a non hyponormal operator generating stieltjes moment sequences abstract a linear operator s in a complex hilbert space h for which the set d s of its c vectors is dense in h and s n f 2 n 0 is a stieltjes moment sequence for every f d s is said to generate stieltjes moment sequences it is shown that there exists a closed non hyponormal operator s which generates stieltjes moment sequences what is more d s is a core of any power s n of s this is established with the help of a weighted shift on a directed tree with one branching vertex the main tool in the construction comes from the theory of indeterminate stieltjes moment sequences as a consequence it is shown that there exists a non hyponormal composition operator in an l 2 space over a finite measure space which is injective paranormal and which generates stieltjes moment sequences the independence assertion of barry simon s theorem which parameterizes von neumann extensions of a closed real symmetric operator with deficiency indices 1 1 is shown to be false

gaps of operators via rank one perturbations in this note we consider rank one perturbations of weighted shifts to examine distinctions between various sorts of weak hyponormalities including p hyponormality p paranormality and absolute p paranormality our examples enable us to add to the small collection of examples that exhibit the gaps between these classes

composition operators with weak hyponormality there are many operator classes that are weaker than p hyponormal these include p quasihyponormal absolute p paranormal p paranormal normaloid and spectraloid in this note we discuss measure theoretic composition operators in these classes

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

enumeration and simulation methods for 0 1 matrices with given marginals data in the form of zero one matrices where conditioning on the marginals is relevant arise in diverse fields such as social networks and ecology directed graphs constitute an important special case an algorithm is given for the complete enumeration of the family of all zero one matrices with given marginals and with a prespecified set of cells with structural zero entries complete enumeration is computationally feasible only for relatively small matrices therefore a more useable monte carlo simulation method for the uniform distribution over this family is given based on unequal probability sampling and ratio estimation this method is applied to testing reciprocity of choices in social networks

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

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

extensions of the partial credit model the partial credit model developed by masters 1982 is a unidimensional latent trait model for responses scored in two or more ordered categories in the present paper some extensions of the model are presented first a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters secondly two statistical tests for evaluating model fit are presented the former test has power against violation of the assumption about the ability distribution the latter test offers the possibility of identifying specific items that do not fit the model

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

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

weak containment and tensor products of group representations ii let g be a locally compact group and g the set of equivalence classes of irreducible unitary representations of g equipped with the jacobson topology is called the dual space of g in this paper we continue our study of problems related to supports in g of tensor products of representations of g it is well known that ifn and are finite dimensional representations of g and g denotes the conjugate representation of q then the tensor product n contains the trivial one dimensional representation 1g if and only ifg and q have a common subrepresentation can this be generalized to the case where n and are arbitrary and containment is replaced by weak containment this question was first discussed by fell 6 and has been taken up in 4 and 21 the object of sect 1 is to add some further results concerning this problem our main results are the following we show that for a polynomially growing discrete group g and any two unitary representations n and of g 1 is weakly contained in nqff i e 1 suppn if and only if suppnnsupp04 0 this extends the corresponding result for locally nilpotent discrete groups in 21 if g is a motion group and n e we give a criterion on n to satisfy that laesuppn is equivalent to ff n for all ed

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

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

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

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

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

partially normal composition operators relevant to weighted directed trees abstract we characterize properties including p hyponormality and p paranormality for composition operators arising from measurable transformations on weighted directed trees in terms of a test at each node v involving the masses at nodes in a neighborhood of nodes near v also constructed are certain graphs e universal for p hyponormality in that the neighborhood of any node in any graph yielding a p hyponormal composition operator is a certain limit of neighborhoods in e these results are applied to some examples with particularly regular graph structures

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

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

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

an efficient mcmc algorithm to sample binary matrices with fixed marginals uniform sampling of binary matrices with fixed margins is known as a difficult problem two classes of algorithms to sample from a distribution not too different from the uniform are studied in the literature importance sampling and markov chain monte carlo mcmc existing mcmc algorithms converge slowly require a long burn in period and yield highly dependent samples chen et al developed an importance sampling algorithm that is highly efficient for relatively small tables for larger but still moderate sized tables 300 30 chen et al s algorithm is less efficient this article develops a new mcmc algorithm that converges much faster than the existing ones and that is more efficient than chen s algorithm for large problems its stationary distribution is uniform the algorithm is extended to the case of square matrices with fixed diagonal for applications in social network theory

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

towards power and sample size calculations for the comparison of two groups of patients with item response theory models evaluation of patient reported outcomes pro is increasingly performed in health sciences pro differs from other measurements because such patient characteristics cannot be directly observed item response theory irt is an attractive way for pro analysis however in the framework of irt sample size justification is rarely provided or ignores the fact that pro measures are latent variables with the use of formulas developed for observed variables it might therefore be inappropriate and might provide inadequately sized studies the objective was to develop valid sample size methodology for the comparison of pro in two groups of patients using irt the proposed approach takes into account questionnaire s items parameters the difference of the latent variables means and its variance whose derivation is approximated using cramer rao bound crb we also computed the associated power we realized a simulation study taking into account sample size number of items and value of the group effect we compared power obtained from crb with the one obtained from simulations sim and with the power based on observed variables obs for a given sample size powers using crb and sim were similar and always lower than obs we observed a strong impact of the number of items for crb and sim the power increasing with the questionnaire s length but not for obs in the context of latent variables it seems important to use an adapted sample size formula because the formula developed for observed variables seems to be inadequate and leads to an underestimated study size

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

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