measurement errors in caries diagnosis some further latent class models latent class models have been proposed for assessing relative errors in discrete measurements arising for example in caries diagnosis those models however that turned out to fit empirical data n 3 869 teeth 5 dentists to a sufficient degree needed the inclusion of interaction terms for pairs of raters at the latent levels in order to describe the observed interrelations of the judgments now it is shown that instead of giving up the concept of local stochastic independence increasing the number of classes while possibly restricting their parameters in the end has the same effect both the unrestricted three class model which can be interpreted to be the generalization of the carlos senning assumptions and a restricted four class model which resembles the latent distance model well known from psychometrics give good and excellent fit respectively to the caries data for the case of the four class model a second solution exists that exhibits exactly the same fit giving rise to warnings against the possibility of multiple solutions to the likelihood equations

spectra of complex networks we propose a general approach to the description of spectra of complex networks for the spectra of networks with uncorrelated vertices and a local treelike structure exact equations are derived these equations are generalized to the case of networks with correlations between neighboring vertices the tail of the density of eigenvalues ensuremath rho ensuremath lambda at large ensuremath lambda is related to the behavior of the vertex degree distribution p k at large k in particular as p k ensuremath sim k ensuremath ensuremath gamma ensuremath rho ensuremath lambda ensuremath sim ensuremath lambda 1 ensuremath 2 ensuremath gamma we propose a simple approximation which enables us to calculate spectra of various graphs analytically we analyze spectra of various complex networks and discuss the role of vertices of low degree we show that spectra of locally treelike random graphs may serve as a starting point in the analysis of spectral properties of real world networks e g of the internet

scaling variables and asymptotic expansions in damped wave equations abstract we study the long time behavior of small solutions to the nonlinear damped wave equationeu u a u n u u u r 0 whereeis a positive not necessarily small parameter we assume that the diffusion coefficienta converges to positive limitsa as and that the nonlinearity n u u u vanishes sufficiently fast asu 0 introducing scaling variables and using various energy estimates we compute an asymptotic expansion of the solutionu in powers of 1 2as and we show that this expansion is entirely determined up to the second order by a linear parabolic equation which depends only on the limiting valuesa in particular this implies that the small solutions of the damped wave equation behave for large like those of the parabolic equation obtained by settinge 0

spectra and eigenvectors of scale free networks we study the spectra and eigenvectors of the adjacency matrices of scale free networks when bidirectional interaction is allowed so that the adjacency matrix is real and symmetric the spectral density shows an exponential decay around the center followed by power law long tails at both spectrum edges the largest eigenvalue ensuremath lambda 1 depends on system size n as ensuremath lambda 1 ensuremath sim n 1 4 for large n and the corresponding eigenfunction is strongly localized at the hub the vertex with largest degree the component of the normalized eigenfunction at the hub is of order unity we also find that the mass gap scales as n ensuremath 0 68

latent structure analysis of a set of multidimensional contingency tables abstract statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables three basic classes of models are considered a models that assume complete homogeneity across tables b models that allow partial homogeneity across tables and c models that allow complete heterogeneity methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of differences among the tables in the estimated parameters to illustrate the wide applicability of these models and methods we present analyses of two quite different sets of data

relationships among the statistical parameters in evolving modern chinese linguistic co occurrence networks abstract a total of 206 co occurrence networks of chinese characters and words are constructed from modern chinese articles spectra of the adjacency matrices especially the largest eigenvalues 1 the second largest eigenvalues the smallest eigenvalues the number of different eigenvalues n the spectral distribution and the spectral density are computed and studied some formulas about the statistical parameters are given by applying multiple linear regression analysis it is found that not only the growth trends of 1 and n but also the properties of spectral distributions and do not change with the network size therefore the spectral behavior of the modern chinese linguistic topology is consistent over time unless something having a major impact on chinese language happen

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

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

stability of perturbed nonlinear parabolic equations with sturmian property abstract we study stability of an equilibrium f of autonomous dynamical systems under asymptotically small perturbations of the equation we show that such stability takes place if the domain of attraction of the equilibrium f contains a one parametric ordered family f in the stability analysis we need a special s relation a kind of restricted partial ordering to be preserved relative to the family f this s relation is inherited from the sturmian zero set properties for linear parabolic equations as main applications we prove stability of the self similar blow up behaviour for the porous medium equation the p laplacian equation and the dual porous medium equation in r with nonlinear lower order perturbations for such one dimensional parabolic equations the s relation is sturm s theorem on the nonincrease of the number of intersections between the solutions and particular solutions with initial data in f this sturmian property plays a key role and is true for the unperturbed pme but is not true for perturbed equations

quenching for a one dimensional fully nonlinear parabolic equation in detonation theory we study and describe the quenching phenomenon for the fully nonlinear parabolic equation u t frac 1 2 u x 2 f c u u xx rm ln u quad x in 0 l t 0 which for f s rm ln e s 1 s represents the evolution of the perturbations of the zel dovich von neuman doering square wave occurring during a detonation in a duct in the general case the function f mathbb r rightarrow mathbb r is smooth and satisfies the parabolicity condition f s 0 in mathbb r c and l are positive constants and we impose neumann boundary conditions ux 0 t ux l t 0 for t 0 and take initial data u x 0 0 with inverse bell shaped form the phenomenon of quenching is characterized by the existence of a finite time t at which the solution u ceases to exist as a classical solution because rm min x u x t rightarrow 0 as t rightarrow t then the equation degenerates and forms a singularity at the level u 0 due to the presence of the logarithmic zero order term we

fixed distance latent class models for the analysis of sets of two way contingency tables this paper develops and describes the application of modified latent class models for analyzing sets of two way contingency tables the proposed fixed distance models differ from traditional latent class models in that the assumption of local stochastic independence is superseded by allowing interactions of the manifest variables within each class which can be represented by a single association parameter as an example two data sets on eye color by hair color collected in caithness n1 5 387 and aberdeen n2 22 361 and fixed distance models with up to six classes three classes per data set are considered finally leading to satisfactory fit and rather simple interpretation

the asymptotic behavior for gaseous ignition models abstract the blowup asymptotics for classical solutions of ut u eu g t are analyzed including the nonlocal case where g has a functional dependence of the form utdx the method of analyzing the evolution of the blowup singularity is a dynamical systems approach using center manifold techniques and analyzing an limit set for a corresponding hamilton jacobi equation

the biplot as a diagnostic tool of local dependence in latent class models a medical application latent class models lcms can be used to assess diagnostic test performance when no reference test a gold standard is available considering two latent classes representing disease or non disease status one of the basic assumptions in such models is that of local or conditional independence all indicator variables tests are statistically independent within each latent class however in practice this assumption is often violated hence the two lcm fits the data poorly in this paper we propose the use of biplot methods to identify the conditional dependence between pairs of manifest variables within each latent class additionally we propose incorporating such dependence in the corresponding latent class using the log linear formulation of the model

phase ordering on small world networks with nearest neighbor edges we investigate global phase coherence in a system of coupled oscillators on small world networks constructed from a ring with nearest neighbor edges the effects of both thermal noise and quenched randomness on phase ordering are examined and compared with the global coherence in the corresponding xy model without quenched randomness it is found that in the appropriate regime phase ordering emerges at finite temperatures even for a tiny fraction of shortcuts the nature of the phase transition is also discussed

variable selection for model based clustering we consider the problem of variable or feature selection for model based clustering the problem of comparing two nested subsets of variables is recast as a model comparison problem and addressed using approximate bayes factors a greedy search algorithm is proposed for finding a local optimum in model space the resulting method selects variables or features the number of clusters and the clustering model simultaneously we applied the method to several simulated and real examples and found that removing irrelevant variables often improved performance compared with methods based on all of the variables our variable selection method consistently yielded more accurate estimates of the number of groups and lower classification error rates as well as more parsimonious clustering models and easier visualization of results

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

laplacian spectra as a diagnostic tool for network structure and dynamics we examine numerically the three way relationships among structure laplacian spectra and frequency synchronization dynamics on complex networks we study the effects of clustering degree distribution and a particular type of coupling asymmetry input normalization all of which are known to have effects on the synchronizability of oscillator networks we find that these topological factors produce marked signatures in the laplacian eigenvalue distribution and in the localization properties of individual eigenvectors using a set of coordinates based on the laplacian eigenvectors as a diagnostic tool for synchronization dynamics we find that the process of frequency synchronization can be visualized as a series of quasi independent transitions involving different normal modes particular features of the partially synchronized state can be understood in terms of the behavior of particular modes or groups of modes for example there are important partially synchronized states in which a set of low lying modes remain unlocked while those in the main spectral peak are locked we find therefore that spectra are correlated with dynamics in ways that go beyond results relating a single threshold to a single extremal eigenvalue

a very singular solution of the porous media equation with absorption turns out to play an important role in the description of both the short and the long time behaviour of positive solutions of eq 1 1 for the short time behaviour it provides together with the one parameter family of singular solutions i of problem i a complete description of the possible types of singular behaviour at the point 0 o 121 for the long time behaviour of solutions u x t of the cauchy problem for 1 1 1 2 it provides the asymptotic form when the initial function decays sufficiently fast as 1x1 co t p u x t w x t 0 ast co uniformly in r 7 81 in this paper we shall show that if

synchronization landscapes in small world connected computer networks motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small world networks embedded in one and two dimensions we find that the synchronization landscape corresponding to the progress of the individual processors exhibits kardar parisi zhang like kinetic roughening on regular networks with short range communication links although the processors on average progress at a nonzero rate their spread the width of the synchronization landscape diverges with the number of nodes desynchronized state hindering efficient data management when random communication links are added on top of the one and two dimensional regular networks resulting in a small world network large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system size limit synchronized state in the resulting synchronization scheme the processors make close to uniform progress with a nonzero rate without global intervention we obtain our results by simulating the simulations based on the exact algorithmic rules supported by coarse grained arguments

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

two step estimation of models between latent classes and external variables we consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables we propose a two step method of estimating such models in its first step the measurement model is estimated alone and in the second step the parameters of this measurement model are held fixed when the structural model is estimated simulation studies and applied examples suggest that the two step method is an attractive alternative to existing one step and three step methods we derive estimated standard errors for the two step estimates of the structural model which account for the uncertainty from both steps of the estimation and show how the method can be implemented in existing software for latent variable modelling

latent class model diagnosis summary in many areas of medical research such as psychiatry and gerontology latent class variables are used to classify individuals into disease categories often with the intention of hierarchical modeling problems arise when it is not clear how many disease classes are appropriate creating a need for model selection and diagnostic techniques previous work has shown that the pearson 2 statistic and the log likelihood ratio g2 statistic are not valid test statistics for evaluating latent class models other methods such as information criteria provide decision rules without providing explicit information about where discrepancies occur between a model and the data identifiability issues further complicate these problems this paper develops procedures for assessing markov chain monte carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using markov chain monte carlo techniques simulations and a psychiatric example are presented to demonstrate the effective use of these methods

universal self similarity of porous media equation with absorption the critical exponent case abstract in this paper we study the large time behavior of non negative solutions to the cauchy problem of u t u m u q in r n 0 where m 1 and q q c m 2 n is a critical exponent for non negative initial value u x 0 u 0 x l 1 r n we show that the solution converges if u 0 x 1 x k is bounded for some k n to a unique fundamental solution of u t u m independent of the initial value with additional logarithmic anomalous decay exponent in time as t

a maximum likelihood method for latent class regression involving a censored dependent variable the standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored this model is generalized by developing a conditional mixture maximum likelihood method for latent class censored regression the proposed method simultaneously estimates separate regression functions and subject membership in k latent classes or groups given a censored dependent variable for a cross section of subjects maximum likelihood estimates are obtained using an em algorithm the proposed method is illustrated via a consumer psychology application

asymptotics in the critical case for whitham type equations abstract consider the cauchy problem for nonlinear dissipative evolution equations u t n u u l u 0 x r t 0 u 0 x u 0 x x r where l is the linear pseudodifferential operator l u f x l u and the nonlinearity is a quadratic pseudodifferential operator n u u f x r a t y u t y u t y d y u f x u is direct fourier transformation let the initial data u 0 h 0 h 0 1 2 are sufficiently small and have a non zero total mass m u 0 x d x 0 here h n m l 2 x m i x n x l 2 is the weighted sobolev space then we prove that the main term of the large time asymptotics of solutions in the critical case is given by the self similar solution defined uniquely by the total mass m of the initial data

linear logistic latent class analysis for polytomous data abstract for latent class analysis a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones a flexible model is presented in order to restrain the unknown class sizes mixing weights and the unknown latent response probabilities two systems of basic equations are stated such that they simultaneously allow parameter fixations the equality of certain parameters as well as linear logistic constraints of each of the original parameters the maximum likelihood equations for the parameters of this linear logistic latent class analysis are given and their estimation by means of the em algorithm is described further the criteria for their local identifiability and statistical tests pearson and likelihood ratio 2 for goodness of fit are outlined the practical applicability of linear logistic latent class analysis is demonstrated by three examples mixed logistic regression a mixed bradley terry model for paired comparisons with ties and a lo

netons vibrations of complex networks we consider atoms interacting with each other through the topological structure of ac omplex network and investigate lattice vibrations of the system the quanta of which we call netons for convenience the density of neton levels obtained numerically reveals that unlike a local regular lattice the system develops a gap of finite width manifesting extreme rigidity of the network structure at low energies two different network models the small world network and the scale free network are compared the characteristic structure of the former is described by an additional peak in the level density whereas a power law tail is observed in the latter indicating excitability of netons at arbitrarily high energies the gap width is also found to vanish in the small world network when the connection range r 1

bayesian latent class models with conditionally dependent diagnostic tests a case study in the assessment of the accuracy of diagnostic tests for infectious diseases the true disease status of the subjects is often unknown due to the lack of a gold standard test latent class models with two latent classes representing diseased and non diseased subjects are often used to analyze this type of data in its basic format latent class analysis requires the observed outcomes to be statistically independent conditional on the disease status in most diagnostic settings this assumption is highly questionable during the last decade several methods have been proposed to estimate latent class models with conditional dependence between the test results a class of flexible fixed and random effects models were described by dendukuri and joseph in a bayesian framework we illustrate these models using the analysis of a diagnostic study of three field tests and an imperfect reference test for the diagnosis of visceral leishmaniasis we show that as observed earlier by albert and dodd different dependence models may result in similar fits to the data while resulting in different inferences given this problem selection of appropriate latent class models should be based on substantive subject matter knowledge if several clinically plausible models are supported by the data a sensitivity analysis should be performed by describing the results obtained from different models and using different priors

spectral analysis of chinese language co occurrence networks from four literary genres abstract the eigenvalues and eigenvectors of the adjacency matrix of a network contain essential information about its topology for each of the chinese language co occurrence networks constructed from four literary genres i e essay popular science article news report and novel it is found that the largest eigenvalue depends on the network size n the number of edges the average shortest path length and the clustering coefficient moreover it is found that their node degree distributions all follow a power law the number of different eigenvalues n is found numerically to increase in the manner of n log n for novel and n n for the other three literary genres an m shape or a triangle like distribution appears in their spectral densities the eigenvector corresponding to the largest eigenvalue is mostly localized to a node with the largest degree for the above observed phenomena mathematical analysis is provided with interpretation from a linguistic perspective

blow up for quasilinear heat equations with critical fujita s exponents we consider the cauchy problem for the quasilinear heat equationwhere 0 is a fixed constant with the critical exponent in the source term c 1 2 n it is well known that if 1 c then any non negative weak solution u x t 0 blows up in a finite time for the semilinear heat equation he with 0 the above result was proved by h fujita 4 in the present paper we prove that u 0 blows up in the critical case 1 2 n with 0 a similar result is valid for the equation with gradient dependent diffusivitywith 0 and the critical exponent 1 2 n

mixture analysis of longitudinal binary data the dependence of longitudinal binary outcomes on covariates and the covariation observed between them is often modelled by multivariate logistic and probit models respectively assuming specified association structure or random effects alternatively latent class models may be used that capture the covariation by assuming heterogeneity of the observational units regarding their reaction tendencies while postulating independence within classes in the presence of a few categorical covariates the multi group method of latent class analysis allows one to relate the class sizes and the class specific response probabilities to these covariates wheeze data from the harvard six cities study on respiratory health are a typical example for such a situation at four occasions the wheeze status of 537 children was examined 187 among them exposed to maternal smoking and 350 not exposed thus there is a single binary covariate maternal smoking versus no maternal smoking making easily applicable the multi group method of latent class analysis based on a series of unrestricted and restricted models having up to three classes for the exposed and not exposed subgroup each no statistically significant effect of maternal smoking on children s wheeze status could be substantiated moreover it was not possible to show statistically significant difference at all between the two distributions of wheeze patterns collected from exposed and not exposed children

bayesian inferences of latent class models with an unknown number of classes this paper focuses on analyzing data collected in situations where investigators use multiple discrete indicators as surrogates for example a set of questionnaires a very flexible latent class model is used for analysis we propose a bayesian framework to perform the joint estimation of the number of latent classes and model parameters the proposed approach applies the reversible jump markov chain monte carlo to analyze finite mixtures of multivariate multinomial distributions in the paper we also develop a procedure for the unique labeling of the classes we have carried out a detailed sensitivity analysis for various hyperparameter specifications which leads us to make standard default recommendations for the choice of priors the usefulness of the proposed method is demonstrated through computer simulations and a study on subtypes of schizophrenia using the positive and negative syndrome scale panss

using latent class models to characterize and assess relative error in discrete measurements whenever a definitive standard is not available to mark accuracy in a classification process discrete measurement error can be discussed only in relative terms if strong assumptions concerning the underlying discrete processes can be made latent class models allow one to characterize patterns of agreement disagreement among raters while simultaneously producing consensus estimates of prevalence a hypothetical definitive standard serves as the latent factor the discrete data are treated as incomplete and log linear models can be used to parameterize latent class models and extensions of latent class models data from the radiographic diagnosis of dental caries by five dentists were explored to estimate prevalence assess relative error and examine the validity of several traditional assumptions concerning diagnostic reliability latent class analysis allowed a more detailed description of diagnostic error than provided by commonly used summary statistics

spectra of modular and small world matrices we compute spectra of symmetric random matrices describing graphs with general modular structure and arbitrary inter and intra module degree distributions subject only to the constraint of finite mean connectivities we also evaluate spectra of a certain class of small world matrices generated from random graphs by introducing shortcuts via additional random connectivity components both adjacency matrices and the associated graph laplacians are investigated for the laplacians we find lifshitz type singular behaviour of the spectral density in a localized region of small values in the case of modular networks we can identify contributions of local densities of state from individual modules for small world networks we find that the introduction of short cuts can lead to the creation of satellite bands outside the central band of extended states exhibiting only localized states in the band gaps results for the ensemble in the thermodynamic limit are in excellent agreement with those obtained via a cavity approach for large finite single instances and with direct diagonalization results

subcritical kuramoto sivashinsky type equation on a half line abstract in this paper we are interested in the global existence and large time behavior of solutions to the initial boundary value problem for subcritical kuramoto sivashinsky type equation 0 1 u t n u u x u xx u xxxx 0 x t r r u x 0 u 0 x x r x j 1 u 0 t 0 for j 1 2 where the nonlinear term n u u x depends on the unknown function u and its derivative u x and satisfy the estimate n u v c u v with 0 1 such that 3 2 2 0 the aim of this paper is to prove the global existence of solutions to the initial boundary value problem 0 1 in subcritical case when the nonlinear term has a time decay rate less than that of the linear terms of eq 0 1 also we find the main term of the asymptotic representation of solutions

on a spectrum of blow up patterns for a higher order semilinear parabolic equation we describe a spectrum of blow up patterns for the 2 m th order semilinear parabolic equation u t m u u p x r n t 0 m 1 p 1 this problem is well understood in the second order case m 1 the semilinear heat equation where for p p s n 2 n 2 the inner space time structure of blow up patterns is locally governed by separable hermite polynomials of arbitrary finite order as eigenfunctions of a linear self adjoint differential operator we consider m 1 and describe a principle idea of constructing of a spectrum of blow up patterns which in the inner self similar region are composed of a countable subset of separable kummer9s polynomials which are eigenfunctions of a non self adjoint linear differential operator a matching procedure extends such linearized structures to the nonlinear intermediate region where the asymptotic blow up behaviour is described by a unique self similar solution of the first order hamilton jacobi equation

invariant sets and solutions to the two dimensional nonlinear reaction diffusion equations abstract in this paper we utilize the method of invariant set to derive exact solutions of the two dimensional nonlinear reaction diffusion equations with source term it is shown that there exists a class of reaction diffusion equations which are invariant with respect to the sets e 1 u u x v x f t f u u y v y f t f u and e 2 u u x a x f t f u u y b y g t f u with f g as a result we obtain exact solutions of the certain nonlinear reaction diffusion equations these solutions extend the well known self similar solutions and instantaneous source type solutions of the porous medium equation the behavior to some solutions and the corresponding interfaces are also described

latent class analysis of complex sample survey data application to dietary data high fruit and vegetable intake is associated with decreased cancer risk however dietary recall data from national surveys suggest that on any given day intake falls below the recommended minima of three daily servings of vegetables and two daily servings of fruit there is no single widely accepted measure of usual intake one approach is to regard the distribution of intake as a mixture of regular relatively frequent and nonregular relatively infrequent consumers using an indicator of whether an individual consumed the food of interest on the recall day we use a new approach to summarizing dietary data latent class analysis lca to estimate usual intake of vegetables the data consist of four 24 hour dietary recalls from the 1985 continuing survey of intakes by individuals collected from 1 028 women traditional lca based on simple random sampling was extended to complex survey data by introducing sample weights into the latent class estimation algorithm and by accounting for the co

synchronization of kuramoto oscillators in small world networks abstract we study the synchronization of kuramoto oscillators on small world networks firstly we analyze the impact of coupling strength rewiring probability and average degree of networks on the phase synchronization in weak coupled system then by increasing the coupling strength we find an interesting phenomenon that when coupling strength is much larger than the synchronization threshold there is another threshold which can decrease the synchronization performance of the system finally in order to enhance the synchronization performance of strong coupled system we adopt a simple way to delete some nodes randomly to construct disordered environment numerical results show that a certain degree of disorder can promote the synchronization performance of strong coupled small world networks

optimization based model fitting for latent class and latent profile analyses statisticians typically estimate the parameters of latent class and latent profile models using the expectation maximization algorithm this paper proposes an alternative two stage approach to model fitting the first stage uses the modified k means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model the second stage then uses mixture modeling treating the class membership as known the proposed approach is theoretically justifiable directly checks the conditional independence assumption and converges much faster than the full likelihood approach when analyzing high dimensional data this paper also develops a new classification rule based on latent variable models the proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease which makes it perfect for analyzing high throughput genomic data simulation studies and real data analysis demonstrate the advantages of the proposed method

constrained latent class analysis simultaneous classification and scaling of discrete choice data a reparameterization of a latent class model is presented to simultaneously classify and scale nominal and ordered categorical choice data latent class specific probabilities are constrained to be equal to the preference probabilities from a probabilistic ideal point or vector model that yields a graphical multidimensional representation of the classification results in addition background variables can be incorporated as an aid to interpreting the latent class specific response probabilities the analyses of synthetic and real data sets illustrate the proposed method

a vibrational approach to node centrality and vulnerability in complex networks we propose a new measure of vulnerability of a node in a complex network the measure is based on the analogy in which the nodes of the network are represented by balls and the links are identified with springs we define the measure as the node displacement or the amplitude of vibration of each node under fluctuation due to the thermal bath in which the network is supposed to be submerged we prove exact relations among the thus defined node displacement the information centrality and the kirchhoff index the relation between the first two suggests that the node displacement has a better resolution of the vulnerability than the information centrality because the latter is the sum of the local node displacement and the node displacement averaged over the entire network

large time behaviour of the solutions of a semilinear parabolic equation in rn abstract the asymptotic behaviour as t tends to of the solution of u t u u u p 1 0 in r n r p 1 was studied it was proved that the behaviour depends strongly on the sign of n 2 n p and also on the rate of decay of the admissible initial data u 0 x as x tends to

structural and spectral properties of a family of deterministic recursive trees rigorous solutions as one of the most significant models the uniform recursive tree urt has found many applications in a variety of fields in this paper we study rigorously the structural features and spectral properties of the adjacency matrix for a family of deterministic uniform recursive trees durts that are deterministic versions of urt firstly from the perspective of complex networks we investigate analytically the main structural characteristics of durts and obtain the accurate solutions for these properties which include degree distribution average path length distribution of node betweenness and degree correlations then we determine the complete eigenvalues and their corresponding eigenvectors of the adjacency matrix for durts our research may shed light on a better understanding of the features for urt also the analytical methods used here are capable of being extended to many other deterministic networks making the precise computation of their properties especially the full spectrum characteristics possible

a new index of fit based on mixture methods for the analysis of contingency tables summary a framework based on mixture methods is proposed for evaluating goodness of fit in the analysis of contingency tables for a given model h applied to a contingency table p we consider the two point mixture p 1 r i1 ri2 with 7r the mixing proportion o r 1 and hi and i2 the tables of probabilities for each latent class or component in the unstructured approach recommended here the mixture model applies h to hi but does not impose any restrictions on i2 a contingency table p can generally be represented as such a two point mixture for an interval of 7r values we define our index of lack of fit ir to be the smallest such 7r i e 7r is the fraction of the population that cannot be described by model h this approach can be contrasted with the structured approach that applies model h to both h and i2 and leads to conventional latent class models when h is the hypothesis of independence the case where h is the hypothesis of row column independence and p is a two way contingency table is covered in detail but the procedure is quite general

large time behavior for the fast diffusion equation with critical absorption we study the large time behavior of nonnegative solutions to the cauchy problem for a fast diffusion equation with critical zero order absorption partial t u delta u m u q 0 quad quad hbox in 0 infty times real n with m c n 2 n 1

mean field theory for scale free random networks random networks with complex topology are common in nature describing systems as diverse as the world wide web or social and business networks recently it has been demonstrated that most large networks for which topological information is available display scale free features here we study the scaling properties of the recently introduced scale free model that can account for the observed power law distribution of the connectivities we develop a mean eld method to predict the growth dynamics of the individual vertices and use this to calculate analytically the connectivity distribution and the scaling exponents the mean eld method can be used to address the properties of two variants of the scale free model that do not display power law scaling c 1999 elsevier science b v all rights reserved

global blow up for a semilinear heat equation on a subspace we study the asymptotic behaviour as t t near a finite blow up time t 0 of decreasing in x solutions to the following semilinear heat equation with a non local term figure presented with neumann boundary conditions and strictly decreasing initial function u0 x with zero mass we prove sharp estimates for u x t as t t revealing a non uniform global blow up figure presented uniformly on any compact set 1 0 1

synchronized clusters in coupled map networks i numerical studies we study the synchronization of coupled maps on a variety of networks including regular one and two dimensional networks scale free networks small world networks tree networks and random networks for small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases when nodes show synchronized behavior we observe two interesting phenomena first there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently second we identify two different ways of cluster formation namely self organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings the synchronized clusters may be of dominant self organized type dominant driven type or mixed type depending on the type of network and the parameters of the dynamics we define different states of the coupled dynamics by considering the number and type of synchronized clusters for the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant and the logistic map parameter ensuremath mu for large coupling strengths and nonlinear coupling we find that the scale free networks and the caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity for most of our study we use the number of connections of the order of the number of nodes as the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase

concomitant variable latent class models abstract this article introduces and illustrates a new type of latent class model in which the probability of latent class membership is functionally related to concomitant variables with known distribution the function or so called submodel may be logistic exponential or another suitable form concomitant variable models supplement latent class models incorporating grouping by providing more parsimonious representations of data for some cases also concomitant variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets although parameter estimates may be calculated using standard iterative procedures such as the newton raphson method sample analyses presented here employ a derivative free approach known as the simplex method a general procedure for imposing linear constraints on the parameter estimates is introduced a data set involving arithmetic test items in a mastery testing context is used to illustrate fitting a

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

on scaling models applied to data from several groups statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups these methods can be used to a compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups b compare the corresponding estimated item reliabilities or item response error rates for the different groups and c test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints i e constraints that describe which parameters in the model are the same for the several groups various kinds of scaling models are considered here in the multiple group context

a latent transition model with logistic regression latent transition models increasingly include covariates that predict prevalence of latent classes at a given time or transition rates among classes over time in many situations the covariate of interest may be latent this paper describes an approach for handling both manifest and latent covariates in a latent transition model a bayesian approach via markov chain monte carlo mcmc is employed in order to achieve more robust estimates a case example illustrating the model is provided using data on academic beliefs and achievement in a low income sample of adolescents in the united states

spectral analysis of deformed random networks we study spectral behavior of sparsely connected random networks under the random matrix framework subnetworks without any connection among them form a network having perfect community structure as connections among the subnetworks are introduced the spacing distribution shows a transition from the poisson statistics to the gaussian orthogonal ensemble statistics of random matrix theory the eigenvalue density distribution shows a transition to the wigner s semicircular behavior for a completely deformed network the range for which spectral rigidity measured by the dyson mehta ensuremath delta 3 statistics follows the gaussian orthogonal ensemble statistics depends upon the deformation of the network from the perfect community structure the spacing distribution is particularly useful to track very slight deformations of the network from a perfect community structure whereas the density distribution and the ensuremath delta 3 statistics remain identical to the undeformed network on the other hand the ensuremath delta 3 statistics is useful for the larger deformation strengths finally we analyze the spectrum of a protein protein interaction network for helicobacter and compare the spectral behavior with those of the model networks

bounds for the spectral radius of a graph when nodes are removed abstract we present a new type of lower bound for the spectral radius of a graph in which m nodes are removed as a corollary cioab s theorem 4 which states that the maximum normalized principal eigenvector component in any graph never exceeds 1 2 with equality for the star appears as a special case of our more general result

spectral reconstruction of complex networks abstract in this paper we study the reconstruction of a network topology from the eigenvalues of its laplacian matrix we introduce a simple cost function and consider the tabu search combinatorial optimization method while comparing its performance when reconstructing different categories of networks random regular small world scale free and clustered from their eigenvalues we show that this combinatorial optimization method together with the information contained in the laplacian spectrum allows an exact reconstruction of small networks and leads to good approximations in the case of networks with larger orders we also show that the method can be used to generate a quasi optimal topology for a network associated to a dynamic process like in the case of metabolic or protein protein interaction networks of organisms

the application of latent class models in adaptive testing this paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework the algorithm incorporates a four stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains the classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered the algorithm appears to be particularly effective when latent class membership is related across the various domains of interest since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made to assess the effectiveness of the proposed algorithm a simulation based upon real data was conducted for this example the algorithm proved to be relatively efficient requiring only 40 of the number of items needed under a nonadaptive approach in addition the algorithm provided classification decisions which in 96 of the cases were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5

classification of singular solutions of a nonlinear heat equation on considere toutes les solutions non negatives de l equation de la chaleur non lineaire avec absorption u t u m u p dans q r n 0 t pour n 1 m p 1 avec des conditions initiales u x 0 0 pour x 0

a hierarchical finite mixture model that accommodates zero inflated counts non independence and heterogeneity a number of mixture modeling approaches assume both normality and independent observations however these two assumptions are at odds with the reality of many data sets which are often characterized by an abundance of zero valued or highly skewed observations as well as observations from biologically related i e non independent subjects we present here a finite mixture model with a zero inflated poisson regression component that may be applied to both types of data this flexible approach allows the use of covariates to model both the poisson mean and rate of zero inflation and can incorporate random effects to accommodate non independent observations we demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia but the same methods are applicable to other types of data characterized by zero inflation and non independence

bivariate modelling of clustered continuous and ordered categorical outcomes simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution the approach is then extended to allow for clustering of the bivariate outcomes the model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome this factorization suggests convenient parameter estimation using estimating equations foetal weight and malformation data from a developmental toxicity experiment illustrate the results

partial and latent ignorability in missing data problems summary when an assumption of missing at random is untenable it becomes necessary to model missingdata indicators which carry information about the parameters of the complete data population within a given application however researchers may believe that some aspects of missingness are ignorable but others are not we argue that there are two different ways to formalize the notion that only part of the missingness is ignorable these approaches correspond to assumptions that we call partially missing at random and latently missing at random we explain these concepts and apply them in a latent class analysis of survey questions with item nonresponse

predicting latent class scores for subsequent analysis latent class regression models relate covariates and latent constructs such as psychiatric disorders though full maximum likelihood estimation is available estimation is often in three steps i a latent class model is fitted without covariates ii latent class scores are predicted and iii the scores are regressed on covariates we propose a new method for predicting class scores that in contrast to posterior probability based methods yields consistent estimators of the parameters in the third step additionally in simulation studies the new methodology exhibited only a minor loss of efficiency finally the new and the posterior probability based methods are compared in an analysis of mobility exercise

asymptotic behaviour of nonlinear parabolic equations with critical exponents a dynamical systems approach we investigate the large time behaviour of solutions to the nonlinear heat conduction equation with absorption ut u 1 u in q rn 0 e with n 1 0 and critical absorption exponent 1 2n the initial function u x 0 0 is assumed to be integrable nonnegative and compactly supported we prove that u converges as t to a unique self similar function which is a contracted version of one of the asymptotic profiles of the nonabsorptive problem ut u 1 the same for any initial data the cornerstone of the proof is a result about limits of infinite dimensional asymptotical dynamical systems combining this result with an asymptotic evaluation of the mass function as well as typical pde estimates gives the behaviour of e for large times similar unusual asymptotic behaviour is obtained for the equation ut div du du u with same conditions on and u x 0 and critical value for 1 2 n

dynamical mean field approximation to small world networks of spiking neurons from local to global and or from regular to random couplings by extending a dynamical mean field approximation previously proposed by the author h hasegawa phys rev e 67 041903 2003 we have developed a semianalytical theory which takes into account a wide range of couplings in a small world network our network consists of noisy n unit fitzhugh nagumo neurons with couplings whose average coordination number z may change from local z n to global couplings z n ensuremath 1 and or whose concentration of random couplings p is allowed to vary from regular p 0 to completely random p 1 we have taken into account three kinds of spatial correlations the on site correlation the correlation for a coupled pair and that for a pair without direct couplings the original 2n dimensional stochastic differential equations are transformed to 13 dimensional deterministic differential equations expressed in terms of means variances and covariances of state variables the synchronization ratio and the firing time precision for an applied single spike have been discussed as functions of z and p our calculations have shown that with increasing p the synchronization is worse because of increased heterogeneous couplings although the average network distance becomes shorter results calculated by our theory are in good agreement with those by direct simulations

localization of eigenvector centrality in networks with a cut vertex we show that eigenvector centrality exhibits localization phenomena on networks that can be easily partitioned by the removal of a vertex cut set the most extreme example being networks with a cut vertex three distinct types of localization are identified in these structures one is related to the well established hub node localization phenomenon and the other two are introduced and characterized here we gain insights into these problems by deriving the relationship between eigenvector centrality and katz centrality this leads to an interpretation of the principal eigenvector as an approximation to more robust centrality measures which exist in the full span of an eigenbasis of the adjacency matrix

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

mixed effects analyses of rank ordered data this paper presents a synthesis of bock s 1972 nominal categories model and luce s 1959 choice model for mixed effects analyses of rank ordered data it is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates relationships to other approaches including takane s 1987 ideal point discriminant model and croon s 1989 latent class version of luce s ranking model are also discussed the application focuses on a ranking study of behavioral traits that parents find desirable in children

localization and centrality in networks eigenvector centrality is a common measure of the importance of nodes in a network here we show that under common conditions the eigenvector centrality displays a localization transition that causes most of the weight of the centrality to concentrate on a small number of nodes in the network in this regime the measure is no longer useful for distinguishing among the remaining nodes and its efficacy as a network metric is impaired as a remedy we propose an alternative centrality measure based on the nonbacktracking matrix which gives results closely similar to the standard eigenvector centrality in dense networks where the latter is well behaved but avoids localization and gives useful results in regimes where the standard centrality fails

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

a boundary modulus of continuity for a class of singular parabolic equations abstract parabolic equations describing diffusion phenomena with change of phase are considered it is demonstrated that weak solutions are continuous up to the parabolic boundary of the domain of definition the continuity is quantitatively described by a modulus determined a priori only in terms of the data

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