cauchy problems of semilinear pseudo parabolic equations abstract this paper concerns with the cauchy problems of semilinear pseudo parabolic equations after establishing the necessary existence uniqueness and comparison principle for mild solutions which are also classical ones provided that the initial data are appropriately smooth we investigate large time behavior of solutions it is shown that there still exist the critical global existence exponent and the critical fujita exponent for pseudo parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations

a new skewed link model for dichotomous quantal response data abstract the logit probit and student t links are widely used in modeling dichotomous quantal response data most of the commonly used link functions are symmetric except the complementary log log link however in some applications the overall fit can be significantly improved by the use of an asymmetric link in this article we propose a new skewed link model for analyzing binary response data with covariates introducing a skewed distribution for the underlying latent variable we develop a class of asymmetric link models for binary response data using a bayesian approach we first characterize the propriety of the posterior distributions using standard improper priors we further propose informative priors using historical data from a similar previous study we examine the proposed method through a large scale simulation study and use data from a prostate cancer study to demonstrate the use of historical data in bayesian model fitting and comparison of skewed link models

modelling conditional dependence between response time and accuracy the assumption of conditional independence between response time and accuracy given speed and ability is commonly made in response time modelling however this assumption might be violated in some cases meaning that the relationship between the response time and the response accuracy of the same item cannot be fully explained by the correlation between the overall speed and ability we propose to explicitly model the residual dependence between time and accuracy by incorporating the effects of the residual response time on the intercept and the slope parameter of the irt model for response accuracy we present an empirical example of a violation of conditional independence from a low stakes educational test and show that our new model reveals interesting phenomena about the dependence of the item properties on whether the response is relatively fast or slow for more difficult items responding slowly is associated with a higher probability of a correct response whereas for the easier items responding slower is associated with a lower probability of a correct response moreover for many of the items slower responses were less informative for the ability because their discrimination parameters decrease with residual response time

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

a latent variable model for discrete multivariate psychometric waiting times a version of the discrete proportional hazards model is developed for psychometrical applications in such applications a primary covariate that influences failure times is a latent variable representing a psychological construct the metropolis hastings algorithm is studied as a method for performing marginal likelihood inference on the item parameters the model is illustrated with a real data example that relates the age at which teenagers first experience various substances to the latent ability to avoid the onset of such behaviors

the global existence and time decay for the solutions of the fractional pseudo parabolic equation abstract we consider the cauchy problem of fractional pseudo parabolic equation on the whole space r n n 1 here the fractional order is related to the diffusion type source term behaving as the usual diffusion term on the high frequency part it has a feature of regularity gain and regularity loss for 1 and 0 1 respectively we establish the global existence and time decay rates for small amplitude solutions to the cauchy problem for 0 in the case that 0 1 we introduce the time weighted energy method to overcome the weakly dissipative property of the equation

numerical simulations of solutions of a two level averaged navier stokes system abstract an averaging procedure for the navier stokes equations has been proposed in an earlier article i moise r m temam renormalization group method application to navier stokes equation discrete contin dyn syst 6 1 2000 191 210 this averaging procedure is based on a two level decomposition of the solution into low and high frequencies the aim of the present article is to investigate with the help of numerical simulations the behavior of the small scales of the corresponding system space periodic solutions with a non resonant period are considered the time evolution of the averaged and standard non averaged small scales are compared at different reynolds numbers and for different values of the cut off level used to separate large and small scales of the flow variables the numerical results illustrate the efficiency of the proposed averaging procedure for the navier stokes equations the averaged small scales provide an accurate prediction of the time averaged small scales of the navier stokes solutions as the computational cost is reduced for the averaged equations long time integrations on more than 50 eddy turnover times have been performed for cut off levels ensuring a proper resolution of the large scales in these cases development of instabilities in the averaged small scale equation is observed

asymptotic robustness study of the polychoric correlation estimation asymptotic robustness against misspecification of the underlying distribution for the polychoric correlation estimation is studied the asymptotic normality of the pseudo maximum likelihood estimator is derived using the two step estimation procedure the t distribution assumption and the skew normal distribution assumption are used as alternatives to the normal distribution assumption in a numerical study the numerical results show that the underlying normal distribution can be substantially biased even though skewness and kurtosis are not large the skew normal assumption generally produces a lower bias than the normal assumption thus it is worth using a non normal distributional assumption if the normal assumption is dubious

a hierarchical bayesian statistical framework for response time distributions this paper provides a statistical framework for estimating higher order characteristics of the response time distribution such as the scale variability and shape consideration of these higher order characteristics often provides for more rigorous theory development in cognitive and perceptual psychology e g luce 1986 rt distribution for a single participant depends on certain participant characteristics which in turn can be thought of as arising from a distribution of latent variables the present work focuses on the three parameter weibull distribution with parameters for shape scale and shift initial value bayesian estimation in a hierarchical framework is conceptually straightforward parameter estimates both for participant quantities and population parameters are obtained through markov chain monte carlo methods the methods are illustrated with an application to response time data in an absolute identification task the behavior of the bayes estimates are compared to maximum likelihood ml estimates through monte carlo simulations for small sample size there is an occasional tendency for the ml estimates to be unreasonably extreme in contrast by borrowing strength across participants bayes estimation shrinks extreme estimates the results are that the bayes estimators are more accurate than the corresponding ml estimators

efficient nonparametric approaches for estimating the operating characteristics of discrete item responses rationale and the actual procedures of two nonparametric approaches called bivariate p d f approach and conditional p d f approach for estimating the operating characteristic of a discrete item response or the conditional probability given latent trait that the examinee s response be that specific response are introduced and discussed these methods are featured by the facts that a estimation is made without assuming any mathematical forms and b it is based upon a relatively small sample of several hundred to a few thousand examinees

expanding the rasch model to a general model having more than one dimension the well known rasch model is generalized to a multicomponent model so that observations of component events are not needed to apply the model it is shown that the generalized model has retained the property of the specific objectivity of the rasch model for a restricted variant of the model maximum likelihood estimates of its parameters and a statistical test of the model are given the results of an application to a mathematics test involving six components are described

on latent trait estimation in multidimensional compensatory item response models making inferences from irt based test scores requires accurate and reliable methods of person parameter estimation given an already calibrated set of item parameters the latent trait could be estimated either via maximum likelihood estimation mle or using bayesian methods such as maximum a posteriori map estimation or expected a posteriori eap estimation in addition warm s psychometrika 54 427 450 1989 weighted likelihood estimation method was proposed to reduce the bias of the latent trait estimate in unidimensional models in this paper we extend the weighted mle method to multidimensional models this new method denoted as multivariate weighted mle mwle is proposed to reduce the bias of the mle even for short tests mwle is compared to alternative estimators i e mle map and eap and shown both analytically and through simulations studies to be more accurate in terms of bias than mle while maintaining a similar variance in contrast bayesian estimators i e map and eap result in biased estimates with smaller variability

the generalized logit linear item response model for binary designed items this paper introduces the generalized logit linear item response model gllirm which represents the item solving process as a series of dichotomous operations or steps the gllirm assumes that the probability function of the item response is a logistic function of a linear composite of basic parameters which describe the operations and the coefficients depend on three design matrices x y and z the gllirm provides a tool for testing hypotheses on the item solving process and generalizes existing models an empirical application is included in which the model is applied to evaluate sources of difficulty and pairwise item interactions in a logical analysis test

asymmetric item characteristic curves and item complexity insights from simulation and real data analyses while item complexity is often considered as an item feature in test development it is much less frequently attended to in the psychometric modeling of test items prior work suggests that item complexity may manifest through asymmetry in item characteristics curves iccs samejima in psychometrika 65 319 335 2000 in the current paper we study the potential for asymmetric irt models to inform empirically about underlying item complexity and thus the potential value of asymmetric models as tools for item validation both simulation and real data studies are presented some psychometric consequences of ignoring asymmetry as well as potential strategies for more effective estimation of asymmetry are considered in discussion

easy bayes estimation for rasch type models a bayes estimation procedure is introduced that allows the nature and strength of prior beliefs to be easily specified and modal posterior estimates to be obtained as easily as maximum likelihood estimates the procedure is based on constructing posterior distributions that are formally identical to likelihoods but are based on sampled data as well as artificial data reflecting prior information improvements in performance of modal bayes procedures relative to maximum likelihood estimation are illustrated for rasch type models improvements range from modest to dramatic depending on the model and the number of items being considered

graded response model based on the logistic positive exponent family of models for dichotomous responses samejima psychometrika 65 319 335 2000 proposed the logistic positive exponent family of models lpef for dichotomous responses in the unidimensional latent space the objective of the present paper is to propose and discuss a graded response model that is expanded from the lpef in the context of item response theory irt this specific graded response model belongs to the general framework of graded response model samejima psychometrika monograph no 17 1969 and no 18 1972 handbook of modern item response theory springer new york 1997 encyclopedia of social measurement academic press san diego 2004 and in particular to the heterogeneous case samejima psychometrika monograph no 18 1972 thus the model can deal with any number of ordered polytomous responses such as letter grades e g a b c d f etc

the multivariate skew normal distribution summary the paper extends earlier work on the so called skew normal distribution a family of distributions including the normal but with an extra parameter to regulate skewness the present work introduces a multivariate parametric family such that the marginal densities are scalar skew normal and studies its properties with special emphasis on the bivariate case

psychometric modeling of response speed and accuracy with mixed and conditional regression human performance in cognitive testing and experimental psychology is expressed in terms of response speed and accuracy data analysis is often limited to either speed or accuracy and or to crude summary measures like mean response time rt or the percentage correct responses this paper proposes the use of mixed regression for the psychometric modeling of response speed and accuracy in testing and experiments mixed logistic regression of response accuracy extends logistic item response theory modeling to multidimensional models with covariates and interactions mixed linear regression of response time extends mixed anova to unbalanced designs with covariates and heterogeneity of variance related to mixed regression is conditional regression which requires no normality assumption but is limited to unidimensional models mixed and conditional methods are both applied to an experimental study of mental rotation univariate and bivariate analyzes show how within subject correlation between response and rt can be distinguished from between subject correlation and how latent traits can be detected given careful item design or content analysis it is concluded that both response and rt must be recorded in cognitive testing and that mixed regression is a versatile method for analyzing test data

arma covariance structures with time heteroscedasticity for repeated measures experiments abstract rochon and helms 1989 presented a model for analyzing repeated measures experiments the general linear model was used to assess the influence of covariate information and arma time series models were put forward to characterize the covariance matrix among the repeated measures practical experience has suggested however that the arma assumption of constant variances and autocovariances over time is too restrictive for many applications for example observations may be relatively stable toward the beginning of the study but become more variable toward the end this article presents a modification to this structure which provides for heteroscedasticity over time maximum likelihood ml estimation procedures are considered and the estimators are found to enjoy optimal large sample properties a scoring algorithm is described for iterating to a solution of the ml equations the model is illustrated with data from a clinical trial investigating human erythropoietin for treating anemia in end

speed accuracy response models scoring rules based on response time and accuracy starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy and a definite trade off between speed and accuracy a response model is derived since the scoring rule is interpreted as a sufficient statistic the model belongs to the exponential family the various marginal and conditional distributions for response accuracy and response time are derived and it is shown how the model parameters can be estimated the model for response accuracy is found to be the two parameter logistic model it is found that the time limit determines the item discrimination and this effect is illustrated with the amsterdam chess test ii

an item response model with internal restrictions on item difficulty an irt model based on the rasch model is proposed for composite tasks that is tasks that are decomposed into subtasks of different kinds there is one subtask for each component that is discerned in the composite tasks a component is a generic kind of subtask of which the subtasks resulting from the decomposition are specific instantiations with respect to the particular composite tasks under study the proposed model constrains the difficulties of the composite tasks to be linear combinations of the difficulties of the corresponding subtask items which are estimated together with the weights used in the linear combinations one weight for each kind of subtask although the model does not belong to the exponential family its parameters can be estimated using conditional maximum likelihood estimation the approach is demonstrated with an application to spelling tasks

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

on a certain renormalization group method in this paper a mathematical study of the renormalization group method recently introduced by chen goldenfeld and oono phys rev e 54 376 1997 phys rev lett 73 1311 1994 nato adv study inst ser ser b 284 375 1991 is given for the case of autonomous nonlinear systems of differential equations we also observe that the approximation results obtained by this method by chen goldenfeld and ono nato adv study inst ser ser b 284 375 1991 are valid over long time intervals moreover a connection between this method and the classical poincare dulac normal forms and the averaging method is briefly discussed

kolmogorov turbulence in a random force driven burgers equation anomalous scaling and probability density functions high resolution numerical experiments described in this work show that velocity fluctuations governed by the one dimensional burgers equation driven by a white in time random noise with the spectrum ensuremath vert f k mathrm ensuremath vert 2 ifmmode bar else textasciimacron fi ensuremath propto mathit k mathrm ensuremath 1 exhibit a biscaling behavior all moments of velocity differences mathit s mathit n mathrm ensuremath le 3 r ensuremath vert u x r u x mathrm ensuremath vert mathit n ifmmode bar else textasciimacron fi ensuremath equiv ensuremath vert ensuremath delta u mathrm ensuremath vert mathit n ifmmode bar else textasciimacron fi ensuremath propto mathit r mathit n 3 while mathit s mathit n g3 r ensuremath propto mathit r mathit n ensuremath xi with ensuremath xi mathit n ensuremath approxeq 1 for real ng0 chekhlov and yakhot phys rev e 51 r2739 1995 the probability density function which is dominated by coherent shocks in the interval ensuremath delta u0 is scrp ensuremath delta u r ensuremath propto ensuremath delta u mathrm ensuremath mathit q with q ensuremath approxeq 4 a phenomenological theory describing the experimental findings is presented

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

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

power of the likelihood ratio test in covariance structure analysis a procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived the procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified using the noncentral chi square distribution the power of the test is approximated by the asymptotic one for a sequence of local alternatives the procedure is illustrated by an example a monte carlo experiment also shows how good the approximation is for a specific case

degenerate quasilinear pseudoparabolic equations with memory terms and variational inequalities abstract the existence of solutions of degenerate quasilinear pseudoparabolic equations where the term t u is replace by t b u with memory terms and quasilinear variational inequalities is shown the existence of solutions of equations is proved under the assumption that the nonlinear function b is monotone and a gradient of a convex continuously differentiable function the uniqueness is proved for lipschitz continuous elliptic parts the existence of solutions of quasilinear variational inequalities is proved under stronger assumptions namely the nonlinear function defining the elliptic part is assumed to be a gradient and the function b to be lipschitz continuous

psychometric latent response models in this paper some psychometric models will be presented that belong to the larger class oflatent response models lrms first lrms are introduced by means of an application in the field ofcomponential item response theory embretson 1980 1984 second a general definition of lrms not specific for the psychometric subclass is given third some more psychometric lrms and examples of how they can be applied are presented fourth a method for obtaining maximum likelihood ml and some maximum a posteriori map estimates of the parameters of lrms is presented this method is then applied to theconjunctive rasch model fifth and last an application of the conjunctive rasch model is presented this model was applied to responses to typical verbal ability items open synonym items

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

additive and multiplicative models for gamma distributed random variables and their application as psychometric models for response times a class of models for gamma distributed random variables is presented these models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expected value in particular both additive multiplicative and combined additive multiplicative models can be formulated as a special case a class of psychometric models for reaction times is presented together with their psychological interpretation by means of a comparison with existing models this class of models is shown to offer some possibilities that are not available in existing methods parameter estimation by means of maximum likelihood ml is shown to have some attractive properties since the models belong to the exponential family then the results of a simulation study of the bias in the ml estimates are presented finally the application of these models is illustrated by an analysis of the data from a mental rotation experiment this analysis is preceded by an evaluation of the appropriateness of the gamma distribution for these data

statistical applications of the multivariate skew normal distribution azzalini and dalla valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter the first part of the present paper examines further probabilistic properties of the distribution with special emphasis on aspects of statistical relevance inferential and other statistical issues are discussed in the following part with applications to some multivariate statistics problems illustrated by numerical examples finally a further extension is described which introduces a skewing factor of an elliptical density

marginal maximum likelihood estimation of item parameters application of an em algorithm maximum likelihood estimation of item parameters in the marginal distribution integrating over the distribution of ability becomes practical when computing procedures based on an em algorithm are used by characterizing the ability distribution empirically arbitrary assumptions about its form are avoided the em procedure is shown to apply to general item response models lacking simple sufficient statistics for ability this includes models with more than one latent dimension

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

a generalized speed accuracy response model for dichotomous items we propose a generalization of the speed accuracy response model sarm introduced by maris and van der maas psychometrika 77 615 633 2012 in these models the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled our generalization is similar to that of the one parameter logistic or rasch model to the two parameter logistic or birnbaum model in item response theory an expectation maximization em algorithm for estimating model parameters and standard errors was developed furthermore methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score the presented methods were evaluated in a small simulation study the results of which indicated good parameter recovery and reasonable type i error rates for the residuals finally the methods were applied to two real data sets it was found that the two parameter sarm showed improved fit compared to the one parameter sarm in both data sets

loss of information in estimating item parameters in incomplete designs in this paper the efficiency of conditional maximum likelihood cml and marginal maximum likelihood mml estimation of the item parameters of the rasch model in incomplete designs is investigated the use of the concept of f information eggen 2000 is generalized to incomplete testing designs the scaled determinant of the f information matrix is used as a scalar measure of information contained in a set of item parameters in this paper the relation between the normalization of the rasch model and this determinant is clarified it is shown that comparing estimation methods with the defined information efficiency is independent of the chosen normalization the generalization of the method to other models than the rasch model is discussed in examples information comparisons are conducted it is found that for both cml and mml some information is lost in all incomplete designs compared to complete designs a general result is that with increasing test booklet length the efficiency of an incomplete design compared to a complete design is increasing as is the efficiency of cml compared to mml the main difference between cml and mml is seen in the effect of the length of the test booklet it will be demonstrated that with very small booklets there is a substantial loss in information about 35 with cml estimation while this loss is only about 10 in mml estimation however with increasing test length the differences between cml and mml quickly disappear

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

logistic positive exponent family of models virtue of asymmetric item characteristic curves the paper addresses and discusses whether the tradition of accepting point symmetric item characteristic curves is justified by uncovering the inconsistent relationship between the difficulties of items and the order of maximum likelihood estimates of ability this inconsistency is intrinsic in models that provide point symmetric item characteristic curves and in this paper focus is put on the normal ogive model for observation it is also questioned if in the logistic model the sufficient statistic has forfeited the rationale that is appropriate to the psychological reality it is observed that the logistic model can be interpreted as the case in which the inconsistency in ordering the maximum likelihood estimates is degenerated the paper proposes a family of models called the logistic positive exponent family which provides asymmetric item chacteristic curves a model in this family has a consistent principle in ordering the maximum likelihood estimates of ability the family is divided into two subsets each of which has its own principle and includes the logistic model as a transition from one principle to the other rationale and some illustrative examples are given

nonparametric estimation of item and respondent locations from unfolding type items unlike their monotone counterparts nonparametric unfolding response models which assume the item response function is unimodal have seen little attention in the psychometric literature this paper studies the nonparametric behavior of unfolding models by building on the work of post 1992 the paper provides rigorous justification for a class of nonparametric estimators of respondents latent attitudes by proving that the estimators consistently rank order the respondents the paper also suggests an algorithm for the rank ordering of items along the attitudes scale finally the methods are evaluated using simulated data

renormalization group and singular perturbations multiple scales boundary layers and reductive perturbation theory perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis with numerous examples we illustrate its application to ordinary differential equation problems involving multiple scales boundary layers with technically difficult asymptotic matching and wkb analysis in contrast to conventional methods the renormalization group approach requires neither ad hoc assumptions about the structure of perturbation series nor the use of asymptotic matching our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally although the latter can be reproduced if desired by appropriate expansion of the renormalization group approximant we show that the renormalization group equation may be interpreted as an amplitude equation and from this point of view develop reductive perturbation theory for partial differential equations describing spatially extended systems near bifurcation points deriving both amplitude equations and the center manifold s1063651x 96 00506 5

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

on the existence of maximum likelihood estimates in logistic regression models summary the problems of existence uniqueness and location of maximum likelihood estimates in log linear models have received special attention in the literature haberman 1974 chapter 2 wedderburn 1976 silvapulle 1981 for multinomial logistic regression models we prove existence theorems by considering the possible patterns of data points which fall into three mutually exclusive and exhaustive categories complete separation quasicomplete separation and overlap our results suggest general rules for identifying infinite parameter estimates in log linear models for frequency tables

optimal large time behavior of the vlasov maxwell boltzmann system in the whole space in this paper we study the large time behavior of classical solutions to the two species vlasov maxwell boltzmann system in the whole space input amssym bbb r 3 the existence of global in time nearby maxwellian solutions is known from strain in 2006 however the asymptotic behavior of these solutions has been a challenging open problem building on our previous work on time decay for the simpler vlasov poisson boltzmann system we prove that these solutions converge to the global maxwellian with the optimal decay rate of o t 3 2 3 2r in the l l norm for any 2 r if initial perturbation is smooth enough and decays in space velocity fast enough at infinity moreover some explicit rates for the electromagnetic field tending to 0 are also provided 2011 wiley periodicals inc

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

stochastic navier stokes equation and renormalization group theory abstract we present an application of a certain renormalization group rng theory developed by chen goldenfeld and oono to the stochastic two dimensional navier stokes equation with additive gaussian noise and periodic boundary conditions this article is a generalization of results of moise and temam which were for the deterministic equation because the classical rng theory e g in a famous work by yakhot and orszag utilizes significantly on adding noise terms our work could be another step towards a rigorous understanding of their method

bayesian estimation of a multilevel irt model using gibbs sampling in this article a two level regression model is imposed on the ability parameters in an item response theory irt model the advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error another advantage is that contrary to observed scores latent scores are test independent which offers the possibility of using results from different tests in one analysis where the parameters of the irt model and the multilevel model can be concurrently estimated the two parameter normal ogive model is used for the irt measurement model it will be shown that the parameters of the two parameter normal ogive model and the multilevel model can be estimated in a bayesian framework using gibbs sampling examples using simulated and real data are given

the lognormal race a cognitive process model of choice and latency with desirable psychometric properties we present a cognitive process model of response choice and response time performance data that has excellent psychometric properties and may be used in a wide variety of contexts in the model there is an accumulator associated with each response option these accumulators have bounds and the first accumulator to reach its bound determines the response time and response choice the times at which accumulator reaches its bound is assumed to be lognormally distributed hence the model is race or minima process among lognormal variables a key property of the model is that it is relatively straightforward to place a wide variety of models on the logarithm of these finishing times including linear models structural equation models autoregressive models growth curve models etc consequently the model has excellent statistical and psychometric properties and can be used in a wide range of contexts from laboratory experiments to high stakes testing to assess performance we provide a bayesian hierarchical analysis of the model and illustrate its flexibility with an application in testing and one in lexical decision making a reading skill

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

advanced structural equation modeling issues and techniques contents g a marcoulides r e schumacker introduction w wothke models for multitrait multimethod matrix analysis k g joreskog f yang nonlinear structural equation models the kenny judd model with interaction effects j j mcardle f hamagami multilevel models from a multiple group structural equation perspective j b willett a g sayer cross domain analyses of change over time combining growth modeling and covariance structure analysis s l hershberger p c m molenaar s e corneal a hierarchy of univariate and multivariate structural times series models y f yung p m bentler bootstrapping techniques in analysis of mean and covariance structures k a bollen a limited information estimator for lisrel models with or without heteroscedastic errors j l arbuckle full information estimation in the presence of incomplete data l j williams h bozdogan l aiman smith inference problems with equivalent models h w marsh j r balla k t hau an evaluation of incremental fit indices a clarification of mathematical and empirical properties

derivation of amplitude equations by the renormalization group method a proper formulation in the perturbative renormalization group method is presented to deduce amplitude equations the formulation makes it possible not only avoiding a serious difficulty in the previous reduction to amplitude equations by eliminating all of the secular terms but also consistent derivation of higher order correction to amplitude equations

probability matrix decomposition models in this paper we consider a class of models for two way matrices with binary entries of 0 and 1 first we considerboolean matrix decomposition conceptualize it as alatent response model lrm and by making use of this conceptualization generalize it to a larger class of matrix decomposition models second probability matrix decomposition pmd models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models third an algorithm for the computation of the maximum likelihood ml and the maximum a posteriori map estimates of the parameters of pmd models is presented this algorithm is an em algorithm and is a special case of a more general algorithm that can be used for the whole class of lrms and fourth as an example a pmd model is applied to data on decision making in psychiatric diagnosis

kernel smoothing approaches to nonparametric item characteristic curve estimation the option characteristic curve the relation between ability and probability of choosing a particular option for a test item can be estimated by nonparametric smoothing techniques what is smoothed is the relation between some function of estimated examinee ability rankings and the binary variable indicating whether or not the option was chosen this paper explores the use of kernel smoothing which is particularly well suited to this application examples show that with some help from the fast fourier transform estimates can be computed about 500 times as rapidly as when using commonly used parametric approaches such as maximum marginal likelihood estimation using the three parameter logistic distribution simulations suggest that there is no loss of efficiency even when the population curves are three parameter logistic the approach lends itself to several interesting extensions

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

existence and uniqueness of the solution to the dissipative 2d quasi geostrophic equations in the sobolev space we study the two dimensional dissipative quasi geostrophic equations in the sobolev space open image in new window existence and uniqueness of the solution local in time is proved in h s when s 2 1 existence and uniqueness of the solution global in time is also proved in h s when s 2 1 and the initial data open image in new window is small for the case s 2 1 we also obtain the unique large global solution in h s provided that open image in new window is small enough

a hierarchical framework for modeling speed and accuracy on test items current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction time research in psychology for instance some of the models have a parameter structure that was chosen to represent a speed accuracy tradeoff while others equate speed directly with response time also several response time models seem to be unclear as to the level of parametrization they represent a hierarchical framework for modeling speed and accuracy on test items is presented as an alternative to these models the framework allows a plug and play approach with alternative choices of models for the response and response time distributions as well as the distributions of their parameters bayesian treatment of the framework with markov chain monte carlo mcmc computation facilitates the approach use of the framework is illustrated for the choice of a normal ogive response model a lognormal model for the response times and multivariate normal models for their parameters with gibbs sampling from the joint posterior distribution

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

extensions of rasch s multiplicative poisson model consideration will be given to a model developed by rasch that assumes scores observed on some types of attainment tests can be regarded as realizations of a poisson process the parameter of the poisson distribution is assumed to be a product of two other parameters one pertaining to the ability of the subject and a second pertaining to the difficulty of the test rasch s model is expanded by assuming a prior distribution with fixed but unknown parameters for the subject parameters the test parameters are considered fixed secondly it will be shown how additional between and within subjects factors can be incorporated methods for testing the fit and estimating the parameters of the model will be discussed and illustrated by empirical examples

em algorithms for ml factor analysis the details of em algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models the algorithm is essentially the same for both cases and involves only simple least squares regression operations the largest matrix inversion required is for aq q symmetric matrix whereq is the matrix of factors the example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation

renormalization group derivation of phase equations abstract phase equations describing the evolution of large scale modulation of spatially periodic patterns in two dimensional systems are derived by employing the renormalization group method a general formula for phase diffusion coefficients is given under certain conditions

locally dependent latent trait model and the dutch identity revisited in this paper we propose a class of locally dependent latent trait models for responses to psychological and educational tests typically item response models treat an individual s multiple response to stimuli as conditional independent given the individual s latent trait in this paper instead the focus is on models based on a family of conditional distributions or kernel that describes joint multiple item responses as a function of student latent trait not assuming conditional independence specifically we examine a hybrid kernel which comprises a component for one way item response functions and a component for conditional associations between items given latent traits the class of models allows the extension of item response theory to cover some new and innovative applications in psychological and educational research an em algorithm for marginal maximum likelihood of the hybrid kernel model is proposed furthermore we delineate the relationship of the class of locally dependent models and the log linear model by revisiting the dutch identity holland 1990

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

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

a mixture cure rate model for responses and response times in time limit tests many large scale standardized tests are intended to measure skills related to ability rather than the rate at which examinees can work time limits imposed on these tests make it difficult to distinguish between the effect of low proficiency and the effect of lack of time this paper proposes a mixture cure rate model approach to address this issue maximum likelihood estimation is proposed for parameter and variance estimation for three cases when examinee parameters are to be estimated given precalibrated item parameters when item parameters are to be calibrated given known examinee parameters and when item parameters are to be estimated without assuming known examinee parameters large sample properties are established for the cases under suitable regularity conditions simulation studies suggest that the proposed approach is appropriate for inferences concerning model parameters in addition not distinguishing between the effect of low proficiency and the effect of lack of time is shown to have considerable consequences for parameter estimation a real data example is presented to demonstrate the new model choice of survival models for the latent power times is also discussed

renormalization group theory for global asymptotic analysis we show with several examples that renormalization group rg theory can be used to understand singular and reductive perturbation methods in a unified fashion amplitude equations describing slow motion dynamics in nonequilibrium phenomena are rg equations the renormalized perturbation approach may be simpler to use than other approaches because it does not require the use of asymptotic matching and yields practically superior approximations

models for ordinal hierarchical classes analysis this paper proposes an ordinal generalization of the hierarchical classes model originally proposed by de boeck and rosenberg 1998 any hierarchical classes model implies a decomposition of a two way two mode binary arraym into two component matrices called bundle matrices which represent the association relation and the set theoretical relations among the elements of both modes inm whereas the original model restricts the bundle matrices to be binary the ordinal hierarchical classes model assumes that the bundles are ordinal variables with a prespecified number of values this generalization results in a classification model with classes ordered along ordinal dimensions the ordinal hierarchical classes model is shown to subsume coombs and kao s 1955 model for nonmetric factor analysis an algorithm is described to fit the model to a given data set and is subsequently evaluated in an extensive simulation study an application of the model to student housing data is discussed

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

estimating multiple classification latent class models this paper presents a new class of models for persons by items data the essential new feature of this class is the representation of the persons every person is represented by its membership tomultiple latent classes each of which belongs to onelatent classification the models can be considered as a formalization of the hypothesis that the responses come about in a process that involves the application of a number ofmental operations two algorithms for maximum likelihood ml and maximum a posteriori map estimation are described they both make use of the tractability of the complete data likelihood to maximize the observed data likelihood properties of the map estimators i e uniqueness and goodness of recovery and the existence of asymptotic standard errors were examined in a simulation study then one of these models is applied to the responses to a set of fraction addition problems finally the models are compared to some related models in the literature

existence of the global smooth solution to the period boundary value problem of fractional nonlinear schrodinger equation in this paper we prove the existence and uniqueness of the global smooth solution to the period boundary value problem of fractional nonlinear schrodinger equation by using energy method

on the relationship between item response theory and factor analysis of discretized variables equivalence of marginal likelihood of the two parameter normal ogive model in item response theory irt and factor analysis of dichotomized variables fa was formally proved the basic result on the dichotomous variables was extended to multicategory cases both ordered and unordered categorical data pair comparison data arising from multiple judgment sampling were discussed as a special case of the unordered categorical data a taxonomy of data for the irt and fa models was also attempted

the nontruncated marginal of a truncated bivariate normal distribution inference is considered for the marginal distribution ofx when x y has a truncated bivariate normal distribution they variable is truncated but only thex values are observed the relationship of this distribution to azzalini s skew normal distribution is obtained method of moments and maximum likelihood estimation are compared for the three parameter azzalini distribution samples that are uniformative about the skewness of this distribution may occur even for largen profile likelihood methods are employed to describe the uncertainty involved in parameter estimation a sample of 87 otis test scores is shown to be well described by this model

rasch s model for reading speed with manifest explanatory variables in educational and psychological measurement we find the distinction between speed and power tests although most tests are partially speeded the speed element is usually neglected here we consider a latent trait model developed by rasch for the response time on a set of pure speed test s which is based on the assumption that the test response times are approximately gamma distributed with known shape parameters and scale parameters depending on subject ability and test difficulty parameters in our approach the subject parameters are treated as random variables having a common gamma distribution from this maximum marginal likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution this basic model can be extended in a number of ways explanatory variables for the latent subject parameters and for the test parameters can be incorporated in the model our methods are illustrated by the analysis of a simulated and an empirical data set

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

a mcmc method for models with continuous latent responses this paper introduces a new technique for estimating the parameters of models with continuous latent data using the rasch model as an example it is shown that existing bayesian techniques for parameter estimation such as the gibbs sampler are not always easy to implement then a new sampling based bayesian technique called the da t gibbs sampler is introduced the da t gibbs sampler relies on the particular latent data structure of latent response models to simplify the computations involved in parameter estimation