurations or patterns rendezvous uniform deployment and formation using both the first and second order models we present the analysis of the stability scaling and geometric patterns of the models on the sphere under different attraction repulsion parameters with illustration of the geometrical patterns and the geometrical isomerism by simulations the closed loop dynamics of agents are invariant with respect to group rotation actions on the sphere

differential effects and generic biases in observational studies there are two treatments each of which may be applied or withheld yielding a 2 2 factorial arrangement with three degrees of freedom between groups the differential effect of the two treatments is the effect of applying one treatment in lieu of the other in randomised experiments the differential effect is of no more or less interest than other treatment contrasts differential effects play a special role in certain observational studies in which treatments are not assigned to subjects at random where differing outcomes may reflect biased assignments rather than effects caused by the treatments differential effects are immune to certain types of unobserved bias called generic biases which are associated with both treatments in a similar way this is explored using several examples and models differential effects are not immune to differential biases whose possible consequences are examined by sensitivity analysis

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

hybrid control for connectivity preserving flocking in this technical note we address the combined problem of motion and network topology control in a group of mobile agents with common objective the flocking behavior of the group instead of assuming network connectivity we enforce it by means of distributed topology control that decides on both deletion and creation of communication links between agents adapting the network to the group s spatial distribution with this protocol ensuring network connectivity a decentralized motion controller aligns agent velocity vectors and regulates inter agent distances to maintain existing network links the stability of the flocking controller is established in continuous time by means of an observability argument on a quadratic form of the graph laplacian that exploits the time delay between link deletion and creation caused by the topology control protocol which induces a dwell time between network switches

properties of and algorithms for fitting three way component models with offset terms prior to a three way component analysis of a three way data set it is customary to preprocess the data by centering and or rescaling them harshman and lundy 1984 considered that three way data actually consist of a three way model part which in fact pertains to ratio scale measurements as well as additive offset terms that turn the ratio scale measurements into interval scale measurements they mentioned that such offset terms might be estimated by incorporating additional components in the model but discarded this idea in favor of an approach to remove such terms from the model by means of centering then estimates for the three way component model parameters are obtained by analyzing the centered data in the present paper the possibility of actually estimating the offset terms is taken up again first it is mentioned in which cases such offset terms can be estimated uniquely next procedures are offered for estimating model parameters and offset parameters simultaneously as well as successively i e providing offset term estimates after the three way model parameters have been estimated in the traditional way on the basis of the centered data these procedures are provided for both the candecomp parafac model and the tucker3 model extended with offset terms the successive and the simultaneous approaches for estimating model and offset parameters have been compared on the basis of simulated data it was found that both procedures perform well when the fitted model captures at least all offset terms actually underlying the data the simultaneous procedures performed slightly better than the successive procedures if fewer offset terms are fitted than there are underlying the model the results are considerably poorer but in these cases the successive procedures performed better than the simultaneous ones all in all it can be concluded that the traditional approach for estimating model parameters can hardly be improved upon and that offset terms can sufficiently well be estimated by the proposed successive approach which is a simple extension of the traditional approach

conditional association and unidimensionality in monotone latent variable models latent variable models represent the joint distribution of observable variables in terms of a simple structure involving unobserved or latent variables usually assuming the conditional independence of the observable variables given the latent variables these models play an important role in educational measurement and psychometrics in sociology and in population genetics and are implicit in some work on systems reliability we study a broad class of latent variable models namely the monotone unidimensional models in which the latent variable is a scalar the observable variables are conditionally independent given the latent variable and the conditional distribution of the observables given the latent variable is stochastically increasing in the latent variable all models in this class imply a new strong form of positive dependence among the observable variables namely conditional positive association this positive dependence condition may be used to test whether any model in this class can provide an adequate fit to observed data various applications generalizations and a numerical example are discussed

testing the conditional independence and monotonicity assumptions of item response theory when item characteristic curves are nondecreasing functions of a latent variable the conditional or local independence of item responses given the latent variable implies nonnegative conditional covariances between all monotone increasing functions of a set of item responses given any function of the remaining item responses this general result provides a basis for testing the conditional independence assumption without first specifying a parametric form for the nondecreasing item characteristic curves the proposed tests are simple have known asymptotic null distributions and possess certain optimal properties in an example the conditional independence hypothesis is rejected for all possible forms of monotone item characteristic curves

brief paper a novel approach to coordination of multiple robots with communication failures via proximity graph in this paper we investigate the coordination problem of multiple robots with limited communication ranges and communication failures a novel rendezvous algorithm via proximity graph is developed so that the robot group can achieve rendezvous when the communication links satisfy an ergodic assumption the convergence proof of the algorithm is established based on the tools from rooted graph theory the effectiveness of the algorithm is illustrated by numerical examples in a 3d space

unidimensional factor models imply weaker partial correlations than zero order correlations in this paper we present a new implication of the unidimensional factor model we prove that the partial correlation between two observed variables that load on one factor given any subset of other observed variables that load on this factor lies between zero and the zero order correlation between these two observed variables we implement this result in an empirical bootstrap test that rejects the unidimensional factor model when partial correlations are identified that are either stronger than the zero order correlation or have a different sign than the zero order correlation we demonstrate the use of the test in an empirical data example with data consisting of fourteen items that measure extraversion

m matrices as covariance matrices of multinormal distributions abstract the class of multivariate normal densities n 0 whose inverse covariance matrix 1 is an m matrix is equivalent to this normal density being multivariate totally positive of order 2 mtp 2 equivalent characterizations are given in terms of certain partial correlation coefficients being positive it is further shown that related partial and multiple regression coefficients and canonical correlation are positive when is an m matrix the corresponding normal random vector components are negatively associated this concept and some extensions are discussed

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

styled velocity flocking of autonomous vehicles a systematic design this paper develops a measure theoretic approach for generating the collective behavior of flocking of planar autonomous vehicles under all to all communication scheme to obtain flocking protocol we formulate the notion of state of styled velocity flocking for the target state of a design problem instead of considering solution ansatzes this notion captures a broader class of flocking behaviors of non parallel motions as well as embodies the two important performances of cohesion maintenance and collision avoidance to pose a control design problem a measure valued transition equation is obtained to induce an auxiliary one body continuum model from the exact multi body particle model of the collective system the design problem is then formulated on the auxiliary continuum model and a systematic design procedure is presented the state of styled velocity flocking of the particle model under the obtained flocking protocol is then verified with an important result on the continuous dependence on initial data of solutions of the measured valued transition equation application to elliptical flocking of mobile robots is presented to illustrate the novelty of the presented theory

manifest characterization and testing for certain latent properties work due to junker and more recently due to junker and ellis characterized desired latent properties of an educational testing procedure in terms of a collection of other manifest properties this is important because one can only propose tests for manifest quantities not latent ones here we complete the conversion of a pair of latent properties to equivalent conditions in terms of four manifest quantities and identify a general method for producing tests for manifest properties 1 introduction item response theory irt is the statistical theory of standardized tests which are commonly used in educational testing applications the goal is to combine the data generated by many examinees answering a collection of test items so as to estimate the value of a parameter or trait say for each of the examinees the parameter is intended to quantify a latent trait such as mathematics ability the traits are latent in the sense that they cannot be measured directly more specifically desired properties of suchtesting procedures are called latent when their statement depends explicitly on the the latent trait being estimated most efforts at modeling involve the introduction of latent parameters one specifies parameters to reflect aspects of the physical problem such as the individual achievement of each examinee the difficulty of each test item specialized knowledge that certain examinees might possess etc this is in contrast to the manifest properties of a testing procedure which can be phrased in a way that does not explicitly depend on the latent trait the limitation of a latent model is that it contains parameters for the latent trait the experimenter wants to estimate each examinee s parameter value and so cannot perform hypothesis tests on a conjectured model in the usual way the solution to this problem is to convert latent models or latent statements about them to physically meaningful manifest properties which are provably mathematically equivalent to the latent properties actually wanted manifest statements are amenable to conventional hypothesis testing and the problem then becomes the identification of optimal hypothesis tests for the manifest quantities in this way one can test hypotheses that are independent of the latent structure at least in principle the goal of characterizing latent properties in terms of manifest properties to be tested begins with stout 1987 stout considers the requirement that

criterion related construct validity established results on latent variable models are applied to the study of the validity of a psychological test when the test predicts a criterion by measuring a unidimensional latent construct not only must the total score predict the criterion but the joint distribution of criterion scores and item responses must exhibit a certain pattern the presence of this population pattern may be tested with sample data using the stratified wilcoxon rank sum test often criterion information is available only for selected examinees for instance those who are admitted or hired three cases are discussed i selection at random ii selection based on the current test and iii selection based on other measures of the latent construct discriminant validity is also discussed

the constrained rayleigh quotient with a general orthogonality constraint and an eigen balanced laplacian matrix the greatest lower bound and applications in cooperative control problems mathematically the rayleigh quotient is defined as the quadratic function of a symmetric matrix and a nonzero usually unconstrained variable vector in this paper we consider the constrained rayleigh quotient in which the variable vector has the orthogonality constraint i e it is constrained to be orthogonal to a nonzero vector this nonzero vector is called the orthogonality constraint vector or abbreviated as the oc vector for the variable vector the matrix for the rayleigh quotient is an eigen balanced eb laplacian matrix a tighter lower bound of the constrained rayleigh quotient has many implications in mathematics as well as in cooperative control problems the main contributions in this paper are as follows first we provide the greatest lower bound or the infimum of the constrained rayleigh quotient with respect to a general oc vector and the eb laplacian matrix whose results are novel and better than the existing results then we interpret the physical meaning of our results in an insightful geometric form and characterize the properties of the results finally as an example to illustrate the merit of the tighter lower bound of the constrained rayleigh quotient we consider the scale of the agents driving by a fundamental consensus protocol and show that the convergence rate of the agents scale is characterized by the greatest lower bound of the constrained rayleigh quotient

local homogeneity in latent trait models a characterization of the homogeneous monotone irt model the stochastic subject formulation of latent trait models contends that within a given subject the event of obtaining a certain response pattern may be probabilistic ordinary latent trait models do not imply that these within subject probabilities are identical to the conditional probabilities specified by the model the latter condition is called local homogeneity it is shown that local homgeneity is equivalent to subpopulation invariance of the model in case of the monotone irt model local homogeneity implies absence of item bias absence of item specific traits and the possibility to join overlapping subtests the following characterization theorem is proved the homogeneous monotone irt model holds for a finite or countable item pool if and only if the pool is experimentally independent and pairwise nonnegative association holds in every positive subpopulation

modification indices for the 2 pl and the nominal response model in this paper it is shown that various violations of the 2 pl model and the nominal response model can be evaluated using the lagrange multiplier test or the equivalent efficient score test the tests presented here focus on violation of local stochastic independence and insufficient capture of the form of the item characteristic curves primarily the tests are item oriented diagnostic tools but taken together they also serve the purpose of evaluation of global model fit a useful feature of lagrange multiplier statistics is that they are evaluated using maximum likelihood estimates of the null model only that is the parameters of alternative models need not be estimated as numerical examples an application to real data and some power studies are presented

comparing item characteristic curves test items are often evaluated and compared by contrasting the shapes of their item characteristics curves icc s or surfaces the current paper develops and applies three general i e nonparametric comparisons of the shapes of two item characteristic surfaces i proportional latent odds ii uniform relative difficulty and iii item sensitivity two items may be compared in these ways while making no assumption about the shapes of item characteristic surfaces for other items and no assumption about the dimensionality of the latent variable also studied is a method for comparing the relative shapes of two item characteristic curves in two examinee populations

tail measurability in monotone latent variable models we consider latent variable models for an infinite sequence or universe of manifest observable variables that may be discrete continuous or some combination of these the main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality monotonicity conditional independence andtail measurability tail measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed the characterizing necessary and sufficient conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence as one conditions upon successively more other manifest variables our main theorem considerably generalizes and sharpens earlier results of ellis and van den wollenberg 1993 holland and rosenbaum 1986 and junker 1993 it is also related to the work of stout 1990 the main theorem is preceded by many results for latent variable modelsin general not necessarily unidimensional and monotone they pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of suppes and zanotti 1981 we discuss new definitions of the concepts of true score and subpopulation which generalize these notions from the stochastic subject random sampling and domain sampling formulations of latent variable models e g holland 1990 lord novick 1968 these definitions do not require the a priori specification of a latent variable model

adjusting for information inflation due to local dependency in moderately large item clusters when multiple items are clustered around a reading passage the local independence assumption in item response theory is often violated the amount of information contained in an item cluster is usually overestimated if violation of local independence is ignored and items are treated as locally independent when in fact they are not in this article we provide a general method that adjusts for the inflation of information associated with a test containing item clusters a computational scheme was presented for the evaluation of the factor of adjustment for clusters in the restrictive case of two items per cluster and the general case of more than two items per cluster the methodology was motivated by a study of the naep reading assessment we present a simulated study along with an analysis of a naep data set

projective visual hulls this article presents a novel method for computing the visual hull of a solid bounded by a smooth surface and observed by a finite set of cameras the visual hull is the intersection of the visual cones formed by back projecting the silhouettes found in the corresponding images we characterize its surface as a generalized polyhedron whose faces are visual cone patches edges are intersection curves between two viewing cones and vertices are frontier points where the intersection of two cones is singular or intersection points where triples of cones meet we use the mathematical framework of oriented projective differential geometry to develop an image based algorithm for computing the visual hull this algorithm works in a weakly calibrated setting that is it only requires projective camera matrices or equivalently fundamental matrices for each pair of cameras the promise of the proposed algorithm is demonstrated with experiments on several challenging data sets and a comparison to another state of the art method

self calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters in this paper the theoretical and practical feasibility of self calibration in the presence of varying intrinsic camera parameters is under investigation the paper s main contribution is to propose a self calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras the feasibility of the approach is illustrated on real and synthetic examples besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self calibration a counting argument is developed which depending on the set of constraints gives the minimum sequence length for self calibration and a method to detect critical motion sequences is proposed

generalized residuals for general models for contingency tables with application to item response theory generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error they have typically been applied to log linear models and to latent class models a general approach to generalized residuals is developed for a very general class of models for contingency tables to illustrate their use generalized residuals are applied to models based on item response theory irt models such models are commonly applied to analysis of standardized achievement or aptitude tests to obtain a realistic perspective on application of generalized residuals actual testing data are employed

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

distributed estimation and control of algebraic connectivity over random graphs in this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad hoc networks in the presence of a random topology first given a generic random graph we introduce a novel stochastic power iteration method that allows each node to estimate and track the algebraic connectivity of the underlying expected graph using results from stochastic approximation theory we prove that the proposed method converges almost surely a s to the desired value of connectivity even in the presence of imperfect communication scenarios the estimation strategy is then used as a basic tool to adapt the power transmitted by each node of a wireless network in order to maximize the network connectivity in the presence of realistic medium access control mac protocols or simply to drive the connectivity toward a desired target value numerical results corroborate our theoretical findings thus illustrating the main features of the algorithm and its robustness to fluctuations of the network graph due to the presence of random link failures

copula functions for residual dependency most item response theory models are not robust to violations of conditional independence however several modeling approaches e g conditioning on other responses additional random effects exist that try to incorporate local item dependencies but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems in this paper a new class of models making use of copulas to deal with local item dependencies is introduced these models belong to the bigger class of marginal models in which margins and association structure are modeled separately it is shown how this approach overcomes some of the problems associated with other local item dependency models

comparing latent structures of the grade of membership rasch and latent class models this paper focuses on model interpretation issues and employs a geometric approach to compare the potential value of using the grade of membership gom model in representing population heterogeneity we consider population heterogeneity manifolds generated by letting subject specific parameters vary over their natural range while keeping other population parameters fixed in the marginal space based on marginal probabilities and in the full parameter space based on cell probabilities the case of a 2 2 contingency table is discussed in detail and a generalization to 2j tables with j 3 is sketched our approach highlights the main distinction between the gom model and the probabilistic mixture of classes by demonstrating geometrically the difference between the concepts of partial and probabilistic memberships by using the geometric approach we show that in special cases the gom model can be thought of as being similar to an item response theory irt model in representing population heterogeneity finally we show that the gom item parameters can provide quantities analogous to more general logistic irt item parameters as a latent structure model the gom model might be considered a useful alternative for a data analysis when both classes of extreme responses and additional heterogeneity that cannot be captured by those latent classes are expected in the population

a bounded distributed connectivity preserving aggregation strategy with collision avoidance property abstract this paper presents a bounded connectivity preserving control strategy for the aggregation of multi agent systems the problem is investigated for two cases of single integrator agents and unicycles under the proposed control strategy if two agents are in the connectivity range at some point in time they will stay connected thereafter the agents finally aggregate while avoiding collision in such a way that the average of the distances between every pair of neighboring agents is bounded by a pre specified positive real number which can be chosen arbitrarily small the results are developed based on some important characteristics of the positive limit set of the closed loop system under the proposed control strategy and a fundamental property of convex real functions the theoretical results are verified by simulation

positive association among three binary variables and cross product ratios we show that when the three way association level among the three binary variables x u 1 and u 2 is fixed dp pr x 1 u 1 1 pr x 11 u 1 0 increases as the cross product ratio of u 1 and u 2 increases under the assumption that x is positively associated with u 1 and u 2 we then discuss some implications of this property

a theory of self calibration of a moving camera there is a close connection between the calibration of a single camera and the epipolar transformation obtained when the camera undergoes a displacement the epipolar transformation imposes two algebraic constraints on the camera calibration if two epipolar transformations arising from different camera displacements are available then the compatible camera calibrations are parameterized by an algebraic curve of genus four the curve can be represented either by a space curve of degree seven contained in the intersection of two cubic surfaces or by a curve of degree six in the dual of the image plane the curve in the dual plane has one singular point of order three and three singular points of order two if three epipolar transformations are available then two curves of degree six can be obtained in the dual plane such that one of the real intersections of the two yields the correct camera calibration the two curves have a common singular point of order three experimental results are given to demonstrate the feasibility of camera calibration based on the epipolar transformation the real intersections of the two dual curves are found by locating the zeros of a function defined on the interval 0 2 the intersection yielding the correct camera calibration is picked out by referring back to the three epipolar transformations

conditional covariance theory and detect for polytomous items this paper extends the theory of conditional covariances to polytomous items it has been proven that under some mild conditions commonly assumed in the analysis of response data the conditional covariance of two items dichotomously or polytomously scored given an appropriately chosen composite is positive if and only if the two items measure similar constructs besides the composite the theory provides a theoretical foundation for dimensionality assessment procedures based on conditional covariances or correlations such as detect and dimtest so that the performance of these procedures is theoretically justified when applied to response data with polytomous items various estimators of conditional covariances are constructed and special attention is paid to the case of complex sampling data such as those from the national assessment of educational progress naep as such the new version of detect can be applied to response data sets not only with polytomous items but also with missing values either by design or at random detect is then applied to analyze the dimensional structure of the 2002 naep reading samples of grades 4 and 8 the detect results show that the substantive test structure based on the purposes for reading is consistent with the statistical dimensional structure for either grade

when are item response models consistent with observed data the problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered the classical assumption of locla independence is weakened to a new condition local nonnegative dependence lnd necessary and sufficient conditions are derived for a lnd item response model to fit a set of data this leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves an example is given to show that lnd is strictly weaker than local independence thus rejection of lnd models implies rejection of all item response models that assume local independence for a given set of data

flocking with connectivity preservation of multiple double integrator systems subject to external disturbances by a distributed control law this paper studies the flocking with connectivity preservation problem of multiple double integrator systems subject to a class of external disturbances we solve the problem by a distributed dynamic position feedback control law under the standard assumptions our approach is a combination of the potential function technique and observer design our result also includes some existing results as special cases

some remarks on scheiblechner s treatment of isop models scheiblechner 1995 proposes a probabilistic axiomatization of measurement called isop isotonic ordinal probabilistic models that replaces rasch s 1980 specific objectivity assumptions with two interesting ordinal assumptions special cases of scheiblechner s model include standard unidimensional factor analysis models in which the loadings are held constant and the rasch model for binary item responses closely related are the doubly monotone item response models of mokken 1971 see also mokken lewis 1982 sijtsma 1988 molenaar 1991 sijtsma junker 1996 and sijtsma hemker in press more generally strictly unidimensional latent variable models have been considered in some detail by holland and rosenbaum 1986 ellis and van den wollenberg 1993 and junker 1990 1993 the purpose of this note is to provide connections with current research in foundations and nonparametric latent variable and item response modeling that are missing from scheiblechner s 1995 paper and to point out important related work by hemker sijtsma molenaar junker 1996 1997 ellis and junker in press and junker and ellis 1997 we also discuss counterexamples to three major theorems in the paper by carrying out these three tasks we hope to provide researchers interested in the foundations of measurement and item response modeling the opportunity to give the isop approach the careful attention it deserves

separating two sources of dependence in repeated influenza outbreaks summary two or more responses measured on a randomly selected individual can be dependent for two quite different reasons in the first place they can be dependent within that is conditional upon each individual secondly dependence is created simply from the heterogeneity between individuals this paper addresses a rare instance of being able to measure separately the dependence from the two sources the data comprise frequencies of the infection profiles for a sample of individuals exposed to four influenza outbreaks two of the outbreaks were caused by the same virus and gave rise to negative withinindividual dependence because infection at the first occasion leads to a reduced probability of infection at the second this negative dependence cannot be estimated from the 2 x 2 table of frequencies for these two outbreaks because it is masked by positive dependence due to between individual heterogeneity however the negative dependence can be estimated using the joint frequencies for three or four outbreaks the two caused by the same virus and one or both of the other two