localized states in the conserved swift hohenberg equation with cubic nonlinearity the conserved swift hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state the resulting phase field crystal model describes a variety of spatially localized structures in addition to different spatially extended periodic structures the location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases and may lie outside of the binodal for these states the results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential and are expected to carry over to related models with a conserved order parameter 2013 american physical society

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

morphology of growing interfacial patterns a study is made of the morphology of the interfacial patterns in the solid on solid model evolving from initial states very far from equilibrium monte carlo simulation is used to study the time dependence of the length the diffuseness and the width of the interface during such evolution in the absence as well as in the presence of quenched random field moreover the technique of walsh fourier transform is introduced for analyzing the noise level in such interfacial patterns a quantity is also introduced that characterizes the interfacial structure locally on a very short length scale finally the latter technique is also applied to the kinetic ising model evolving from a random initial configuration

non conservative perturbations of homoclinic snaking scenarios abstract homoclinic snaking refers to the continuation of homoclinic orbits to an equilibrium e near a heteroclinic cycle connecting e and a periodic orbit p typically homoclinic snaking appears in one parameter families of reversible conservative systems here we discuss perturbations of this scenario which are both non reversible and non conservative we treat this problem analytically in the spirit of the work 3 the continuation of homoclinic orbits happens with respect to both the original continuation parameter and the perturbation parameter the continuation curves are parametrised by the dwelling time l of the homoclinic orbit near p it turns out that l tends to zero while the vs l diagram displays isolas or criss cross snaking curves in a neighbourhood of the original snakes and ladder structure in the course of our studies we adapt both fenichel coordinates near p and the analysis of shilnikov problems near p to the present situation

anisotropy and scaling of eden clusters in two and three dimensions for two dimensional eden clusters grown on flat substrates the way the perimeter per unit length and the surface width depend on the orientation of the substrate with respect to the lattice is measured the evolution of the perimeter per unit length during growth is shown to be independent of the substrate length for the surface width strong corrections to scaling are observed the anisotropy of three dimensional eden clusters and its implications for the scaling of the surface width are investigated the largest two and three dimensional clusters studied are more than one order of magnitude larger than in previous simulations

eden growth on multifractal lattices a modified eden model has been investigated in which the growth probabilities are determined by a fractal measure on the underlying lattice both the spatial distribution and probability distribution of surface sites on the growing clusters have been investigated for the case where the multifractal substrate is constructed using a 2 2 multiplicative generator with the probabilities p1 1 p2 r p3 r3 and p4 r3 the spatial distribution of surface sites and the sites comprising the inner and outer hulls have a fractal geometry which can be described by dimensionalities which depend on r for the total surface this dimensionality converges to a value of about 1 76 or 0 01 as r to 0 for the inner and outer hulls the fractal dimensionality approaches a value of about 1 48 or 0 02

sample size determination within the scope of conditional maximum likelihood estimation with special focus on testing the rasch model this paper refers to the exponential family of probability distributions and the conditional maximum likelihood cml theory it is concerned with the determination of the sample size for three groups of tests of linear hypotheses known as the fundamental trinity of wald score and likelihood ratio tests the main practical purpose refers to the special case of tests of the class of rasch models the theoretical background is discussed and the formal framework for sample size calculations is provided given a predetermined deviation from the model to be tested and the probabilities of the errors of the first and second kinds

rasch models for item bundles this paper discusses the application of a class of rasch models to situations where test items are grouped into subsets and the common attributes of items within these subsets brings into question the usual assumption of conditional independence the models are all expressed as particular cases of the random coefficients multinomial logit model developed by adams and wilson this formulation allows a very flexible approach to the specification of alternative models and makes model testing particularly straightforward the use of the models is illustrated using item bundles constructed in the framework of the solo taxonomy of biggs and collis

loglinear multidimensional irt models for polytomously scored items a loglinear irt model is proposed that relates polytomously scored item responses to a multidimensional latent space the analyst may specify a response function for each response indicating which latent abilities are necessary to arrive at that response each item may have a different number of response categories so that free response items are more easily analyzed conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear irt models

heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible hamiltonian hopft bifurcation this paper considers an unfolding of a degenerate reversible 1 1 resonance or hamiltonian hopf bifurcation for four dimensional systems of time reversible ordinary differential equations odes this bifurcation occurs when a complex quadruple of eigenvalues of an equilibrium coalesce on the imaginary axis to become imaginary pairs the degeneracy occurs via the vanishing of a normal form coefficient q2 0 that determines whether the bifurcation is super or subcritical of particular concern is the behaviour of homoclinic and heteroclinic connections between the trivial equilibrium and simple periodic orbits a partial unfolding of such solutions already occurs in the work of dias and iooss eur j mech b fluids 15 1996 367 393 given a sign of the coefficient of a higher order term q4 0 and 1 q2 0 the normal form then shows a small amplitude bifurcating branch of homoclinic solutions terminating at a heteroclinic connection to a simple periodic orbit a genericity argument shows that this connection is not structurally stable and should break into a pair of heteroclinic tangencies this is confirmed by numerics which shows that branches of the simplest homoclinic orbits undergo an infinite snaking sequence of limit points accumulating on the parameter values of the two tangencies at each limit point the homoclinic orbit generates another bump close to the periodic orbit as q2 is further decreased from zero the snake widens until at a critical value a branch is formed of heteroclinic connections from the origin to a nontrivial equilibrium a kink for q2 less than this value the kinks heteroclinic tangencies and snake like curves no longer occur

existence and stability of spatially localized patterns abstract spatially localized patterns have been observed in numerous physical contexts and their bifurcation diagrams often exhibit similar snaking behavior symmetric solution branches connected by bifurcating asymmetric solution branches wind back and forth in an appropriate parameter previous papers have addressed existence of such solutions here we address their stability taking the necessary first step of unifying existence and uniqueness proofs for symmetric and asymmetric solutions we then show that under appropriate assumptions temporal eigenvalues of the front and back underlying a localized solution are added with multiplicity in the right half plane in a companion paper we analyze the behavior of eigenvalues at 0 and inside the essential spectrum our results show that localized snaking solutions are stable if and only if the underlying fronts and backs are stable unlike localized non oscillatory solutions no interaction eigenvalues are present we use the planar swift hohenberg system to illustrate our results

item bias detection using loglinear irt a method is proposed for the detection of item bias with respect to observed or unobserved subgroups the method uses quasi loglinear models for the incomplete subgroup test score item 1 itemk contingency table if subgroup membership is unknown the models are haberman s incomplete latent class models the conditional rasch model is formulated as a quasi loglinear model the parameters in this loglinear model that correspond to the main effects of the item responses are the conditional estimates of the parameters in the rasch model item bias can then be tested by comparing the quasi loglinear rasch model with models that contain parameters for the interaction of item responses and the subgroups

structural analysis of subjective categorical data a general approach to the analysis of subjective categorical data is considered in which agreement matrices of two or more raters are directly expressed in terms of error and agreement parameters the method provides focused analyses of ratings from several raters for whom ratings have measurement error distributions that may induce bias in the evaluation of substantive questions of interest each rater s judgment process is modeled as a mixture of two components an error variable that is unique for the rater in question as well as an agreement variable that operationalizes the true values of the units of observation the statistical problems of identification estimation and testing of such measurement models are discussed

logistic latent trait models with linear constraints two linearly constrained logistic models which are based on the well known dichotomous rasch model the linear logistic test model lltm and the linear logistic model with relaxed assumptions llra are discussed necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned

mcmc estimation and some model fit analysis of multidimensional irt models a bayesian procedure to estimate the three parameter normal ogive model and a generalization of the procedure to a model with multidimensional ability parameters are presented the procedure is a generalization of a procedure by albert 1992 for estimating the two parameter normal ogive model the procedure supports analyzing data from multiple populations and incomplete designs it is shown that restrictions can be imposed on the factor matrix for testing specific hypotheses about the ability structure the technique is illustrated using simulated and real data

a class of multidimensional irt models for testing unidimensionality and clustering items we illustrate a class of multidimensional item response theory models in which the items are allowed to have different discriminating power and the latent traits are represented through a vector having a discrete distribution we also show how the hypothesis of unidimensionality may be tested against a specific bidimensional alternative by using a likelihood ratio statistic between two nested models in this class for this aim we also derive an asymptotically equivalent wald test statistic which is faster to compute moreover we propose a hierarchical clustering algorithm which can be used when the dimensionality of the latent structure is completely unknown for dividing items into groups referred to different latent traits the approach is illustrated through a simulation study and an application to a dataset collected within the national assessment of educational progress 1996

on the existence and uniqueness of maximum likelihood estimates in the rasch model necessary and sufficient conditions for the existence and uniqueness of a solution of the so called unconditional uml and the conditional cml maximum likelihood estimation equations in the dichotomous rasch model are given the basic critical condition is essentially the same for uml and cml estimation for complete data matricesa it is formulated both as a structural property ofa and in terms of the sufficient marginal sums in case of incomplete data the condition is equivalent to complete connectedness of a certain directed graph it is shown how to apply the results in practical uses of the rasch model

swift hohenberg equation with broken reflection symmetry the bistable swift hohenberg equation possesses a variety of time independent spatially localized solutions organized in the so called snakes and ladders structure this structure is a consequence of a phenomenon known as homoclinic snaking and is in turn a consequence of spatial reversibility of the equation we examine here the consequences of breaking spatial reversibility on the snakes and ladders structure we find that the localized states now drift and show that the snakes and ladders structure breaks up into a stack of isolas we explore the evolution of this new structure with increasing reversibility breaking and study the dynamics of the system outside of the snaking region using a combination of numerical and analytical techniques

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

hole distribution in eden clusters clusters grown by the eden process have few empty sites in their interior these sites are concentrated near the cluster surface the number of clusters of connected empty sites is investigated by computer simulation and shown to disagree with a simple percolation approximation

classification of some deposition and growth processes stochastic models of surface deposition and growth processes fall into two classes with different scaling properties of the surface fluctuations the class to which a given model belongs is determined by the variation of the macroscopic growth velocity with surface inclination a distinction is made between deposition and growth processes and it is shown that the non linearity of the surface evolution equation is due to different mechanisms in the two cases

exact tests for the rasch model via sequential importance sampling rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability this paper furthers rasch s approach by 1 providing an efficient monte carlo methodology for accurately approximating the required probability and 2 illustrating the usefulness of rasch s approach for several important testing problems through simulation studies our monte carlo methodology is shown to compare favorably to other monte carlo methods proposed for this problem in two respects it is considerably faster and it provides more reliable estimates of the monte carlo standard error

a latent trait finite mixture model for the analysis of rating agreement this article presents a latent distribution model for the analysis of agreement on dichotomous or ordered category ratings the model includes parameters that characterize bias category definitions and measurement error for each rater or test parameter estimates can be used to evaluate rater performance and to improve classification or measurement with use of multiple ratings a simple maximum likelihood estimation procedure is described two examples illustrate the approach although considered in the context of analyzing rater agreement the model provides a general approach for mixture analysis using two or more ordered caregory measures

scaling properties of the surface of the eden model in d 2 3 4 the surface of the eden model is investigated numerically by finite size scaling using a strip geometry three different versions are studied and it shows that the one mostly used previously exhibits strong finite size corrections in two dimensions it is found that the surface thickness simply grows as the square root of the width of the strip for infinitely long strips this result as well as the results in d 3 and d 4 suggest that the surface of the eden shares some properties with the equilibrium models used to describe the roughening transition moreover it is found that the surface thickness scales differently with the height of the cluster for infinitely large strips

loglinear rasch model tests existing statistical tests for the fit of the rasch model have been criticized because they are only sensitive to specific violations of its assumptions contingency table methods using loglinear models have been used to test various psychometric models in this paper the assumptions of the rasch model are discussed and the rasch model is reformulated as a quasi independence model the model is a quasi loglinear model for the incomplete subgroup score item 1 item 2 itemk contingency table using ordinary contingency table methods the rasch model can be tested generally or against less restrictive quasi loglinear models to investigate specific violations of its assumptions

predicting the bifurcation structure of localized snaking patterns abstract we expand upon a general framework for studying the bifurcation diagrams of localized spatially oscillatory structures building on work by beck et al the present work provides rigorous analytical results on the effects of perturbations to systems exhibiting snaking behavior starting with a reversible variational system possessing an additional z 2 symmetry we elucidate the distinct effects of breaking symmetry and breaking variational structure and characterize the resulting changes in both the bifurcation diagram and the solutions themselves we show how to predict the branch reorganization and drift speeds induced by any particular given perturbative term and illustrate our results via numerical continuation we further demonstrate the utility of our methods in understanding the effects of particular perturbations breaking reversibility our approach yields an analytical explanation for previous numerical results on the effects of perturbations in the one dimensional cubic quintic swift hohenberg model and allows us to make predictions on the effects of perturbations in more general settings including planar systems while our numerical results involve the swift hohenberg model system we emphasize the general applicability of the analytical results

computing maximum likelihood estimates of loglinear models from marginal sums with special attention to loglinear item response theory in this paper algorithms are described for obtaining the maximum likelihood estimates of the parameters in loglinear models modified versions of the iterative proportional fitting and newton raphson algorithms are described that work on the minimal sufficient statistics rather than on the usual counts in the full contingency table this is desirable if the contingency table becomes too large to store special attention is given to loglinear irt models that are used for the analysis of educational and psychological test data to calculate the necessary expected sufficient statistics and other marginal sums of the table a method is described that avoids summing large numbers of elementary cell frequencies by writing them out in terms of multiplicative model parameters and applying the distributive law of multiplication over summation these algorithms are used in the computer program logimo the modified algorithms are illustrated with simulated data

nonparametric goodness of fit tests for the rasch model a monte carlo algorithm realizing a family of nonparametric tests for the rasch model is introduced which are conditional on the item and subject marginals the algorithm is based on random changes of elements of data matrices without changing the marginals most powerful tests against all alternative hypotheses are given for which a monotone characteristic may be computed from the data matrix alternatives may also be composed computation times are long but exactp values are approximated with the quality of approximation only depending on calculation time but not on the number of persons the power and the flexibility of the procedure is demonstrated by means of an empirical example where among others indicators for increased item similarities the existence of subscales violations of sufficiency of the raw score as well as learning processes were found many of the features described are implemented in the program t rasch 1 0 by ponocny and ponocny seliger 1999

noise reduction in eden models ii surface structure and intrinsic width for pt i see ibid vol 20 p 257 1987 the authors suggest a picture of the intrinsic surface width in eden models and show that it is a major source of corrections to scaling of the surface roughness using the multiple hit noise reduction method they can control the intrinsic width and thereby improve the scaling behaviour systematically as is demonstrated in detailed calculations on the square lattice they calculate the number of excess perimeter sites as a function of time and find that its asymptotic value decays with a power law as a function of increasing hitting number substrate effects and anisotropy become more apparent if noise reduction is applied

paradoxical results and item bundles hooker finkelman and schwartzman psychometrika 2009 in press defined a paradoxical result as the attainment of a higher test score by changing answers from correct to incorrect and demonstrated that such results are unavoidable for maximum likelihood estimates in multidimensional item response theory the potential for these results to occur leads to the undesirable possibility of a subject s best answer being detrimental to them this paper considers the existence of paradoxical results in tests composed of item bundles when compensatory models are used we demonstrate that paradoxical results can occur when bundle effects are modeled as nuisance parameters for each subject however when these nuisance parameters are modeled as random effects or used in a bayesian analysis it is possible to design tests comprised of many short bundles that avoid paradoxical results and we provide an algorithm for doing so we also examine alternative models for handling dependence between item bundles and show that using fixed dependency effects is always guaranteed to avoid paradoxical results

two dimensional diffusion limited aggregation a finite size scaling approach finite size scaling in the diffusion limited aggregation model of witten and sander 1981 1983 is studied in two dimensions via monte carlo simulations on semi infinite strips of width n 2 20 due to a crossover between self avoiding walk like growth for small n and dendritic growth for large n wide strips n 8 20 are needed to deduce the witten sander fractal dimension d approximately 5 3 from the finite size scaling analysis

localized states in the generalized swift hohenberg equation the swift hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable wealth of stable spatially localized states the presence of these states is related to a phenomenon called homoclinic snaking numerical computations are used to illustrate the changes in the localized solution as it grows in spatial extent and to determine the stability properties of the resulting states the evolution of the localized states once they lose stability is illustrated using direct simulations in time i introduction ever since the observation that the subcritical complex ginzburg landau equation exhibits stable spatially localized states 1 there has been considerable interest in the properties of these states the presence of these states has important consequences for other systems described by partial differential equations on the line since the ginzburg landau equation describes the behavior of such systems near bifurcation from the trivial state of the system specifically the complex ginzburg landau equation describes the evolution of a long wavelength oscillatory instability as well as oscillatory instabilities at finite wavelength in systems with broken reflection symmetry in contrast near a steady state bifurcation with finite wavelength the evolution of the instability is described by the real ginzburg landau equation and this equation possesses only unstable spatially localized states it is of interest therefore to examine what happens to these unstable states at larger amplitude where the real ginzburg landau equation no longer provides an adequate description of the system in this paper we show that the localized states can become stable at such amplitudes and indeed that there is a large multiplicity of coexisting stable localized states under very general conditions we are able to relate the existence of these states to a phenomenon sometimes called homoclinic snaking that is well known from the theory of reversible systems with 1 1 resonance and use this theory to construct a large number of such states the stability properties of these states are also determined and the evolution of nonstationary localized states is studied by numerical integration in time it is an interesting fact that closely related phenomena have already been described in several areas involving pattern formation the theory was originally developed in the context of water waves where localized states have been studied by moving into a reference frame of the waves and converting the problem into an ordinary differential equation ode the resulting localized states are called solitary waves and in some cases turn out to be solitons kirchgassner 2 has pioneered a successful approach to this type of problem that led to a number of advances in this area specifically the ode is viewed as a dynamical system in space and localized states are sought as homoclinic orbits connecting the trivial state to itself whether such orbits are possible depends in part on the stability properties of the trivial state eigenvalues with positive real part indicate that a nontrivial state can grow from x while eigenvalues with negative real part indicate that such a state may return under appropriate conditions back to the trivial state as x the spectrum of the linearization about the trivial state is influenced by spatial symmetries of the system in many cases and in particular in the case considered here the ode is reversible as a result the bifurcations that are encountered as a parameter is increased are nongeneric in the present case the spatial dynamics of the system near the trivial state turn out to be described by the reversible 1 1 resonance the unfolding of this resonance has been worked out in detail by iooss and peroueme 3 and can be used to understand the appearance of a variety of homoclinic orbits in this system and hence of localized states with different spatial structure

the equivalence of two methods of parameter estimation for the rasch model two methods of estimating parameters in the rasch model are compared it is shown that estimates for a certain loglinear model for the score item response table are equivalent to the unconditional maximum likelihood estimates for the rasch model

extended range ballistic aggregation exact results and scaling the authors present the exact solution of an infinite range ballistic aggregation model the density is found to decrease as n 1 2 as n to infinity where n is the number of columns in which particles move exact expressions for the correlation function and the hole size distribution are derived both decay exponentially over their entire domain using a scaling ansatz similar to that made in finite size scaling in critical phenomena they extrapolate these results to large but finite ranges computer simulations test the proposed scaling

invasion percolation and invading eden growth on multifractal lattices eden growth and invasion percolation models have been explored on square lattices with a multifractal distribution of growth probabilities these models generate structures with a mass fractal dimensionality of 2 and surfaces which can be described in terms of self similar fractal geometry with a fractal dimensionality larger than 1 and smaller than 2 for the eden growth models the fractal dimensions of the total perimeter internal hull and external hull depend on the probabilities associated with the generator of the multifractal measure for the invasion percolation model the three fractal dimensionalities are relatively insensitive to the structure of the generator and may be universal the distribution of growth probabilities associated with the eden models can also be described as a fractal measure and the spectrum of singularities f alpha associated with this measure has been estimated for some of these models for the eden growth models the fractal dimensionalities describing the structure of total perimeter internal hull and external hull are given by d d xi where xi is the variance of the logarithms of the probabilities used in the multiplicative generators for the multifractal growth probability measure

noise reduction in eden models i the authors adapt the multiple hit method of noise reduction introduced earlier for diffusion limited growth to eden models a and c on the square lattice the dynamic scaling is improved considerably they obtain 0 33 or 0 015 model a for the dynamic exponent beta of surface roughening with relatively small computing effort results for model c support universality

phase transition in the 2d ballistic growth model with quenched disorder abstract quenched disorder is introduced in the two dimensional ballistic growth model by randomly distributing growing rates equal to and 1 on the sites of a square lattice with probabilities p and 1 p the model is studied by means of numerical simulations in a strip geometry of width up to l 2048 and heights up to 15l with periodic boundary conditions at the edges of the strip numerical results on the bulk density and the surface thickness are consistent with the existence of a phase transition in the limit 0 l at a critical value p 0 305 0 001 it is shown that the fraction of rate sites included in the bulk during the growth process can be considered as an order parameter critical exponents are estimated and are found to be different than for the eden model in the same random environment

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

a dynamic generalization of the rasch model in the present paper a model for describing dynamic processes is constructed by combining the common rasch model with the concept of structurally incomplete designs this is accomplished by mapping each item on a collection of virtual items one of which is assumed to be presented to the respondent dependent on the preceding responses and or the feedback obtained it is shown that in the case of subject control no unique conditional maximum likelihood cml estimates exist whereas marginal maximum likelihood mml proves a suitable estimation procedure a hierarchical family of dynamic models is presented and it is shown how to test special cases against more general ones furthermore it is shown that the model presented is a generalization of a class of mathematical learning models known as luce s beta model

equivalence between conditional and mixture approaches to the rasch model and matched case control studies with applications analyses of data using rasch models including the special case of matched case control studies are common applications of conditional likelihood in which the usual inferential procedures are applied only after conditioning on an approximately ancillary statistic another common approach to the analysis of rasch models is to integrate the nuisance parameters over a mixing distribution using the marginal likelihood obtained as the basis for inference we show that the full conditional likelihood can always be obtained exactly via the marginal approach given a particular choice of mixing distribution and derive necessary and sufficient conditions for the two approaches to agree previous work has shown that with sufficient flexibility in the mixing distribution the maxima of the marginal and conditional likelihoods will be equivalent under concordance criteria our argument requires no such criteria and for any dataset guarantees the equivalence of the whole of the two likelihoods not just their maxi

sample size determination for rasch model tests this paper is concerned with supplementing statistical tests for the rasch model so that additionally to the probability of the error of the first kind type i probability the probability of the error of the second kind type ii probability can be controlled at a predetermined level by basing the test on the appropriate number of observations an approach to determining a practically meaningful extent of model deviation is proposed and the approximate distribution of the wald test is derived under the extent of model deviation of interest

wulff construction and anisotropic surface properties of two dimensional eden clusters a relation between the shape of eden clusters and the number of perimeter sites per unit area of the surface is derived which is analogous to the wulff construction of equilibrium shapes in thermodynamic systems new data are presented for the surface width and the surface skewness of eden clusters grown on a square lattice the width depends on the average orientation of the surface with respect to the underlying lattice its corrections to scaling are discussed the skewness has unexpected changes of sign

loglinear rasch models for the analysis of stability and change loglinear unidimensional and multidimensional rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change models of purely quantitative change in latent traits are proposed as well as models including structural change a conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales rasch models in the context of longitudinal research this renders possible the statistical test of homogeneity of change against subject specific change in latent traits applications to two empirical data sets illustrate the use of the models

some improved diagnostics for failure of the rasch model although several goodness of fit tests have been developed for the rasch model for dichotomous items most of them are of a global asymptotic and confirmatory type this paper based on ideas from a recent thesis by van den wollenberg offers some suggestions for local small sample and exploratory techniques difficulty plots for person groups scoring right and wrong on a specific item a slope test per item based on a binomial distribution per score group and a unidimensionality check based on an extended hypergeometric distribution per score group

morphology of the interfacial patterns growing from unstable initial states in crystal growth models using the walsh fourier transform of the interface function the author introduces a new method for the analysis of the morphology of the complex interfacial patterns evolving with time on discrete lattices in a wide class of physical systems including crystal growth models for the crystal growth models he also generalises an old technique for characterising the interfacial patterns on small length scales to patterns evolving from initial states far from equilibrium

item response theory with estimation of the latent population distribution using spline based densities the purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines a spline based density estimation system provides a flexible alternative to existing procedures that use a normal distribution or a different functional form for the population distribution a simulation study shows that the new procedure is feasible in practice and that when the latent distribution is not well approximated as normal two parameter logistic 2pl item parameter estimates and expected a posteriori scores eaps can be improved over what they would be with the normal model an example with real data compares the new method and the extant empirical histogram approach

two new test statistics for the rasch model it is shown that the presently available statistical tests for the rasch model are insensitive to violation of the unidimensionality axiom two new test statistics are presented the first one q 1 is sensitive to the same effects as the presently available statistics but has some desirable properties of a nonstatistical nature the second statistic q 2 is sensitive to violation of local stochastic independence and unidimensionality and thus fills an existing gap

conjunctive item response theory kernels conjunctive item response models are introduced such that a sufficient statistics for latent traits are not necessarily additive in item scores b items are not necessarily locally independent and c existing compensatory additive item response models including the binomial rasch logistic and general locally independent model are special cases simple estimates and hypothesis tests for conjunctive models are introduced and evaluated as well conjunctive models are also identified with cognitive models that assume the existence of several individually necessary component processes for a global ability it is concluded that conjunctive models and methods may show promise for constructing improved tests and uncovering conjunctive cognitive structure it is also concluded that conjunctive item response theory may help to clarify the relationships between local dependence multidimensionality and item response function form

the derivation of some tests for the rasch model from the multinomial distribution the present paper is concerned with testing the fit of the rasch model it is shown that this can be achieved by constructing functions of the data on which model tests can be based that have power against specific model violations it is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product multinomial models the model tests are presented in two versions one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation

exponential dichotomies for solitary wave solutions of semilinear elliptic equations on infinite cylinders in applications solitary wave solutions of semilinear elliptic equations u g u u 0 x y r in infinite cylinders frequently arise as travelling waves of parabolic equations as such their bifurcations are an interesting issue interpreting elliptic equations on infinite cylinders as dynamical systems inxhas proved very useful still there are major obstacles in obtaining for instance bifurcation results similar to those for ordinary differential equations in this article persistence and continuation of exponential dichotomies for linear elliptic equations is proved with this technique at hands lyapunov schmidt reduction near solitary waves can be applied as an example existence of shift dynamics near solitary waves is shown if a perturbation h x u u periodic inxis added

snakes and ladders in an inhomogeneous neural field model continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity we analyze stationary localized structures in a neural field model with periodic modulation of the synaptic connectivity kernel and find that they are arranged in a snakes and ladders bifurcation structure in the case of heaviside firing rates we construct analytically symmetric and asymmetric states and hence derive closed form expressions for the corresponding bifurcation diagrams we show that the ideas proposed by beck and co workers to analyze snaking solutions to the swift hohenberg equation remain valid for the neural field model even though the corresponding spatial dynamical formulation is non autonomous we investigate how the modulation amplitude affects the bifurcation structure and compare numerical calculations for steep sigmoidal firing rates with analytic predictions valid in the heaviside limit

scaling properties of eden clusters in three and four dimensions we study the scaling properties of noise reduced eden clusters in three and four dimensions for variant b in the strip geometry we find that the width w for large times behaves as a s g lsd 1 where l is the width of the strip s the noise reduction parameter d the dimension of space and a s a decreasing function of s g is a scaling function with the property g u 12 as u 0 and g u ux as u where is the roughness exponent this scaling result leads to a new way of determining in 3 dimensions our numerical values for support a recent conjecture by kim and kosterlitz 2 d 2 and contradict all the former analytical conjectures in 4 dimensions we cannot distinguish between the conjectures of kim and kosterlitz and the conjecture of wolf and kertesz because large crossovers and finite size effects make the measurement of the exponents difficult

the role of collateral information about examinees in item parameter estimation standard procedures for estimating item parameters in item response theory irt ignore collateral information that may be available about examinees such as their standing on demographic and educational variables this paper describes circumstances under which collateral information about examineesmay be used to make inferences about item parameters more precise and circumstances under which itmust be used to obtain correct inferences

universal scaling properties of ballistic deposition and eden growth on surfaces the structures generated by ballistic deposition and eden growth from a surface can be divided in a natural way defined by the growth process into trees or clusters of connected sites or particles the structure of these trees can be characterised by the exponents nu perpendicular to p and nu sub q which describe how their heights h and widths w grow with increasing size s w approximately sp h approximately sq in addition the distribution of sizes can be described by the power law ns approximately s tau where ns is the number of trees of size s both the individual trees and the complete deposit are compact so that the exponents p q and tau satisfy the simple scaling relationships d 1 p q 1 and tau 2 q the exponents p q and tau seem to be universal for off lattice ballistic deposition on lattice ballistic deposition and eden growth models however the corresponding exponents for the river network model are different from those for eden growth and ballistic deposition from the two dimensional eden model and ballistic deposition models values of about 0 40 0 60 and 1 40 were obtained for p q and tau respectively in three dimensions p approximately 0 28 q approximately 0 46 and tau approximately 1 54

an exact and optimal standardized person test for assessing consistency with the rasch model the rasch model predicts that an individual s ability level is invariant over subtests of the total test and thus all subtests measure the same latent trait a person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic given a particular level of ability does not depend on the absolute value of the examinee s ability parameter the test can be routinely performed by applying a computer program designed by and obtainable from the author finally a suboptimal test is derived that is extremely easy to use and an overall group test of the invariance hypothesis discussed all tests considered do not rely on asymptotic approximations hence they may be applied when the test is of only moderate length and the group of examinees is small

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

a model for repeated measurements of a multivariate binary response abstract this article presents a logit model for a vector of binary variables observed for each subject under multiple conditions the model contains a vector of random effects to account for correlations among the repeated measurements a nonparametric treatment of the random effects implies a multivariate log linear model having quasi symmetric structure for the cross classification of responses at the various conditions the fit yields estimates of within subject effects comparing the conditions for each variable the estimates are identical to conditional maximum likelihood estimates for a fixed effects version of the logit model extensions incorporate independent groups or allow variables to have multiple response categories

dynamic scaling and phase transitions in interface growth abstract the dynamic scaling approach is an effective tool for understanding the temporal evolution of fluctuating interfaces the surface width w obeys the scaling form w l t l t l where and are exponents which characterize how the surface width grows with the length scale l and the time t applications of dynamic scaling to a number of surface growth models are discussed the results of a large scale simulation of the ballistic deposition model in three dimensions are presented and compared with recent conjectures the question of universality in interface growth is addressed and a finite temperature generalization of the restricted solid on solid model is studied this model appears to undergo a phase transition from the usual rough phase at high temperatures to a new phase at low temperatures numerical solutions of the generalized langevin equation indicate that there is no phase transition in 2 1 dimensions thus the relation between the continuum equation and the discrete models is still an open question

surface structure of random aggregates on the cayley tree growth through ballistic aggregation and biased diffusion limited aggregation is investigated on the cayley tree for a general branching ratio it is shown that the surface width of a ballistic aggregate remains finite of order one as the cluster mass goes to infinity dla with an attractive bias is treated approximately for non zero bias strength the surface width is asymptotically finite in the limit of isotropic diffusion zero bias a roughening transition occurs which can be described in terms of a single diverging length scale

the surface statistics of a granular aggregate the problem of the surface fluctuations in a settled granular material is posed a simple model is given which describes the process by which a particle settles and comes to rest on the existing surface of the packing and from this a set of langevin equations for the fourier modes of the surface are derived these equations imply that the fourier amplitudes behave like the velocities of a set of independent brownian particles we show that this results in logarithmically divergent surface fluctuations if the flux of particles onto the surface is random the divergence being removed by a more accurate description of the settling material for example by having the granules fall through a sieve

surface structure and anisotropy of eden clusters the simple eden model is simulated with clusters which are orders of magnitude larger than those of some previous work the surface perimeter is slightly anisotropic and feels the underlying structure of the square lattice even for 17 million cluster sites the width of the surface layer increases with increasing cluster mass with an effective exponent presumably larger than 1 4 for averages over the whole circumference and perhaps equal to 1 4 for flat surfaces width averages over a small angle are compared with the recent prediction of plischke and racz 1985 even 17 million sites are not enough to see directly the asymptotic behaviour

exponential asymptotics of localised patterns and snaking bifurcation diagrams abstract localised patterns emerging from a subcritical modulation instability are analysed by carrying the multiple scales analysis beyond all orders the model studied is the swift hohenberg equation of nonlinear optics which is equivalent to the classical swift hohenberg equation with a quadratic and a cubic nonlinearity applying the asymptotic technique away from the maxwell point first it is shown how exponentially small terms determine the phase of the fast spatial oscillation with respect to their slow sech type amplitude in the vicinity of the maxwell point the beyond all orders calculation yields the pinning range of parameters where stable stationary fronts connect the homogeneous and periodic states the full bifurcation diagram for localised patterns is then computed analytically including snake and ladder bifurcation curves this last step requires the matching of the periodic oscillation in the middle of a localised pattern both with an up and a down front to this end a third super slow spatial scale needs to be introduced in which fronts appear as boundary layers in addition the location of the maxwell point and the oscillation wave number of localised patterns are required to fourth order accuracy in the oscillation amplitude