multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints abstract this paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control in which the returns of assets are characterized by possibilistic mean values a possibilistic absolute deviation is defined as the risk control of portfolio a new multiperiod mean absolute deviation fuzzy portfolio selection model with transaction cost borrowing constraints threshold constraints and cardinality constraints is proposed based on the theory of possibility measure the proposed model is transformed into a crisp nonlinear programming problem because of the transaction cost the multiperiod portfolio selection is a dynamic optimization problem with path dependence the discrete approximate iteration method is designed to obtain the optimal portfolio strategy and is proved convergent finally an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the shanghai stock exchange

a constrained multi period robust portfolio model with behavioral factors and an interval semi absolute deviation abstract in this paper a multi period portfolio selection model is presented considering the behavioral factors of investors the behavioral factors are presented in the form of prospect theory with three main parameters as reference dependence risk aversion and diminishing sensitivity these parameters define the behavioral features of investors that can influence their investing the future return of assets is regarded according to the interval based on uncertainty besides a criterion of interval semi absolute deviation is presented to control the risk of investing the influence of uncertainty exists in the optimal parameters the final result is controlled by a robust optimization approach in order to make this model applicable and adapting it to the conditions of the real world we considered the cardinality constraints entropy and the possibility of risk free borrowing and lending with different rates first the model is solved by gams in small size to check the feasibility then due to the np hard feature of the model we used three meta heuristic algorithms which are more appropriate for solving large problems to solve the proposed model to survey the model s performance we used real data from a case study the results show that the model reflects the behavioral factors of investors in their portfolio and it also maintains the robustness level in accordance with the degree of conservatism besides the sensitivity analysis is performed to show the model s efficiency finally we compared the results of different meta heuristic algorithms and benchmark model s performance

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

a pearson type vii item response model for assessing person fluctuation using lumsden s thurstonian fluctuation model as a starting point this paper attempts to develop a unidimensional item response theory model intended for binary personality items under some additional assumptions a new model is obtained in which the item characteristic curves are defined by a cumulative pearson type vii distribution and the person response curves are two parameter normal ogives procedures for fitting the new model are proposed furthermore the relations between individual fluctuation and scalability are discussed and a scalability index based on the new model is proposed all the developments in this paper are illustrated using two empirical examples

solving a class of fuzzy linear programs by using semi infinite programming techniques this paper deals with a class of fuzzy linear programming problems characterized by the fact that the coefficients in the constraints are modeled as lr fuzzy numbers with different shapes solving such problems is usually more complicated than finding a solution when all the fuzzy coefficients have the same shape we propose a primal semi infinite algorithm as a valuable tool for solving this class of fuzzy linear programs and we illustrate it by means of several examples

reliability of test scores in nonparametric item response theory three methods for estimating reliability are studied within the context of nonparametric item response theory two were proposed originally by mokken 1971 and a third is developed in this paper using a monte carlo strategy these three estimation methods are compared with four classical lower bounds to reliability finally recommendations are given concerning the use of these estimation methods

marginal maximum likelihood estimation for the one parameter logistic model two algorithms are described for marginal maximum likelihood estimation for the one parameter logistic model the more efficient of the two algorithms is extended to estimation for the linear logistic model numerical examples of both procedures are presented

fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio a new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper beyond the well known sharpe ratio i e the reward to variability ratio in modern portfolio theory we initiate the so called fuzzy sharpe ratio in the fuzzy modeling context in addition to the introduction of the new risk measure we also put forward the reward to uncertainty ratio to assess the portfolio performance in fuzzy modeling corresponding to two approaches based on rm t rm m and rm t rm w fuzzy arithmetic two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized while the fuzzy sharpe ratio is maximized these models are solved by the fuzzy approach or by the genetic algorithm ga solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean variance optimization mvo model used prevalently in the financial literature in terms of portfolio performance evaluated by the fuzzy sharpe ratio and the reward to uncertainty ratio the model using rm t rm w fuzzy arithmetic results in higher performance portfolios than those obtained by both the mvo and the fuzzy model which employs rm t rm m fuzzy arithmetic we also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using ga although ga can offer a series of well diversified portfolio solutions diagrammed in a pareto frontier

item response theory observed score kernel equating item response theory irt observed score kernel equating is introduced for the non equivalent groups with anchor test equating design using either chain equating or post stratification equating t

nearest interval approximation of a fuzzy number the problem of the interval approximation of fuzzy numbers is discussed a new interval approximation operator which is the best one with respect to a certain measure of distance between fuzzy numbers is suggested

a new fuzzy multi objective higher order moment portfolio selection model for diversified portfolios abstract due to the important effect of the higher order moments to portfolio returns the aim of this paper is to make use of the third and fourth moments for fuzzy multi objective portfolio selection model firstly in order to overcome the low diversity of the obtained solution set and lead to corner solutions for the conventional higher moment portfolio selection models a new entropy function based on minkowski measure is proposed as a new objective function and a novel fuzzy multi objective weighted possibilistic higher order moment portfolio model is presented secondly to solve the proposed model efficiently a new multi objective evolutionary algorithm is designed thirdly several portfolio performance evaluation techniques are used to evaluate the performance of the portfolio models finally some experiments are conducted by using the data of shanghai stock exchange and the results indicate the efficiency and effectiveness of the proposed model and algorithm

a novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty abstract in today s business environments the high importance of economic benefits and environmental impacts of using scrapped products has caused most companies to move to designing the closed loop supply chain network this paper considers the closed loop supply chain network design problem under hybrid uncertainty while there are two sources of uncertainty for most parameters thus require fortifying of the robustness of the decision the first source is that some uncertain parameters may be based on the future scenarios which are considered according to the probability of their occurrence the second source is that the values of these parameters in each scenario are usually imprecise and can be specified by possibilistic distributions in this case the best robust decision has some additional properties in terms of mean value and variability of the objective function we introduced two types of the variability named scenario variability and possibilistic variability possibility theory is used to choose a solution in such a problem and a novel robust fuzzy stochastic programming approach is proposed that has significant advantages the performance of the proposed model is also compared with that of other models in term of the mean cost and variability by simulation

on weighted possibilistic mean and variance of fuzzy numbers dubois and prade defined an interval valued expectation of fuzzy numbers viewing them as consonant random sets carlsson and fuller defined an interval valued mean value of fuzzy numbers viewing them as possibility distributions in this paper we shall introduce the notation of weighted interval valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval valued probabilistic mean we shall also introduce the notations of crisp weighted possibilistic mean value variance and covariance of fuzzy numbers which are consistent with the extension principle furthermore we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

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

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

optimum examinee samples for item parameter estimation in item response theory a multi objective programming approach this paper proposes a multi objective programming method for determining samples of examinees needed for estimating the parameters of a group of items in the numerical experiments optimum samples are compared to uniformly and normally distributed samples the results show that the samples usually recommended in the literature are well suited for estimating the difficulty parameters furthermore they are also adequate for estimating the discrimination parameters in the three parameter model butnot for the guessing parameters

multiobjective programming in optimization of the interval objective function abstract in this paper the mathematical programming problem whose objective function has interval coefficients is investigated to maximize the interval objective function the order relations which represent the decision maker s preference between interval profits are defined by the right limit the left limit the center and the width of an interval the maximization problem with the interval objective function is converted into a multiobjective problem using the order relations the minimization problem is also converted into a multiobjective problem using the order relations which represent the decision maker s preference between interval costs

on comparing interval numbers abstract this paper first presents a brief survey of the existing works on comparing and ranking any two interval numbers on the real line and then on the basis of this gives two approaches to compare any two interval numbers the first one describes a value judgement index along with a discussion on its strength and weakness over the other approaches this index has also been called an optimistic decision maker s preference index the other approach defines strict and fuzzy preference ordering between any two interval numbers from a pessimistic decision maker s point of view choice of different decision makers with different degrees of pessimism has also been considered

a new index for bond management in an uncertain environment within the framework of assets liability management we understand that immunization is the main method to assure a certain yield in a future date departing from an initial portfolio although the objective of passive strategies is to design a portfolio that will achieve the performance of a predetermined benchmark active bond management strategies rely on expectations of interest rate movements or changes in yield spread relationships however the variation of the duration increases the risk of a portfolio that why the decision maker will have to choose the combination of expected return and risk which provides the higher utility finally the construction of a fuzzy return risk map will allow the decision maker to know the over risk and the over return as regards immunization strategy for each duration and for each risk aversion of the decision maker the construction of a risk return map presents the results in an appropriate way it will help the decision maker to choose the best duration for the decision maker interest rate forecast finally this methodology is applied to the spanish debt so that the decision maker can select the duration that brings him a greater preference

the theoretical detect index of dimensionality and its application to approximate simple structure in this paper a theoretical index of dimensionality called the theoretical detect index is proposed to provide a theoretical foundation for the detect procedure the purpose of detect is to assess certain aspects of the latent dimensional structure of a test important to practitioner and research alike under reasonable modeling restrictions referred to as approximate simple structure the theoretical detect index is proven to be maximized at thecorrect dimensionality based partition of a test where the number of item clusters in this partition corresponds to the number of substantivelyseparate dimensions present in the test and by correct is meant that each cluster in this partition contains only items that correspond to the same separate dimension it is argued that the separation into item clusters achieved by detect is appropriate from the applied perspective of desiring a partition into clusters that are interpretable as substantively distinct between clusters and substantively homogeneous within cluster moreover the maximum detect index value is a measure of the amount of multidimensionality present the estimation of the theoretical detect index is discussed and a genetic algorithm is developed to effectively execute detect the study of detect is facilitated by the recasting of two factor analytic concepts in a multidimensional item response theory setting a dimensionally homogeneous item cluster and an approximate simple structure test

an inequality for correlations in unidimensional monotone latent variable models for binary variables it is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations the negative logarithm of the correlations satisfies the triangle inequality this inequality is not implied by the condition that the correlations are nonnegative the criterion that coefficient h exceeds 0 30 or manifest monotonicity the inequality implies both a lower bound and an upper bound for each correlation between two items based on the correlations of those two items with every possible third item it is discussed how this can be used in mokken s a theory and procedure of scale analysis mouton the hague 1971 scale analysis

test theory and psychometrika the past twenty five years on the occasion ofpsychometrika s fiftieth anniversary the past twenty five years developments in mental test theory are reviewed with special emphasis on the topics receiving attention in the pages of this journal analogous reviews forpsychometrika s first quarter century were given by gulliksen and guilford in 1961 much of the recent progress in test theory and in other branches of psychometrics as well has been made by treating the problems in this field as being essentially ones of statistical inference it is concluded that a research in test theory is in a healthy state and b psychometrika is an important source of information about that research

information matrices and standard errors for mles of item parameters in irt the paper clarifies the relationship among several information matrices for the maximum likelihood estimates mles of item parameters it shows that the process of calculating the observed information matrix also generates a related matrix that is the middle piece of a sandwich type covariance matrix monte carlo results indicate that standard errors ses based on the observed information matrix are robust to many but not all conditions of model distribution misspecifications ses based on the sandwich type covariance matrix perform most consistently across conditions results also suggest that ses based on other matrices are either not consistent or perform not as robust as those based on the sandwich type covariance matrix or the observed information matrix

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

bias reduction of maximum likelihood estimates summary it is shown how in regular parametric problems the first order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function in exponential families with canonical parameterization the effect is to penalize the likelihood by the jeffreys invariant prior in binomial logistic models poisson log linear models and certain other generalized linear models the jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data

interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming abstract the modern trend in operations research methodology deserves modelling of all relevant vague or uncertain information involved in a real decision problem generally vagueness is modelled by a fuzzy approach and uncertainty by a stochastic approach in some cases a decision maker may prefer using interval numbers as coefficients of an inexact relationship as a coefficient an interval assumes an extent of tolerance or a region that the parameter can possibly take however its use in the optimization problems is not much attended as it merits this paper defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment on the basis of a comparative study on ordering interval numbers inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined a numerical example is also given

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

generalized fiducial inference for binary logistic item response models generalized fiducial inference gfi has been proposed as an alternative to likelihood based and bayesian inference in mainstream statistics confidence intervals cis can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a bayesian posterior distribution however no prior distribution needs to be specified which renders gfi more suitable when no a priori information about model parameters is available in the current paper we apply gfi to a family of binary logistic item response theory models which includes the two parameter logistic 2pl bifactor and exploratory item factor models as special cases asymptotic properties of the resulting fiducial distribution are discussed random draws from the fiducial distribution can be obtained by the proposed markov chain monte carlo sampling algorithm we investigate the finite sample performance of our fiducial percentile ci and two commonly used wald type cis associated with maximum likelihood ml estimation via monte carlo simulation the use of gfi in high dimensional exploratory item factor analysis was illustrated by the analysis of a set of the eysenck personality questionnaire data

artificial bee colony algorithm for constrained possibilistic portfolio optimization problem abstract in this paper we discuss the portfolio optimization problem with real world constraints under the assumption that the returns of risky assets are fuzzy numbers a new possibilistic mean semiabsolute deviation model is proposed in which transaction costs cardinality and quantity constraints are considered due to such constraints the proposed model becomes a mixed integer nonlinear programming problem and traditional optimization methods fail to find the optimal solution efficiently thus a modified artificial bee colony mabc algorithm is developed to solve the corresponding optimization problem finally a numerical example is given to illustrate the effectiveness of the proposed model and the corresponding algorithm

an exact method for partitioning dichotomous items within the framework of the monotone homogeneity model the monotone homogeneity model mhm also known as the unidimensional monotone latent variable model is a nonparametric irt formulation that provides the underpinning for partitioning a collection of dichotomous items to form scales ellis psychometrika 79 303 316 2014 doi 10 1007 s11336 013 9341 5 has recently derived inequalities that are implied by the mhm yet require only the bivariate inter item correlations in this paper we incorporate these inequalities within a mathematical programming formulation for partitioning a set of dichotomous scale items the objective criterion of the partitioning model is to produce clusters of maximum cardinality the formulation is a binary integer linear program that can be solved exactly using commercial mathematical programming software however we have also developed a standalone branch and bound algorithm that produces globally optimal solutions simulation results and a numerical example are provided to demonstrate the proposed method

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

mean variance skewness model for portfolio selection with fuzzy returns numerous empirical studies show that portfolio returns are generally asymmetric and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same in order to measure the asymmetry of fuzzy portfolio return a concept of skewness is defined as the third central moment in this paper and its mathematical properties are studied as an extension of the fuzzy mean variance model a mean variance skewness model is presented and the corresponding variations are also considered in order to solve the proposed models a genetic algorithm integrating fuzzy simulation is designed finally several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm

ordinal test fidelity estimated by an item sampling model a test theory using only ordinal assumptions is presented it is based on the idea that the test items are a sample from a universe of items the sum across items of the ordinal relations for a pair of persons on the universe items is analogous to a true score using concepts from ordinal multiple regression it is possible to estimate the tau correlations of test items with the universe order from the taus among the test items these in turn permit the estimation of the tau of total score with the universe it is also possible to estimate the odds that the direction of a given observed score difference is the same as that of the true score difference the estimates of the correlations between items and universe and between total score and universe are found to agree well with the actual values in both real and artificial data

conditional covariance theory and detect for polytomous items this paper extends the theory of conditional covariances to polytomous items it has been proven that under some mild conditions commonly assumed in the analysis of response data the conditional covariance of two items dichotomously or polytomously scored given an appropriately chosen composite is positive if and only if the two items measure similar constructs besides the composite the theory provides a theoretical foundation for dimensionality assessment procedures based on conditional covariances or correlations such as detect and dimtest so that the performance of these procedures is theoretically justified when applied to response data with polytomous items various estimators of conditional covariances are constructed and special attention is paid to the case of complex sampling data such as those from the national assessment of educational progress naep as such the new version of detect can be applied to response data sets not only with polytomous items but also with missing values either by design or at random detect is then applied to analyze the dimensional structure of the 2002 naep reading samples of grades 4 and 8 the detect results show that the substantive test structure based on the purposes for reading is consistent with the statistical dimensional structure for either grade

high dimensional multivariate probit analysis a computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model the procedure is applied to five variables from the pneumoconiosis field trial two variables of which were previously analyzed by ashford and sowden 1970 biometrics 26 535 546

portfolio selection under independent possibilistic information this paper deals with a portfolio selection problem with independently estimated possibilistic return rates under such a circumstance a distributive investment has been regarded as a good solution in the traditional portfolio theory however the conventional possibilistic approach yields a concentrated investment solution considering the reason why a distributive investment is advocated a new approach to the possibilistic portfolio selection is proposed

fuzzy portfolio optimization under downside risk measures this paper presents two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return we assume that the rates of returns on securities are approximated as lr fuzzy numbers of the same shape and that the expected return and risk are evaluated by interval valued means we establish the relationship between those mean interval definitions for a given fuzzy portfolio by using suitable ordering relations finally we formulate the portfolio selection problem as a linear program when the returns on the assets are of trapezoidal form

a nonparametric approach for assessing latent trait unidimensionality assuming a nonparametric family of item response theory models a theory based procedure for testing the hypothesis of unidimensionality of the latent space is proposed the asymptotic distribution of the test statistic is derived assuming unidimensionality thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait based upon a new notion of dimensionality the test is shown to have asymptotic power 1 a 6300 trial monte carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice

a cutting plane algorithm for mv portfolio selection model this paper deals with a portfolio selection problem with fuzzy return rates a possibilistic mean variance fmvc portfolio selection model was proposed the possibilistic programming problem can be transformed into a linear optimal problem with an additional quadratic constraint by possibilistic theory for such problems there are no special standard algorithms we propose a cutting plane algorithm to solve fmvc the nonlinear programming problem can be solved by sequence linear programming problem a numerical example is given to illustrate the behavior of the proposed model and algorithm

portfolio selection based on fuzzy probabilities and possibility distributions abstract in this paper two kinds of portfolio selection models are proposed based on fuzzy probabilities and possibility distributions respectively rather than conventional probability distributions in markowitz s model since fuzzy probabilities and possibility distributions are obtained depending on possibility grades of security data offered by experts investment experts knowledge can be reflected a numerical example of a portfolio selection problem is given to illustrate our proposed approaches

analysis of residuals for the multinomial item response model using the item response model as developed on the multinomial distribution asymptotic variances are obtained for residuals associated with response patterns and first and second order marginal frequencies of manifest variables when the model does not fit well an examination of these residuals may reveal the source of the poor fit finally a limited information test of fit for the model is developed by using residuals defined for the first and second order marginals model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse

a comparison of three simple test theory models in very simple test theory models such as the rasch model a single parameter is used to represent the ability of any examinee or the difficulty of any item simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available and are themselves of real practical value for small or even medium samples they can also serve a normative role in test design as an alternative to the rasch model or the rasch model with a correction for guessing a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference this model provides a natural account of guessing and has other useful things to contribute as well it also offers an alternative to the rasch model with the usual correction for guessing the three models are compared in terms of statistical properties and fits to actual data the goal of the paper is to widen the range of minimal models available to test analysts

an item response model for nominal data based on the rising selection ratios criterion complete response vectors of all answer options in multiple choice items can be used to estimate ability the rising selection ratios criterion is necessary for scoring individuals because it implies that estimated ability always increases when the correct alternative is selected this paper introduces the generalized dlt model which assumes rising selection ratios and uses three parameters to describe each incorrect alternative it is shown that the nominal categories and the thissen and steinberg model do not meet the criterion a simulation study on goodness of recovery and an example with real data are also included

portfolios with fuzzy returns selection strategies based on semi infinite programming this paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables the investor s problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset the corresponding optimal portfolio is derived using semi infinite programming in a soft framework the return on each asset and their membership functions are described using historical data the investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio this approach is illustrated with a numerical example

em and beyond the basic theme of the em algorithm to repeatedly use complete data methods to solve incomplete data problems is also a theme of several more recent statistical techniques these techniques multiple imputation data augmentation stochastic relaxation and sampling importance resampling combine simulation techniques with complete data methods to attack problems that are difficult or impossible for em

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

fuzzy compromise programming for portfolio selection the aim of this paper is to solve a portfolio selection problem using sharpe s single index model in a soft framework estimations of subjective or imprecise future beta for every asset can be represented through fuzzy numbers constructed on the basis of statistical data and the relevant knowledge of the financial analyst the model therefore works with data that contain more information than any classical model and dealing with it does not involve a great extra computational effort in order to solve the portfolio selection problem we have formulated a fuzzy compromise programming problem for this task we have introduced the fuzzy ideal solution concept based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their a cuts the accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and using discrepancy between fuzzy numbers in our analysis a major feature of this model is its sensitivity to the analyst s opinion as well as to the decision maker s preferences this allows interaction with both when it comes to design the best portfolio

on the regularity of an obstacle control problem an optimal control problem of the obstacle for an elliptic variational inequality is considered in which the obstacle is regarded as the control to get the regularity of the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new control problem the regularity of the optimal pair to the original problem is obtained it turns out that the regularity obtained is sharp in general some other interesting properties of the optimal pair are also established

a model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test abstract the purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests usually the diagnostic tests are correlated conditional on disease status and the reference test is subject to error in the chlamydia trachomatis study five screening tests for detecting chlamydia in endocervical specimens were compared the five tests are correlated and the reference test the cell culture test has less than 100 sensitivity the conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis we propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test the model also can estimate the effects of covariates it is a generalized linear mixed model with two unobserved variables one continuous and one dichotomous we use a hybrid

the dutch identity a new tool for the study of item response models the dutch identity is a useful way to reexpress the basic equations of item response models that relate the manifest probabilities to the item response functions irfs and the latent trait distribution the identity may be exploited in several ways for example a to suggest how item response models behave for large numbers of items they are approximate submodels of second order loglinear models for 2 j tables b to suggest new ways to assess the dimensionality of the latent trait principle components analysis of matrices composed of second order interactions from loglinear models c to give insight into the structure of latent class models and d to illuminate the problem of identifying the irfs and the latent trait distribution from sample data

existence and uniqueness of solutions to a quasilinear parabolic equation with quadratic gradients in financial markets a quasilinear parabolic equation with quadratic gradient terms is analyzed the equation models an optimal portfolio in so called incomplete financial markets consisting of risky assets and non tradable state variables its solution allows to compute an optimal portfolio strategy the quadratic gradient terms are essentially connected to the assumption that the so called relative risk aversion function is not logarithmic the existence of weak global in time solutions in any dimension is shown under natural hypotheses the proof is based on the monotonicity method of frehse furthermore the uniqueness of solutions is shown under a smallness condition on the derivatives of the covariance diffusion matrices using a nonlinear test function technique developed by barles and murat finally the influence of the non tradable state variables on the optimal value function is illustrated by a numerical example in three dimensions

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

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

specifying optimum examinees for item parameter estimation in item response theory information functions are used to find the optimum ability levels and maximum contributions to information for estimating item parameters in three commonly used logistic item response models for the three and two parameter logistic models examinees who contribute maximally to the estimation of item difficulty contribute little to the estimation of item discrimination this suggests that in applications that depend heavily upon the veracity of individual item parameter estimates e g adaptive testing or text construction better item calibration results may be obtained for fixed sample sizes from examinee calibration samples in which ability is widely dispersed

portfolio selection based on fuzzy cross entropy in this paper the kapur cross entropy minimization model for portfolio selection problem is discussed under fuzzy environment which minimizes the divergence of the fuzzy investment return from a priori one first three mathematical models are proposed by defining divergence as cross entropy average return as expected value and risk as variance semivariance and chance of bad outcome respectively in order to solve these models under fuzzy environment a hybrid intelligent algorithm is designed by integrating numerical integration fuzzy simulation and genetic algorithm finally several numerical examples are given to illustrate the modeling idea and the effectiveness of the proposed algorithm

latent variable structural equation modeling with categorical data abstract structural equation modeling with latent variables is overviewed for situations involving a mixture of dichotomous ordered polytomous and continuous indicators of latent variables special emphasis is placed on categorical variables models in psychometrics econometrics and biometrics are interrelated via a general model due to muthen limited information least squares estimators and full information estimation are discussed an example is estimated with a model for a four wave longitudinal data set where dichotomous responses are related to each other and a set of independent variables via latent variables with a variance component structure

decision analysis based on fused double exponential possibility distributions abstract in this paper the possibility grades given by an expert are approximated by double possibility distributions called upper and lower possibility distributions to characterize uncertainty knowledge from this expert the upper and lower possibility distributions have some similarities to upper and lower approximations in rough set theory multi source knowledge from multiple experts is represented by a set of exponential possibility distributions based on the consistency index defined by the possibility measure of each pair of possibility distributions a fusion model is proposed to integrate multiple possibility distributions into a new one representing a refined knowledge as an application a portfolio selection problem with multiple experts is considered

a comment on some standard errors in item response theory in maximum likelihood estimation the standard error of the location parameter of the three parameter logistic model can be large due to inaccurate estimation of the lower asymptote thissen and wainer who demonstrated this effect suggested that the introduction of a prior distribution for the lower asymptote might alleviate the problems here it is demonstrated in some detail that the standard error of the location parameter can be made acceptably small in this way

some standard errors in item response theory the mathematics required to calculate the asymptotic standard errors of the parameters of three commonly used logistic item response models is described and used to generate values for some common situations it is shown that the maximum likelihood estimation of a lower asymptote can wreak havoc with the accuracy of estimation of a location parameter indicating that if one needs to have accurate estimates of location parameters say for purposes of test linking equating or computerized adaptive testing the sample sizes required for acceptable accuracy may be unattainable in most applications it is suggested that other estimation methods be used if the three parameter model is applied in these situations

generalized fiducial inference for logistic graded response models samejima s graded response model grm has gained popularity in the analyses of ordinal response data in psychological educational and health related assessment obtaining high quality point and interval estimates for grm parameters attracts a great deal of attention in the literature in the current work we derive generalized fiducial inference gfi for a family of multidimensional graded response model implement a gibbs sampler to perform fiducial estimation and compare its finite sample performance with several commonly used likelihood based and bayesian approaches via three simulation studies it is found that the proposed method is able to yield reliable inference even in the presence of small sample size and extreme generating parameter values outperforming the other candidate methods under investigation the use of gfi as a convenient tool to quantify sampling variability in various inferential procedures is illustrated by an empirical data analysis using the patient reported emotional distress data

sequential sampling designs for the two parameter item response theory model in optimal design research designs are optimized with respect to some statistical criterion under a certain model for the data the ideas from optimal design research have spread into various fields of research and recently have been adopted in test theory and applied to item response theory irt models in this paper a generalized variance criterion is used for sequential sampling in the two parameter irt model some general principles are offered to enable a researcher to select the best sampling design for the efficient estimation of item parameters

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

on the interval approximation of a fuzzy number the notion of an approximation interval of a fuzzy number is introduced it is the interval which fulfills two conditions in the first its width is equal to the width of a fuzzy number being approximated in the second the hamming distance between this interval and the approximated number is minimal the introduced notion is compared with the notion of expected interval of a fuzzy number known in literature

an optimal control problem governed by quasi linear variational inequalities an optimal control problem governed by quasi linear variational inequality is considered the cost functional to be minimized contains the solution of a quasi linear variational inequality to get the existence regularity and necessary condition for the optimal pair a new related control problem is introduced by proving the existence of an optimal pair to such a new problem the existence and regularity of the optimal pair to the original problem are obtained it turns out that the regularity obtained is sharp in general some necessary conditions of the optimal pair are also obtained

a possibilistic approach to selecting portfolios with highest utility score the mean variance methodology for the portfolio selection problem originally proposed by markowitz has been one of the most important research fields in modern finance in this paper we will assume that i each investor can assign a welfare or utility score to competing investment portfolios based on the expected return and risk of the portfolios and ii the rates of return on securities are modelled by possibility distributions rather than probability distributions we will present an algorithm of complexity o n3 for finding an exact optimal solution in the sense of utility scores to the n asset portfolio selection problem under possibility distributions

bayes modal estimation in item response models this article describes a bayesian framework for estimation in item response models with two stage prior distributions on both item and examinee populations strategies for point and interval estimation are discussed and a general procedure based on the em algorithm is presented details are given for implementation under one two and three parameter binary logistic irt models novel features include minimally restrictive assumptions about examinee distributions and the exploitation of dependence among item parameters in a population of interest improved estimation in a moderately small sample is demonstrated with simulated data

minimax d optimal designs for item response theory models various different item response theory irt models can be used in educational and psychological measurement to analyze test data one of the major drawbacks of these models is that efficient parameter estimation can only be achieved with very large data sets therefore it is often worthwhile to search for designs of the test data that in some way will optimize the parameter estimates the results from the statistical theory on optimal design can be applied for efficient estimation of the parameters a major problem in finding an optimal design for irt models is that the designs are only optimal for a given set of parameters that is they are locally optimal locally optimal designs can be constructed with a sequential design procedure in this paper minimax designs are proposed for irt models to overcome the problem of local optimality minimax designs are compared to sequentially constructed designs for the two parameter logistic model and the results show that minimax design can be nearly as efficient as sequentially constructed designs

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

portfolio selection based on upper and lower exponential possibility distributions in this paper two kinds of possibility distributions namely upper and lower possibility distributions are identified to reflect experts knowledge in portfolio selection problems portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems it can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution in addition a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems a numerical example of a portfolio selection problem is given to illustrate our proposed approaches

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

constrained fuzzy hierarchical analysis for portfolio selection under higher moments marginal impacts of assets on portfolio higher moments are characterized by triangular fuzzy numbers and then evaluated by fuzzy ranking procedures in order to assemble fuzzy reciprocal matrices that are needed for the constrained fuzzy analytic hierarchy process ahp methods the proposed methodology increases the scope for emphasizing objective quantitative measures thus alleviating the influence of subjective qualitative factors employing constrained fuzzy arithmetic during fuzzy ahp application produces greater precision and reliability compared with applications of the standard fuzzy arithmetic by reference to higher moments the investor is able to strategize portfolios so that there is a reduction not only in exposure to normal risk i e volatility but also to risk of asymmetry skewness and the risk of fat tails kurtosis the efficiency of the proposed approach is highlighted in the ability to handle investor preferences regarding higher moment risks more optimal values for a particular risk can be obtained if that risk is of more concern moreover in terms of obtaining portfolio diversification the method is shown to be more useful than conventional optimization models

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

conditional covariance structure of generalized compensatory multidimensional items some nonparametric dimensionality assessment procedures such as dimtest and detect use nonparametric estimates of item pair conditional covariances given an appropriately chosen subtest score as their basic building blocks such conditional covariances given some subtest score can be regarded as an approximation to the conditional covariances given an appropriately chosen unidimensional latent composite where the composite is oriented in the multidimensional test space direction in which the subtest score measures best in this paper the structure and properties of such item pair conditional covariances given a unidimensional latent composite are thoroughly investigated assuming a semiparametric irt modeling framework called a generalized compensatory model it is shown that such conditional covariances are highly informative about the multidimensionality structure of a test the theory developed here is very useful in establishing properties of dimensionality assessment procedures current and yet to be developed that are based upon estimating such conditional covariances in particular the new theory is used to justify the dimtest procedure because of the importance of conditional covariance estimation a new bias reducing approach is presented a byproduct of likely independent importance beyond the study of conditional covariances is a rigorous score information based definition of an item s and a score s direction of best measurement in the multidimensional test space

portfolio selection problems with random fuzzy variable returns this paper considers several portfolio selection problems including probabilistic future returns with ambiguous expected returns assumed as random fuzzy variables random fuzzy portfolio selection problems are formulated as nonlinear programming problems based on both stochastic and fuzzy programming approaches since there is no efficient solution method to solve these problems directly main problems are transformed into equivalent deterministic quadratic programming problems using probabilistic chance constraints possibility measure and fuzzy goals and their efficient solution methods to find a global optimal solution of each problem is constructed furthermore numerical examples of portfolio selection problems are provided to illustrate our proposed models and solution methods compared with several previous basic models and to show that our proposed model is a versatile model to be applicable to various unexpected conditions

a multi objective genetic algorithm for cardinality constrained fuzzy portfolio selection this paper presents a new procedure that extends genetic algorithms from their traditional domain of optimization to fuzzy ranking strategy for selecting efficient portfolios of restricted cardinality the uncertainty of the returns on a given portfolio is modeled using fuzzy quantities and a downside risk function is used to describe the investor s aversion to risk the fitness functions are based both on the value and the ambiguity of the trapezoidal fuzzy number which represents the uncertainty on the return the soft computing approach allows us to consider uncertainty and vagueness in databases and also to incorporate subjective characteristics into the portfolio selection problem we use a data set from the spanish stock market to illustrate the performance of our approach to the portfolio selection problem

on structural equation modeling with data that are not missing completely at random a general latent variable model is given which includes the specification of a missing data mechanism this framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data here missing completely at random is not a prerequisite for unbiased estimation in large samples as when using the traditional listwise or pairwise present data approaches the theory is connected with old and new results in the area of selection and factorial invariance it is pointed out that in many applications maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software such as lisrel and liscomp several sets of artifical data are generated within the general model framework the proposed estimator is compared to the two traditional ones and found superior

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures