global solvability and boundedness to a coupled chemotaxis fluid model with arbitrary porous medium diffusion abstract in this paper we deal with the following coupled chemotaxis fluid model n t u n n m n 1 n c n n 2 c t u c c c n u t u n u 0 in a bounded domain r 3 with zero flux boundary for n c and no slip boundary for u it is shown that for any large initial datum for any m 0 0 the problem admits a global weak solution which is uniformly bounded on the basis of this the stability of the steady states also be discussed the study of this paper improve the results in 15 in which the global existence and boundedness of weak solutions are established for m 1 3 6 5 m

weighted minimum and maximun operations in fuzzy sets theory abstract this short note comments on the interpretation of weighted minimum and maximum operations introduced in a previous paper as medians and corrects a misleading statement about it

global boundedness of classical solutions to a two species cancer invasion haptotaxis model with tissue remodeling abstract in this paper we deal with a haptotaxis cancer invasion model describing the migration and proliferation of two families of cancer cells the epithelial mesenchymal transition between two families cancer cells the dynamics of matrix degrading enzymes and the evolution and re modeling of the extracellular matrix under appropriate regularity assumptions on initial data by making some a priori estimates and applying iterative techniques we establish the global existence and uniform boundedness of the unique classical solution in two dimensional spatial domain for arbitrary cancer cells proliferation rates and in three dimensional spatial setting for large cancer cells proliferation rates these results improve and extend previously known ones

temporal constraint networks abstract this paper extends network based methods of constraint satisfaction to include continuous variables thus providing a framework for processing temporal constraints in this framework called temporal constraint satisfaction problem tcsp variables represent time points and temporal information is represented by a set of unary and binary constraints each specifying a set of permitted intervals the unique feature of this framework lies in permitting the processing of metric information namely assessments of time differences between events we present algorithms for performing the following reasoning tasks finding all feasible times that a given event can occur finding all possible relationships between two given events and generating one or more scenarios consistent with the information provided we distinguish between simple temporal problems stps and general temporal problems the former admitting at most one interval constraint on any pair of time points we show that the stp which subsumes the major part of vilain and kautz s point algebra can be solved in polynomial time for general tcsps we present a decomposition scheme that performs the three reasoning tasks considered and introduce a variety of techniques for improving its efficiency we also study the applicability of path consistency algorithms as preprocessing of temporal problems demonstrate their termination and bound their complexities

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

temporal scenario modelling and recognition based on possibilistic logic we propose in this paper a new approach for the modelling and recognition of temporal scenarios a scenario is represented by three different structures the first one models the logical dependency between the elements of the scenario using possibilistic logic while the second one is the minimal temporal graph representing all temporal constraints between the events the third structure explains the way the matching between observations and scenarios has to be done the consistency between the three structures is ensured

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

a mixed effects regression model for longitudinal multivariate ordinal data summary a mixed effects item response theory model that allows for three level multivariate ordinal outcomes and accommodates multiple random subject effects is proposed for analysis of multivariate ordinal outcomes in longitudinal studies this model allows for the estimation of different item factor loadings item discrimination parameters for the multiple outcomes the covariates in the model do not have to follow the proportional odds assumption and can be at any level assuming either a probit or logistic response function maximum marginal likelihood estimation is proposed utilizing multidimensional gauss hermite quadrature for integration of the random effects an iterative fisher scoring solution which provides standard errors for all model parameters is used an analysis of a longitudinal substance use data set where four items of substance use behavior cigarette use alcohol use marijuana use and getting drunk or high are repeatedly measured over time is used to illustrate application of the proposed model

energy type estimates and global solvability in a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant this paper deals with the coupled chemotaxis haptotaxis model ut u u v u w u 1 u w x t 0 0 v u v x t 0 wt vw w 1 w u x t 0 which was initially proposed by chaplain and lolas 2006 10 to describe the interactions between cancer cells the matrix degrading enzyme and the host tissue in a process of cancer cell invasion of tissue extracellular matrix here r2 is a bounded domain with smooth boundary and and are positive parameters as compared to previous mathematical studies the novelty here consists of allowing for positive values of reflecting processes of self remodeling of the extracellular matrix under zero flux boundary conditions it is shown that for any sufficiently smooth initial data u0 w0 satisfying first order compatibility conditions the model admits a unique global smooth solution a crucial ingredient in the proof is an energy like inequality which given t 0 yields boundedness of u t in llogl this serves as a starting point for a bootstrap argument used to derive higher regularity estimates sufficient for global extensibility of solutions

the asymptotic posterior normality of the latent trait in an irt model it has long been part of the item response theory irt folklore that under the usual empirical bayes unidimensional irt modeling approach the posterior distribution of examinee ability given test response is approximately normal for a long test under very general and nonrestrictive nonparametric assumptions we make this claim rigorous for a broad class of latent models

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

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

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

the small convection limit in a two dimensional chemotaxis navier stokes system this paper deals with an initial boundary value problem for the chemotaxis navier stokes system begin aligned left begin array lcll n t u cdot nabla n delta n nabla cdot n nabla c qquad quad x in omega t 0 c t u cdot nabla c delta c nc qquad quad x in omega t 0 u t kappa u cdot nabla u delta u nabla p n nabla phi qquad quad x in omega t 0 nabla cdot u 0 qquad quad x in omega t 0 end array right end aligned in a bounded convex domain omega subset mathbb r 2 with smooth boundary with kappa in mathbb r and a given smooth potential phi omega rightarrow mathbb r it is known that for each kappa in mathbb r and all sufficiently smooth initial data this problem possesses a unique global classical solution n kappa c kappa u kappa the present work asserts that these solutions stabilize to n 0 c 0 u 0 uniformly with respect to the time variable more precisely it is shown that there exist mu 0 and c 0 such that whenever kappa in 1 1 begin aligned big vert n kappa cdot t n 0 cdot t big vert l infty omega big vert c kappa cdot t c 0 cdot t big vert l infty omega quad big vert u kappa cdot t u 0 cdot t big vert l infty omega le c kappa e mu t end aligned for all t 0 this result thereby provides an example for a rigorous quantification of stability properties in the stokes limit process as frequently considered in the literature on chemotaxis fluid systems in application contexts involving low reynolds numbers

boundedness in a keller segel system with external signal production abstract we study the neumann initial boundary problem for the chemotaxis system u t u u v x t 0 v t v v u f x t x t 0 u v 0 x t 0 u x 0 u 0 x v x 0 v 0 x x in a smooth bounded domain r n with n 2 and f l 0 l n 2 0 c 0 with some 0 and 0 0 1 first we prove local existence of classical solutions for reasonably regular initial values afterwards we show that in the case of n 2 and f being constant in time requiring the nonnegative initial data u 0 to fulfill the property u 0 d x 4 ensures that the solution is global and remains bounded uniformly in time thereby we extend the well known critical mass result by nagai senba and yoshida for the classical keller segel model coinciding with f 0 in the system above to the case f 0 under certain smallness conditions imposed on the initial data and f we furthermore show that for more general space dimension n 2 and f not necessarily constant in time the solutions are also global and remain bounded uniformly in time accordingly we extend a known result given by winkler for the classical keller segel system to the present situation

the partial credit model and null categories a category where the frequency of responses is zero either for sampling or structural reasons will be called anull category one approach for ordered polytomous item response models is to downcode the categories i e reduce the score of each category above the null category by one thus altering the relationship between the substantive framework and the scoring scheme for items with null categories it is discussed why this is often not a good idea and a method for avoiding the problem is described for the partial credit model while maintaining the integrity of the original response framework this solution is based on a simple reexpression of the basic parameters of the model

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

global solutions and asymptotic behavior for a parabolic degenerate coupled system arising from biology abstract in this paper we will focus on a parabolic degenerate system with respect to unknown functions u and w on a bounded domain of the two dimensional euclidean space this system appears as a mathematical model for some biological processes global existence and uniqueness of a nonnegative classical holder continuous solution are proved the last part of the paper is devoted to the study of the asymptotic behavior of the solutions

an extension of the rating scale model with an application to the measurement of change the polytomous unidimensional rasch model with equidistant scoring also known as the rating scale model is extended in such a way that the item parameters are linearly decomposed into certain basic parameters the extended model is denoted as the linear rating scale model lrsm a conditional maximum likelihood estimation procedure and a likelihood ratio test of hypotheses within the framework of the lrsm are presented since the lrsm is a generalization of both the dichotomous rasch model and the rating scale model the present algorithm is suited for conditional maximum likelihood estimation in these submodels as well the practicality of the conditional method is demonstrated by means of a dichotomous rasch example with 100 items of a rating scale example with 30 items and 5 categories and in the light of an empirical application to the measurement of treatment effects in a clinical study

the asymptotic posterior normality of the latent trait for polytomous irt models chang and stout 1993 presented a derivation of the asymptotic posterior normality of the latent trait given examinee responses under nonrestrictive nonparametric assumptions for dichotomous irt models this paper presents an extention of their results to polytomous irt models in a fairly straightforward manner in addition a global information function is defined and the relationship between the global information function and the currently used information functions is discussed an information index that combines both the global and local information is proposed for adaptive testing applications

boundedness of solutions to a quasilinear chemotaxis haptotaxis model we study global solutions of a class of chemotaxis haptotaxis systems generalizing the prototype u t u 1 m 1 u u u 1 q 1 v u u 1 p 1 w h u w 0 v v u w t v w in a bounded domain r n n 1 with smooth boundary h u w u 1 u r 1 w with parameters m 1 r 1 and positive constants p q it is shown that either max q 1 p 2 p m max m 2 n r or max q 1 p 2 p m r and b 0 is large enough then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded the results of this paper improve the results of tao and winkler 2014 46 51

global existence of a two dimensional chemotaxis haptotaxis model with remodeling of non diffusible attractant abstract this paper deals with the cancer invasion model u t u u v u w u 1 u w x t 0 v t v v u x t 0 w t v w w 1 w u x t 0 in a bounded smooth domain r 2 with zero flux boundary conditions where and are positive parameters compared to previous mathematical studies the novelty here lies in first our treatment of the full parabolic chemotaxis haptotaxis system and second allowing for positive values of reflecting processes with self remodeling of the extracellular matrix under appropriate regularity assumptions on the initial data u 0 v 0 w 0 by using adapted l p estimate techniques we prove the global existence and uniqueness of classical solutions when is sufficiently large i e in the high cell proliferation rate regime

analysis of multiple partially ordered responses to belief items with don t know option understanding beliefs values and preferences of patients is a tenet of contemporary health sciences this application was motivated by the analysis of multiple partially ordered set poset responses from an inventory on layman beliefs about diabetes the partially ordered set arises because of two features in the data first the response options contain a don t know dk option and second there were two consecutive occasions of measurement as predicted by the common sense model of illness beliefs about diabetes were not necessarily stable across the two measurement occasions instead of analyzing the two occasions separately we studied the joint responses across the occasions as a poset response few analytic methods exist for data structures other than ordered or nominal categories poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data leading to the loss of nuanced information that might be present within poset categories in this paper we developed a general class of item response models for analyzing the poset data collected from the common sense model of diabetes inventory the inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model to apply an item response model to the poset diabetes inventory we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard irt software could be directly used for the purpose of item estimation and individual scoring simulation experiments were used to examine parameter recovery for the proposed poset model

an analysis of item response theory and rasch models based on the most probable distribution method the most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system the item response theory logistic models with a particular focus on the one parameter logistic model or rasch model and their properties and assumptions are discussed for both infinite and finite populations

kullback leibler information and its applications in multi dimensional adaptive testing this paper first discusses the relationship between kullback leibler information kl and fisher information in the context of multi dimensional item response theory and is further interpreted for the two dimensional case from a geometric perspective this explication should allow for a better understanding of the various item selection methods in multi dimensional adaptive tests mat which are based on these two information measures the kl information index ki method is then discussed and two theorems are derived to quantify the relationship between ki and item parameters due to the fact that most of the existing item selection algorithms for mat bear severe computational complexity which substantially lowers the applicability of mat two versions of simplified kl index ski built from the analytical results are proposed to mimic the behavior of ki while reducing the overall computational intensity

a repetitive branch and bound procedure for minimum within cluster sums of squares partitioning minimization of the within cluster sums of squares wcss is one of the most important optimization criteria in cluster analysis although cluster analysis modules in commercial software packages typically use heuristic methods for this criterion optimal approaches can be computationally feasible for problems of modest size this paper presents a new branch and bound algorithm for minimizing wcss algorithmic enhancements include an effective reordering of objects and a repetitive solution approach that precludes the need for splitting the data set while maintaining strong bounds throughout the solution process the new algorithm provided optimal solutions for problems with up to 240 objects and eight well separated clusters poorly separated problems with no inherent cluster structure were optimally solved for up to 60 objects and six clusters the repetitive branch and bound algorithm was also successfully applied to three empirical data sets from the classification literature

log multiplicative association models as item response models log multiplicative association lma models which are special cases of log linear models have interpretations in terms of latent continuous variables two theoretical derivations of lma models based on item response theory irt arguments are presented first we show that anderson and colleagues anderson vermunt 2000 anderson bockenholt 2000 anderson 2002 who derived lma models from statistical graphical models made the equivalent assumptions as holland 1990 when deriving models for the manifest probabilities of response patterns based on an irt approach we also present a second derivation of lma models where item response functions are specified as functions of rest scores these various connections provide insights into the behavior of lma models as item response models and point out philosophical issues with the use of lma models as item response models we show that even for short tests lma and standard irt models yield very similar to nearly identical results when data arise from standard irt models log multiplicative association models can be used as item response models and do not require numerical integration for estimation

a critical virus production rate for blow up suppression in a haptotaxis model for oncolytic virotherapy abstract in a two dimensional smoothly bounded domain we consider the oncolytic virotherapy model given by u t u u v u z v t u w v w t d w w w u z z t d z z z u z w with parameters d w 0 d z 0 0 and 0 according to previous findings a corresponding neumann initial boundary value problem possesses a globally defined classical solution whenever the prescribed initial data are suitably regular and satisfy appropriate positivity assumptions in the present study it is shown that if 1 then any such solution is uniformly bounded this complements a recent result which in the case 0 has asserted the existence of unbounded solutions whenever 1

an extension of the partial credit model with an application to the measurement of change the partial credit model is considered under the assumption of a certain linear decomposition of the item category parameters ih into basic parameters j this model is referred to as the linear partial credit model a conditional maximum likelihood algorithm for estimation of the j is presented based on a recurrences for the combinatorial functions involved and b using a quasi newton approach the so called broyden fletcher goldfarb shanno bfgs method a guarantees numerically stable results b avoids the direct computation of the hesse matrix yet produces a sequence of certain positive definite matricesb k k 1 2 converging to the asymptotic variance covariance matrix of the hat alpha j the practicality of these numerical methods is demonstrated both by means of simulations and of an empirical application to the measurement of treatment effects in patients with psychosomatic disorders

characterizing the manifest probability distributions of three latent trait models for accuracy and response time in this paper we study the statistical relations between three latent trait models for accuracies and response times the hierarchical model hm of van der linden psychometrika 72 3 287 308 2007 the signed residual time model sm proposed by maris and van der maas psychometrika 77 4 615 633 2012 and the drift diffusion model dm as proposed by tuerlinckx and de boeck psychometrika 70 4 629 650 2005 one important distinction between these models is that the hm and the dm either assume or imply that accuracies and response times are independent given the latent trait variables while the sm does not in this paper we investigate the impact of this conditional independence property or a lack thereof on the manifest probability distribution for accuracies and response times we will find that the manifest distributions of the latent trait models share several important features such as the dependency between accuracy and response time but we also find important differences such as in what function of response time is being modeled our method for characterizing the manifest probability distributions is related to the dutch identity holland in psychometrika 55 6 5 18 1990

sub logistic source can prevent blow up in the 2d minimal keller segel chemotaxis system it is well known that the neumann initial boundary value problem for the minimal keller segel chemotaxis system in a 2d bounded smooth domain has no blow ups for any presence of logistic source of cell kinetics here for a large class of cell kinetics including sub logistic sources we find an explicit condition involving the chemotactic strength the asymptotic damping rate and the initial mass of cells to ensure the uniform in time boundedness for the corresponding 2d neumann initial boundary value problem our finding in particular shows that sub logistic source can prevent blow up in 2d indicating that logistic damping is not the weakest damping to guarantee boundedness for the 2d keller segel minimal chemotaxis model

stability of solutions of chemotaxis equations in reinforced random walks in this paper we consider a nonlinear system of differential equations consisting of one parabolic equation and one ordinary differential equation the system arises in chemotaxis a process whereby living organisms respond to chemical substance by moving toward higher or lower concentrations of the chemical substance or by aggregating or dispersing we prove that stationary solutions of the system are asymptotically stable

a person fit test for irt models for polytomous items a person fit test based on the lagrange multiplier test is presented for three item response theory models for polytomous items the generalized partial credit model the sequential model and the graded response model the test can also be used in the framework of multidimensional ability parameters it is shown that the lagrange multiplier statistic can take both the effects of estimation of the item parameters and the estimation of the person parameters into account the lagrange multiplier statistic has an asymptotic 2 distribution the type i error rate and power are investigated using simulation studies results show that test statistics that ignore the effects of estimation of the persons ability parameters have decreased type i error rates and power incorporating a correction to account for the effects of the estimation of the persons ability parameters results in acceptable type i error rates and power characteristics incorporating a correction for the estimation of the item parameters has very little additional effect it is investigated to what extent the three models give comparable results both in the simulation studies and in an example using data from the neo personality inventory revised

global boundedness in a three dimensional chemotaxis haptotaxis model abstract this paper studies the chemotaxis haptotaxis model of cancer invasion u t u u v u w u 1 u w x t 0 v t v v u x t 0 w t v w x t 0 in a bounded smooth domain r 3 with zero flux boundary conditions where the parameters and are positive it is shown that the corresponding initial boundary problem possesses a unique classical solution which is global in time and bounded under the explicit condition 11 2 2 w 0 l 2 2 37 2 4 2 w 0 l 2 and suitable regularity assumptions on the initial data u 0 v 0 w 0

abstract lp estimates for the cauchy problem with applications to the navier stokes equations in exterior domains abstract we apply an abstract perturbation theorem to derive global in time lq estimates for the cauchy problem and lq ls estimates for the nonstationary stokes equations in exterior domains this will be applied to obtain various new global in time estimates for weak solutions of the navier stokes equations

large time behavior of solution to a fully parabolic chemotaxis haptotaxis model in higher dimensions abstract this paper deals with the chemotaxis haptotaxis model of cancer invasion u t u u v u w u 1 u w x t 0 v t v v u x t 0 w t v w x t 0 in a bounded smooth domain r n with zero flux boundary conditions where and are positive parameters it is shown that if is suitably large then for all sufficiently smooth initial data the associated initial boundary value problem possesses a unique global in time classical solution that is bounded in 0 and if the initial data w 0 is small w becomes asymptotically negligible moreover we prove that when domain is convex 1 1 0 is globally asymptotically stable provided that u 0 0 and thereby extends the result of hillen et al 2013 18 to the higher space dimensions

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

measuring growth in a longitudinal large scale assessment with a general latent variable model the aim of the research presented here is the use of extensions of longitudinal item response theory irt models in the analysis and comparison of group specific growth in large scale assessments of educational outcomes a general discrete latent variable model was used to specify and compare two types of multidimensional item response theory mirt models for longitudinal data a a model that handles repeated measurements as multiple correlated variables over time and b a model that assumes one common variable over time and additional variables that quantify the change using extensions of these mirt models we approach the issue of modeling and comparing group specific growth in observed and unobserved subpopulations the analyses presented in this paper aim at answering the question whether academic growth is homogeneous across types of schools defined by academic demands and curricular differences in order to facilitate answering this research question a a model with a single two dimensional ability distribution was compared to b a model assuming multiple populations with potentially different two dimensional ability distributions based on type of school and to c a model that assumes that the observations are sampled from a discrete mixture of unobserved populations allowing for differences across schools with respect to mixing proportions for this purpose we specified a hierarchical mixture distribution variant of the two mirt models the latter model c is a growth mixture mirt model that allows for variation of the mixing proportions across clusters in a hierarchically organized sample we applied the proposed models to the pisa i plus data for assessing learning and change across multiple subpopulations the results of this study support the hypothesis of differential growth

polytomous latent scales for the investigation of the ordering of items we propose three latent scales within the framework of nonparametric item response theory for polytomously scored items latent scales are models that imply an invariant item ordering meaning that the order of the items is the same for each measurement value on the latent scale this ordering property may be important in for example intelligence testing and person fit analysis we derive observable properties of the three latent scales that can each be used to investigate in real data whether the particular model adequately describes the data we also propose a methodology for analyzing test data in an effort to find support for a latent scale and we use two real data examples to illustrate the practical use of this methodology

on the sampling theory roundations of item response theory models item response theory it models are now in common use for the analysis of dichotomous item responses this paper examines the sampling theory foundations for statistical inference in these models the discussion includes some history on the stochastic subject versus the random sampling interpretations of the probability in irt models the relationship between three versions of maximum likelihood estimation for irt models estimating versus estimating predictors irt models and loglinear models the identifiability of irt models and the role of robustness and bayesian statistics from the sampling theory perspective

towards a general theory of action and time abstract a formalism for reasoning about actions is proposed that is based on a temporal logic it allows a much wider range of actions to be described than with previous approaches such as the situation calculus this formalism is then used to characterize the different types of events processes actions and properties that can be described in simple english sentences in addressing this problem we consider actions that involve non activity as well as actions that can only be defined in terms of the beliefs and intentions of the actors finally a framework for planning in a dynamic world with external events and multiple agents is suggested

multicategorical spline model for item response theory additional information contained in incorrect responses calls for a multicategorical rather than a binary analysis of multiple choice data a nonparametric divided by total model for joint maximum likelihood estimation of probability of choice functions for particular responses and of latent ability is proposed the model approximates probability functions by rational splines some illustrative examples of real test data analysis and the results of a monte carlo study are presented

dampening effect of logistic source in a two dimensional haptotaxis system with nonlinear zero order interaction abstract this paper deals with the oncolytic virotherapy model u t u u v u z u 1 u v t u w v w t d w w w u z z t d z z z u z w in a bounded domain r 2 with smooth boundary where d w d z and are prescribed positive parameters for any given suitably regular initial data the global existence of classical solution to the corresponding homogeneous neumann initial boundary problem for a more general model allowing 0 was previously verified in y tao m winkler j differential equations 268 2020 4973 4997 this work further shows that whenever 0 the above mentioned global classical solution to is uniformly bounded and moreover if 1 then the solution u v w z stabilizes to the constant equilibrium 1 0 0 0 in the topology l p l 3 with any p 1 in a large time limit

what can we learn from plausible values in this paper we show that the marginal distribution of plausible values is a consistent estimator of the true latent variable distribution and furthermore that convergence is monotone in an embedding in which the number of items tends to infinity we use this result to clarify some of the misconceptions that exist about plausible values and also show how they can be used in the analyses of educational surveys

latent trait models and dichotomization of graded responses this paper discusses thecompatibility of the polychotomous rasch model with dichotomization of the response continuum it is argued that in the case of graded responses the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement because of this arbitrariness the measurement outcome should be independent of the specific polychotomization applied for example presenting a specific multicategory response format should not affect the measurement outcome when such is the case the original polychotomous model is called compatible with dichotomization

stochastic ordering of the latent trait by the sum score under various polytomous irt models the sum score is often used to order respondents on the latent trait measured by the test therefore it is desirable that under the chosen model the sum score stochastically orders the latent trait it is known that unlike dichotomous item response theory irt models most polytomous irt models do not imply stochastic ordering it is unknown however 1 whether stochastic ordering is often or rarely violated and 2 whether violations yield a serious problem for practical data analysis these are the central issues of this paper first some unanswered questions that pertain to polytomous irt models implying stochastic ordering were investigated second simulation studies were conducted to evaluate stochastic ordering in practical situations it was found that for most polytomous irt models that do not imply stochastic ordering the sum score can be used safely to order respondents on the latent trait

em algorithm estimation of a structural equation model for the longitudinal study of the quality of life health related quality of life hrqol data are measured via patient questionnaires completed by the patients themselves at different time points we focused on oncology data gathered through the use of european organization for research and treatment of cancer questionnaires which decompose hrqol into several functional dimensions several symptomatic dimensions and the global health status ghs we aimed to perform a global analysis of hrqol and reduce the number of analyses required by using a two step approach first a structural equation model sem was used for each time point in these models the ghs is explained by two latent variables each latent variable is a factor that summarizes respectively the functional dimensions and the symptomatic dimensions to the global measurement this is achieved through the maximization of the likelihood of each sem using the em algorithm which has the advantage of giving an estimation of the subject specific factors and the influence of additional explanatory variables then to consider the longitudinal aspect the ghs variable and the two factors were concatenated for each patient visit at which the questionnaire was completed the ghs and the two factors estimated in the first step can then be explained by additional explanatory variables using a linear mixed model

blow up prevention by logistic sources in a parabolic elliptic keller segel system with singular sensitivity abstract this paper is concerned with the parabolic elliptic keller segel system with singular sensitivity and logistic source u t u u v v r u u 2 x t 0 0 v v u x t 0 under homogeneous neumann boundary conditions in a smoothly bounded domain r 2 where 0 r r 0 with nonnegative initial data 0 u 0 c 0 it is shown that in this two dimensional setting the absorptive character of the logistic kinetics is sufficient to enforce global existence of classical solutions even for arbitrarily large 0 and any 0 and r r it is moreover shown that if in addition r 0 is sufficiently large then all these solutions are uniformly bounded a main step in the derivation of these results consists of establishing appropriate positive a priori bounds from below for the mass functional u which due to the presence of logistic kinetics is not preserved these in turn provide pointwise lower bounds for v which then allow for the choice of p 1 explicitly depending inter alia on inf v such that u p x t d x can be suitably bounded from above

global classical solutions and convergence to a mathematical model for cancer cells invasion and metastatic spread abstract in this paper we consider the following system u t u u v t d v v v m t d m m u m t 1 u m in two dimensional space with zero flux boundary conditions this model was proposed by franssen et al 7 to characterize the invasion and metastatic spread of cancer cells we first establish the global existence of uniformly bounded global strong solutions then using the decay of ecm and the positivity of mde we further improve the regularity of obtained solutions and achieve the uniform boundedness of solutions in the classical sense subsequently we also prove the uniqueness of solutions after that we turn our attention to the large time behavior of solutions and show that the global classical solution strongly converges to a semi trivial steady state in the large time limit

a rasch model for continuous ratings a unidimensional latent trait model for continuous ratings is developed this model is an extension of andrich s rating formulation which assumes that the response process at latent thresholds is governed by the dichotomous rasch model item characteristic functions and information functions are used to illustrate that the model takes ceiling and floor effects into account both the dichotomous rasch model and a linear model with normally distributed error can be derived as limiting cases the separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined