metric transformations and the filtered monotonic polynomial item response model the theta metric in item response theory is often not the most useful metric for score reporting or interpretation in this paper i demonstrate that the filtered monotonic polynomial fmp item response model a recently proposed nonparametric item response model liang browne in j educ behav stat 40 5 34 2015 can be used to specify item response models on metrics other than the theta metric specifically i demonstrate that any item response function irf defined within the fmp framework can be re expressed as another fmp irf by taking monotonic transformations of the latent trait i derive the item parameter transformations that correspond to both linear and nonlinear transformations of the latent trait metric these item parameter transformations can be used to define an item response model based on any monotonic transformation of the theta metric so long as the metric transformation is approximated by a monotonic polynomial i demonstrate this result by defining an item response model directly on the approximate true score metric and discuss the implications of metric transformations for applied testing situations

stress gradient versus strain gradient constitutive models within elasticity abstract a stress gradient elasticity theory is developed which is based on the eringen method to address nonlocal elasticity by means of differential equations by suitable thermodynamics arguments involving the free enthalpy instead of the free internal energy the restrictions on the related constitutive equations are determined which include the well known eringen stress gradient constitutive equations as well as the associated so far uncertain boundary conditions the proposed theory exhibits complementary characters with respect to the analogous strain gradient elasticity theory the associated boundary value problem is shown to admit a unique solution characterized by a hellinger reissner type variational principle the main differences between the eringen stress gradient model and the concomitant aifantis strain gradient model are pointed out a rigorous formulation of the stress gradient euler bernoulli beam is provided the response of this beam model is discussed as for its sensitivity to the stress gradient effects and compared with the analogous strain gradient beam model

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

a note on the identifiability of fixed effect 3pl models in this note we prove that the 3 parameter logistic model with fixed effect abilities is identified only up to a linear transformation of the ability scale under mild regularity conditions contrary to the claims in theorem 2 of san martin et al psychometrika 80 2 450 467 2015a

identification of the 1pl model with guessing parameter parametric and semi parametric results in this paper we study the identification of a particular case of the 3pl model namely when the discrimination parameters are all constant and equal to 1 we term this model 1pl g model the identification analysis is performed under three different specifications the first specification considers the abilities as unknown parameters it is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero the second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter it is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero the third specification corresponds to a semi parametric 1pl g model where the distribution g generating the abilities is a parameter of interest it is not only shown that after fixing a difficulty parameter and a guessing parameter at zero the item parameters are identified but also that under those restrictions the distribution g is not identified it is finally shown that after introducing two identification restrictions either on the distribution g or on the item parameters the distribution g and the item parameters are identified provided an infinite quantity of items is available

strain gradient theory in orthogonal curvilinear coordinates in this short note general formulations of the toupin mindlin strain gradient theory in orthogonal curvilinear coordinate systems are derived and are then specified for the cases of cylindrical coordinates and spherical coordinates expressions convenient for practical use are presented for the corresponding equilibrium equations boundary conditions and the physical components for strains and strain gradients in the two coordinate systems the results obtained in this paper are general and complete and can be useful for a wide range of applications such as asymptotic crack tip field analysis cylindrical and spherical cavity expansion problems and the interpretation of micro nano indentation tests and bending twisting tests on small scales

uniqueness studies in boundary value problems involving some second gradient models abstract enhanced models such as second gradient models have been mainly theoretically developed during the sixties and the seventies new attention has been paid to these models recently when it has been recognized that classical inelastic constitutive equations especially the ones not obeying a normality rule induce ill posed boundary value problems however little work has been done to study the well posedness properties of boundary value problems involving these enhanced models the aim of this paper is a partial study of this point only uniqueness of solution of numerical discretization of boundary value problems involving second gradient models is considered we extend to second gradient models a numerical search method to find non uniqueness already established for classical media in the case of loss of uniqueness for the underlying model our numerical results show clearly that in some cases uniqueness is lost for second gradient model as well it seems that second gradient extensions of classical models do not restore the uniqueness properties but only the objectivity of the numerical computation finally our numerical experiments show once more that post peak behavior is a structural effect they also suggest that some constitutive equations often used in geomaterials modeling may be questionable and may not be complete because even adding second gradient enhancement to these models yields non unique solutions

identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes this article considers the identification conditions of confirmatory factor analysis cfa models for ordered categorical outcomes with invariance of different types of parameters across groups the current practice of invariance testing is to first identify a model with only configural invariance and then test the invariance of parameters based on this identified baseline model this approach is not optimal because different identification conditions on this baseline model identify the scales of latent continuous responses in different ways once an invariance condition is imposed on a parameter these identification conditions may become restrictions and define statistically non equivalent models leading to different conclusions by analyzing the transformation that leaves the model implied probabilities of response patterns unchanged we give identification conditions for models with invariance of different types of parameters without referring to a specific parametrization of the baseline model tests based on this approach have the advantage that they do not depend on the specific identification condition chosen for the baseline model

equivalent linear logistic test models this paper is about the linear logistic test model lltm we demonstrate that there are infinitely many equivalent ways to specify a model an implication is that there may well be many ways to change the specification of a given lltm and achieve the same improvement in model fit to illustrate this phenomenon we analyze a real data set using a lagrange multiplier test for the specification of the model this lagrange multiplier test is similar to the modification index used in structural equation modeling

equivalent models in covariance structure analysis defining equivalent models as those that reproduce the same set of covariance matrices necessary and sufficient conditions are stated for the local equivalence of two expanded identified modelsm1 andm2 when fitting the more restricted modelm0 assuming several regularity conditions the rank deficiency of the jacobian matrix composed of derivatives of the covariance elements with respect to the union of the free parameters ofm1 andm2 which characterizes modelm12 is a necessary and sufficient condition for the local equivalence ofm1 andm2 this condition is satisfied in practice when the analysis dealing with the fitting ofm0 predicts that the decreases in the chi square goodness of fit statistic for the fitting ofm1 orm2 orm12 are all equal for any set of sample data except on differences due to rounding errors

linking item response model parameters with a few exceptions the problem of linking item response model parameters from different item calibrations has been conceptualized as an instance of the problem of test equating scores on different test forms this paper argues however that the use of item response models does not require any test score equating instead it involves the necessity of parameter linking due to a fundamental problem inherent in the formal nature of these models their general lack of identifiability more specifically item response model parameters need to be linked to adjust for the different effects of the identifiability restrictions used in separate item calibrations our main theorems characterize the formal nature of these linking functions for monotone continuous response models derive their specific shapes for different parameterizations of the 3pl model and show how to identify them from the parameter values of the common items or persons in different linking designs

remarks on the identifiability of thurstonian ranking models case v case iii or neither it is well known that the representations of the thurstonian case iii and case v models for paired comparison data are not unique similarly when analyzing ranking data other equivalent covariance structures can substitute for those given by thurstone in these cases that is we may more broadly define the family of covariance structures satisfying case iii and case v conditions this paper introduces the notion of equivalence classes which defines a more meaningful partition of the covariance structures of the thurstonian ranking models in addition the equivalence classes of case v and case iii are completely characterized

a micromechanics based approach for the derivation of constitutive elastic coefficients of strain gradient media a micromechanics based approach for the derivation of the effective properties of periodic linear elastic composites which exhibit strain gradient effects at the macroscopic level is presented at the local scale all phases of the composite obey the classic equations of three dimensional elasticity but since the assumption of strict separation of scales is not verified the macroscopic behavior is described by the equations of strain gradient elasticity the methodology uses the series expansions at the local scale for which higher order terms which are generally neglected in standard homogenization framework are kept in order to take into account the microstructural effects an energy based micro macro transition is then proposed for upscaling and constitutes in fact a generalization of the hill mandel lemma to the case of higher order homogenization problems the constitutive relations and the definitions for higher order elasticity tensors are retrieved by means of the state law associated to the derived macroscopic potential as an illustration purpose we derive the closed form expressions for the components of the gradient elasticity tensors in the particular case of a stratified periodic composite for handling the problems with an arbitrary microstructure a fft based computational iterative scheme is proposed in the last part of the paper its efficiency is shown in the particular case of composites reinforced by long fibers

gradient plasticity theory with a variable length scale parameter the definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects however a fixed value of the material length scale is not always realistic and different problems could require different values moreover a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings this work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem it is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro bending and micro torsion tests if a definite and fixed length scale parameter is used a generalized gradient plasticity model with a non fixed length scale parameter is proposed based on dislocation mechanics this model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled or to the way in which the statically stored and geometrically necessary dislocations are coupled in addition a physically based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed the proposed model gives good predictions of the size effect in micro bending tests of thin films and micro torsion tests of thin wires

time and space adaptive methods applied to localization phenomena in empty and saturated micropolar and standard porous materials localization phenomena as e g shear bands occur as a result of local concentrations of plastic strains in small bands of finite width the reason for this behaviour lies in the basic properties of elasto plastic frictional materials where variations of the lode angle together with the non associated plastic dilatation result in local softening effects proceeding from non viscous empty porous materials it is well known that the computation of shear bands reveals an ill posed problem to overcome this behaviour two different regularization strategies are considered which are 1 the inclusion of independent rotational degrees of freedom micropolar formulation and 2 the inclusion of viscosity effects standard formulation by taking into consideration viscoplastic properties of the solid matrix or a viscous pore fluid respectively the numerical treatment furthermore proceeds from time and space adaptive strategies to refine and to coarsen both the time step and the mesh size considering quasi static problems the space discretization yields a dae system of index 1 in the time domain which can be successfully treated by sdirk methods thus allowing for an efficient estimation of the time error and as a consequence for an adaptive time step control in the space domain the present investigation proceeds from an error indicator of zienkiewicz zhu type where smoothened values of the l2 norms of characteristic quantities are compared to the respective discrete values the efficiency of this procedure is demonstrated by the computation of the biaxial experiment on an empty and a liquid saturated porous soil material and of the slope failure problem of a fluid saturated soil copyright 2001 john wiley sons ltd

remarks on equivalent linear logistic test models by bechger verstralen and verhelst 2002 this paper discusses a new form of specifying and normalizing a linear logistic test model lltm as suggested by bechger verstralen and verhelst psychometrika 2002 it is shown that there are infinitely many ways to specify the same normalization moreover the relationship between some of their results and equivalent previous results in the literature is clarified and it is shown that the goals of estimating and testing a single element of the weight matrix for which they propose new methods can be reached by means of simple well known tools already implemented in published lltm software

identifiability of nonlinear logistic test models the linear logistic test model lltm specifies the item parameters as a weighted sum of basic parameters the lltm is a special case of a more general nonlinear logistic test model nltm where the weights are partially unknown this paper is about the identifiability of the nltm sufficient and necessary conditions for global identifiability are presented for a nltm where the weights are linear functions while conditions for local identifiability are shown to require a model with less restrictions it is also discussed how these conditions are checked using an algorithm due to bekker merckens and wansbeek 1994 several illustrations are given

on the unidentifiability of the fixed effects 3pl model the paper offers a general review of the basic concepts of both statistical model and parameter identification and revisits the conceptual relationships between parameter identification and both parameter interpretability and properties of parameter estimates all these issues are then exemplified for the 1pl 2pl and 1pl g fixed effects models for the 3pl model however we provide a theorem proving that the item parameters are not identified do not have an empirical interpretation and that it is not possible to obtain consistent and unbiased estimates of them

equivalent mirid models it is shown that in the context of the model with internal restrictions on the item difficulties mirid different componential theories about an item set may lead to equivalent models furthermore we provide conditions for the identifiability of the mirid model parameters and it will be shown how the mirid model relates to the linear logistic test model lltm while it is known that the lltm is a special case of the mirid we show that it is possible to construct an lltm that encompasses the mirid the mirid model places a bilinear restriction on the item parameters of the rasch model it is explained how this fact is used to simplify the results of bechger verhelst and verstralen 2001 and bechger verstralen and verhelst 2002 and extend their scope to a wider class of models

non local yield limit degradation presented is a new type of a non local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit the key idea which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation is to apply the non local concept only to those parameters which cause the degradation while keeping the definition of the strains local compared to the previously advanced fully non local continuum formulation the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions the new formulation exhibits no zero energy periodic modes imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient two dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy the formulation is applied to tunnel excavation in a soil stabilized by cement grouting with the objective of preventing cave in burst of the tunnel sides due to compression softening

post necking behaviour modelled by a gradient dependent plasticity theory abstract the delay of the onset of localization and the post necking behaviour for stretched thin sheets are determined by three dimensional effects thus a 2 d finite element analysis based on a local plasticity theory will give a physically unrealistic mesh dependent solution this in spite of the fact that the stress state is essentially two dimensional by incorporating a length scale with relation to the thickness of the sheet it is demonstrated how a 2 d finite element analysis based on a gradient dependent plasticity theory can give a good approximation of the post necking behaviour this is illustrated by numerical comparison of results from a full 3 d finite element analysis with results from a 2 d finite element model based on a finite strain version of a gradient dependent j 2 flow theory some numerical problems in the modeling will be discussed briefly

energy relaxation of non convex incremental stress potentials in a strain softening elastic plastic bar abstract we propose a fundamentally new concept to the treatment of material instabilities and localization phenomena based on energy minimization principles in a strain softening elastic plastic bar the basis is a recently developed incremental variational formulation of the local constitutive response for generalized standard media it provides a quasi hyperelastic stress potential that is obtained from a local minimization of the incremental energy density with respect to the internal variables the existence of this variational formulation induces the definition of the material stability of inelastic solids based on convexity properties in analogy to treatments in elasticity furthermore localization phenomena are understood as micro structure development associated with a non convex incremental stress potential in analogy to phase decomposition problems in elasticity for the one dimensional bar considered the two phase micro structure can analytically be resolved by the construction of a sequentially weakly lower semicontinuous energy functional that envelops the not well posed original problem this relaxation procedure requires the solution of a local energy minimization problem with two variables which define the one dimensional micro structure developing the volume fraction and the intensity of the micro bifurcation the relaxation analysis yields a well posed boundary value problem for an objective post critical localization analysis the performance of the proposed method is demonstrated for different discretizations of the elastic plastic bar which document on the mesh independence of the results

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

limit theorems for gradient dependent elastoplastic geomaterials in this paper the limit theorems proposed by drucker and co workers are reformulated to address a class of gradientdependent elastoplastic geomaterials the gradient effects are accounted for by incorporating strain gradients and their conjugate higher order stresses into the constitutive descriptions gradient dependent equilibrium equations and higher order boundary conditions are defined for both statically admissible and kinematically admissible states and the associated lower bound and upper bound theories are recast for the gradient enhanced limit theorems a generalised drucker prager yield criterion that includes the gradient influence on the deviatoric stress is proposed and then employed to investigate the collapse loads for soil layers under conditions of generalised plane strain simple shear and uniaxial compression the corresponding lower and upper bounds are found for these problems it is demonstrated that the predicted collapse bounds are generally dependent on both the conventional and gradient properties with normalised length scale s being present in the results this feature enables us to give physically reasonable interpretations for size effects and shear banding during material collapse comparisons are also made between the gradient dependent bounds and those obtained through conventional plasticity theories influences of model parameters and sample dimensions on the predictions are also discussed it is shown that the proposed gradient dependent limit theorems can be used to provide physically meaningful predictions for general geotechnical applications 2006 elsevier ltd all rights reserved

identifiability and equivalence of gllirm models the generalized logit linear item response model gllirm is a linearly constrained nominal categories model ncm that computes the scale and intercept parameters for categories as a weighted sum of basic parameters this paper addresses the problems of the identifiability of the basic parameters and the equivalence between different gllirm models it is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions moreover two models are observationally equivalent if the product of the respective coefficient matrices has full column rank finally the paper also explores the relations between the parameters of nested models

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

numerical approximation of incremental infinitesimal gradient plasticity we investigate a representative model of continuum infinitesimal gradient plasticity the formulation is an extension of classical rate independent infinitesimal plasticity based on the additive decomposition of the symmetric strain tensor into elastic and plastic parts it is assumed that dislocation processes contribute to the storage of energy in the material whereby the curl of the plastic distortion appears in the thermodynamic potential and leads to an additional nonlocal backstress tensor the formulation is cast into a numerical framework by a saddle point approximation of the corresponding minimization problem in each incremental loading step this allows one to reformulate the nonlocal dissipation inequality to a point wise flow rule and yields a solution scheme which is a direct extension of the standard approach in classical plasticity our numerical results show the regularizing effects of the additional physically motivated terms copyright 2008 john wiley sons ltd

on the bayesian nonparametric generalization of irt type models we study the identification and consistency of bayesian semiparametric irt type models where the uncertainty on the abilities distribution is modeled using a prior distribution on the space of probability measures we show that for the semiparametric rasch poisson counts model simple restrictions ensure the identification of a general distribution generating the abilities even for a finite number of probes for the semiparametric rasch model only a finite number of properties of the general abilities distribution can be identified by a finite number of items which are completely characterized the full identification of the semiparametric rasch model can be only achieved when an infinite number of items is available the results are illustrated using simulated data

disturbed state constitutive modeling based on stress strain and nondestructive behavior the proposed disturbed state concept dsc is based on the idea that a deforming material element can be treated as a mixture of two constituent parts in the relative intact ri and fully adjusted fa states referred to as reference states during external loading the material experiences internal changes in its microstructure due to a process of self adjustment and as a consequence the initial ri state transforms continuously to the fa state the self adjustment process which may involve relative motions of material particles that can lead to microcracking and damage or strengthening can cause disturbances in the observed response with respect to the responses under the two reference states then the observed response is expressed in terms of the responses for the ri and fa states that are determined from laboratory tests on material specimens the dsc permits development of unified constitutive models that include hierarchically other previous continuum and damage models as special cases various aspects of the dsc are verified here with respect to laboratory behavior of two materials a cemented sand and a ceramic composite some of the unique features of this study are that 1 the constitutive behavior and parameters can be obtained from the stress strain volume change behavior and from the measurements of ultrasonic p wave velocities 2 correlations between mechanical and ultrasonic response can be established 3 the concept can provide a description of the crack density and 4 it can be simplified for predicting the remaining life of materials through definition of constitutive models and evaluation of design moduli affected by mechanical and environmental loading

an algorithm for gradient regularized plasticity coupled to damage based on a dual mixed fe formulation abstract a thermodynamically consistent theory of gradient regularized plasticity with coupling to isotropic damage was presented by svedberg and runesson 23 its main purpose was to describe the successive development of the localization zone that is pertinent to the softening regime due to excessive damage close to failure explicit constitutive relations were established for a model problem based on von mises plasticity with isotropic hardening of two types local and gradient enhanced the main purpose of this paper is to describe a new numerical algorithm for the gradient enhanced formulation using the backward euler rule leads to a gradient enhanced format of the classical closest point projection method the plastic multiplier increment is solved via a dual mixed method which is a convenient feature in the present context this leads to an unambiguous representation of the constitutive relations in the equilibrium equation moreover the classical local algebraic kuhn tucker conditions are obtained in a straightforward fashion in the limit case of local theory the developed algorithm was implemented in the educational finite element package 5 numerical results are shown for the extension of a plate in plane stress these results demonstrate the convergence characteristics with mesh refinement as well as the salient features of the adopted damage based constitutive model