testing a new theory of fechnerian scaling the case of auditory intensity discrimination recently dzhafarov and colonius psych bull rev 6 239 268 1999 proposed a theory that refines fechner s ideas of deriving the perceptual distance between stimuli from discriminability measures in the unidimensional case and generalizes it to multidimensional stimulus domains in this theory the existence of a fechnerian metric is based on testable assumptions about the shape of the psychometric functions thus same different psychometric functions 1 have to attain a single minimum at some point 2 must be locally symmetric around their minima and 3 must show the same degree of cuspidness or flatness along the stimulus continuum in the present investigation these assumptions were evaluated experimentally employing acoustical stimuli differing along one stimulus dimension intensity in a same different paradigm using the method of constant stimuli seven 1000 hz tones deviating from 0 to 2 1 db with respect to a standard were presented diotically to five observers for every

a new linear adaptive controller design analysis and performance the certainty equivalence and polynomial approach widely used for designing adaptive controllers leads to simple adaptive control designs that guarantee stability asymptotic error convergence and robustness but not necessarily good transient performance backstepping and tuning functions techniques on the other hand are used to design adaptive controllers that guarantee stability and good transient performance at the expense of a highly nonlinear controller in this paper we use elements from both design approaches to develop a new certainty equivalence based adaptive controller by combining backstepping based control law with a normalized adaptive law the new adaptive controller guarantees stability and performance as well as parametric robustness for the nonadaptive controller that are comparable with the tuning functions scheme without the use of higher order nonlinearities

acquiescent responding in balanced multidimensional scales and exploratory factor analysis personality tests often consist of a set of dichotomous or likert items these response formats are known to be susceptible to an agreeing response bias called acquiescence the common assumption in balanced scales is that the sum of appropriately reversed responses should be reasonably free of acquiescence however inter item correlation or covariance matrices can still be affected by the presence of variance due to acquiescence to analyse these correlation matrices we propose a method that is based on an unrestricted factor analysis and can be applied to multidimensional scales this method obtains a factor solution in which acquiescence response variance is isolated in an independent factor it is therefore possible without the potentially confounding effect of acquiescence to a examine the dominant factors related to content latent variables and b estimate participants factor scores on content latent variables this method which is illustrated by two empirical data examples has proved to be useful for improving the simplicity of the factor structure

analysis of dispersion of multinomial responses abstract in analogy to analysis of variance for linear models analyses of dispersion for loglinear models for multinomial responses are constructed the analyses which are based on the entropy and concentration measures are used to construct tests of independence and measures of association

quadratic prediction of factor scores factor scores are naturally predicted by means of their conditional expectation given the indicators y under normality this expectation is linear in y but in general it is an unknown function of y ii is discussed that under nonnormality factor scores can be more precisely predicted by a quadratic function of y

brief lq performance bounds for adaptive output feedback controllers for functionally uncertain nonlinear systems we consider functionally uncertain systems which can be written in an output feedback form where the nonlinearities are functions of the output only the uncertainty is described by a weighted l 2 norm about a nominal system and an approximate adaptive design is given which ensures output practical stability the main result requires knowledge of the weighted l 2 uncertainty level an upper bound on the lq performance of the output transient and the control input is derived where the cost penalises the output transient and the control effort on the time interval where the output lies outside the prescribed neighbourhood of zero to which we achieve convergence

robust adaptive asymptotic tracking of nonlinear systems with additive disturbance this note deals with the tracking control of multiple input multiple output mimo nonlinear parametric strict feedback systems in the presence of additive disturbances and parametric uncertainties for such systems c sup 0 robust adaptive controllers usually cannot ensure asymptotic tracking or even regulation in this work under the assumption the disturbances are c sup 2 with bounded time derivatives we present a c sup 0 robust adaptive control construction that guarantees the tracking error is asymptotically driven to zero

bias in estimation of misclassification rates when a simple random sample of size n is employed to establish a classification rule for prediction of a polytomous variable by an independent variable the best achievable rate of misclassification is higher than the corresponding best achievable rate if the conditional probability distribution is known for the predicted variable given the independent variable in typical cases this increased misclassification rate due to sampling is remarkably small relative to other increases in expected measures of prediction accuracy due to samplings that are typically encountered in statistical analysis

restricted multidimensional scaling models for asymmetric proximities restricted multidimensional scaling models bentler weeks 1978 allowing constraints on parameters are extended to the case of asymmetric data separate functions are used to model the symmetric and antisymmetric parts of the data the approach is also extended to the case in which data are presumed to be linearly related to squared distances examples of several models are provided using journal citation data possible extensions of the models are considered

on equivalence between a partial credit item and a set of independent rasch binary items given a masters partial credit item withn known step difficulties conditions are stated for the existence of a set of locally independent rasch binary items such that their raw score and the partial credit raw score have identical probability density functions the conditions are those for the existence ofn positive values with predetermined elementary symmetric functions and include the requirement that then step difficulties form an increasing sequence

on the relations among regular equal unique variances and image factor analysis models we investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model we show that the two models will give similar matrices of factor loadings if schneeweiss condition that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings holds furthermore we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from joreskog s image factor analysis model especially we discuss guttman s condition i e the number of variables increases without limit for the two models to agree in relation with the condition we have shown and conclude that schneeweiss condition is a generalization of guttman s condition some implications for practice are discussed

lower bounds to the reliabilities of factor score estimators under the general common factor model the reliabilities of factor score estimators might be of more interest than the reliability of the total score the unweighted sum of item scores in this paper lower bounds to the reliabilities of thurstone s factor score estimators bartlett s factor score estimators and mcdonald s factor score estimators are derived and conditions are given under which these lower bounds are equal the relative performance of the derived lower bounds is studied using classic example data sets the results show that estimates of the lower bounds to the reliabilities of thurstone s factor score estimators are greater than or equal to the estimates of the lower bounds to the reliabilities of bartlett s and mcdonald s factor score estimators

on the loss of information in conditional maximum likelihood estimation of item parameters in item response models of the rasch type fischer molenaar 1995 item parameters are often estimated by the conditional maximum likelihood cml method this paper addresses the loss of information in cml estimation by using the information concept of f information liang 1983 this concept makes it possible to specify the conditions for no loss of information and to define a quantification of information loss for the dichotomous rasch model the derivations will be given in detail to show the use of the f information concept for making comparisons for different estimation methods it is shown that by using cml for item parameter estimation some information is almost always lost but compared to jml joint maximum likelihood as well as to mml marginal maximum likelihood the loss is very small the reported efficiency in the use of information of cml to jml and to mml in several comparisons is always larger than 93 and in tests with a length of 20 items or more larger than 99

adaptive control and robustness in the gap metric we consider the construction of adaptive controllers for minimum phase linear systems that achieve nonzero robustness margins in the sense of the gap metric the gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties working in both and settings and within the framework of the nonlinear gap metric universal adaptive controllers are first given achieving stabilization for first order nominal plants and the results are then generalized to relative degree one nominal plants a notion of a semiuniversal control design is introduced which is the property that a bound on performance exists that is independent of the a priori known uncertainty level and a characterization is given for when semiuniversal designs outperform the class of memoryless controllers and the class of linear time invariant controllers robust semiuniversal adaptive control designs are given for nominal plants under the classical assumptions of adaptive control in both the and settings the results are applied throughout to explicit classes of unmodeled dynamics including the rohrs example

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

paradoxical results in multidimensional item response theory in multidimensional item response theory mirt it is possible for the estimate of a subject s ability in some dimension to decrease after they have answered a question correctly this paper investigates how and when this type of paradoxical result can occur we demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of linearly compensatory models maximum likelihood estimates are guaranteed to do so in light of these findings the appropriateness of multidimensional item response methods for assigning scores in high stakes testing is called into question

models and methods for the analysis of correlation coefficients abstract the normal distribution plays a very prominant role in statistics and in multivariate analysis the multinormal model is even more dominant than in the classical univariate or bivariate situations in this paper we show that the assumption of continuous multinormal observations can be relaxed in various ways for continuous multivariate analysis most of the existing large sample theory can be applied without assuming multivariate normality we also develop several discrete multinormal models the first one is the classical pearson model which results from discreticizing multinormal variables the second one is inspired by correspondence analysis and the third one by loglinear analysis the models are presented in terms of correlation coefficients and applied to the spearman model of factor analyses using an example from political science

constrained least squares estimators of oblique common factors an expression is given for weighted least squares estimators of oblique common factors constrained to have the same covariance matrix as the factors they estimate it is shown that if as in exploratory factor analysis the common factors are obtained by oblique transformation from the lawley rao basis the constrained estimators are given by the same transformation finally a proof of uniqueness is given

measuring latent quantities a distinction is proposed between measures and predictors of latent variables the discussion addresses the consequences of the distinction for the true score model the linear factor model structural equation models longitudinal and multilevel models and item response models a distribution free treatment of calibration and error of measurement is given and the contrasting properties of measures and predictors are examined

numerical computation of a certain dirichlet series attached to siegel modular forms of degree two the rankin convolution type dirichlet series df g s of siegel modular forms f and g of degree two which was introduced by kohnen and the second author is computed numerically for various f and g in particular we prove that the series df g s which share the same functional equation and analytic behavior with the spinor l functions of eigenforms of the same weight are not linear combinations of those in order to conduct these experiments a numerical method to compute the petersson scalar products of jacobi forms is developed and discussed in detail

coefficients alpha beta omega and the glb comments on sijtsma there are three fundamental problems in sijtsma psychometrika 2008 1 contrary to the name the glb is not the greatest lower bound of reliability but rather is systematically less than t mcdonald test theory a unified treatment erlbaum hillsdale 1999 2 we agree with sijtsma that when considering how well a test measures one concept is not appropriate but recommend t rather than the glb and 3 the end user needs procedures that are readily available in open source software

alpha dimension free and model based internal consistency reliability as pointed out by sijtsma in press coefficient alpha is inappropriate as a single summary of the internal consistency of a composite score better estimators of internal consistency are available in addition to those mentioned by sijtsma an old dimension free coefficient and structural equation model based coefficients are proposed to improve the routine reporting of psychometric internal consistency the various ways to measure internal consistency are also shown to be appropriate to binary and polytomous items

regression among factor scores structural equation models with latent variables are sometimes estimated using an intuitive three step approach here denoted factor score regression consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest in this simple example estimation of the structural parameter proceeds as follows first common factor models areseparately estimated for each latent variable second factor scores areseparately assigned to each latent variable based on the estimates third ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter we investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables it is demonstrated that the conventional approach to factor score regression performs very badly revised factor score regression using regression factor scores for the explanatory latent variables and bartlett scores for the response latent variables produces consistent estimators for all parameters

necessary conditions for mean square convergence of the best linear factor predictor several sufficient conditions are available for mean square convergence of factor predictors a necessary and sufficient condition is given in the heywood case with respect to confirmatory factor analysis this condition generalizes that of krijnen 2006 and performs better than a signal to noise type of condition schneeweiss mathes 1995

the asymptotic covariance matrix of maximum likelihood estimates in factor analysis the case of nearly singular matrix of estimates of unique variances this paper is concerned with the asymptotic covariance matrix acm of maximum likelihood estimates mles of factor loadings and unique variances when one element of mles of unique variances is nearly zero i e the matrix of mles of unique variances is nearly singular in this situation standard formulas break down we give explicit formulas for the acm of mles of factor loadings and unique variances that could be used even when an element of mles of unique variances is very close to zero we also discuss an alternative approach using the augmented information matrix under a nearly singular matrix of mles of unique variances and derive the partial derivatives of the alternative constraint functions with respect to the elements of factor loadings and unique variances 2000 elsevier science inc all rights reserved ams classification 62h25 62f12

robustness of the tuning functions adaptive backstepping design for linear systems we study robustness of the adaptive backstepping design with tuning functions for linear systems under assumptions on unmodeled dynamics and disturbances equal to those for certainty equivalence schemes we address an adaptive scheme not based on the certainty equivalence principle in the process of redesign for robustness we employ only leakage in the estimator we do not employ normalization neither static nor dynamic a fundamental difference between the tuning functions design and the certainty equivalence designs is that the controller in the former is inherently nonlinear while in the latter it is nonlinear only in the parameter estimate as a result achievable robustness results for the tuning functions scheme are not global but regional with a region of attraction inversely proportional to the size of the unmodeled dynamics the tracking error is proportional to the size of the uncertainties

robust continuous time adaptive control by parameter projection the problem of adaptive control of a continuous time plant of arbitrary relative degree in the presence of bounded disturbances as well as unmodeled dynamics is addressed the adaptation considered is the usual gradient update law with parameter projection the latter being the only robustness enhancement modification employed it is shown that if the unmodeled dynamics which consists of multiplicative as well as additive system uncertainty is small enough then all the signals in the closed loop system are bounded this shows that extra modifications are not necessary for robustness with respect to bounded disturbances and small unmodeled dynamics in the nominal case where unmodeled dynamics and disturbances are absent the asymptotic error in tracking a given reference signal is zero moreover the performance of the adaptive controller is also robust

robust model reference adaptive control we propose a new model reference adaptive control algorithm and show that it provides the robust stability of the resulting closed loop adaptive control system with respect to unmodeled plant uncertainties the robustness is achieved by using a relative error signal in combination with a dead zone and a projection in the adaptive law the extra a priori information needed to design the adaptive law are bounds on the plant parameters and an exponential bound on the impulse response of the inverse plant transfer function

tscale a new multidimensional scaling procedure based on tversky s contrast model tversky s contrast model of proximity was initially formulated to account for the observed violations of the metric axioms often found in empirical proximity data this set theoretic approach models the similarity dissimilarity between any two stimuli as a linear or ratio combination of measures of the common and distinctive features of the two stimuli this paper proposes a new spatial multidimensional scaling mds procedure called tscale based on tversky s linear contrast model for the analysis of generally asymmetric three way two mode proximity data we first review the basic structure of tversky s conceptual contrast model a brief discussion of alternative mds procedures to accommodate asymmetric proximity data is also provided the technical details of the tscale procedure are given as well as the program options that allow for the estimation of a number of different model specifications the nonlinear estimation framework is discussed as are the results of a modest monte carlo analysis two consumer psychology applications are provided one involving perceptions of fast food restaurants and the other regarding perceptions of various competitive brands of cola soft drinks finally other applications and directions for future research are mentioned

the greatest lower bound to the reliability of a test and the hypothesis of unidimensionality to assess the reliability of congeneric tests specifically designed reliability measures have been proposed this paper emphasizes that such measures rely on a unidimensionality hypothesis which can neither be confirmed nor rejected when there are only three test parts and will invariably be rejected when there are more than three test parts jackson and agunwamba s 1977 greatest lower bound to reliability is proposed instead although this bound has a reputation for overestimating the population value when the sample size is small this is no reason to prefer the unidimensionality based reliability firstly the sampling bias problem of the glb does not play a role when the number of test parts is small as is often the case with congeneric measures secondly glb and unidimensionality based reliability are often equal when there are three test parts and when there are more test parts their numerical values are still very similar to the extent that the bias problem of the greatest lower bound does play a role unidimensionality based reliability is equally affected although unidimensionality and reliability are often thought of as unrelated this paper shows that from at least two perspectives they act as antagonistic concepts a measure based on the same framework that led to the greatest lower bound is discussed for assessing how close is a set of variables to unidimensionality it is the percentage of common variance that can be explained by a single factor an empirical example is given to demonstrate the main points of the paper

latent curve analysis as a method for representing development latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth maximum likelihood parameter estimates and associated asymptotic tests follow directly these procedures may be viewed as an alternative to standard repeated measures anova and to first order auto regressive methods as formulated the model encompasses cohort sequential designs and allow for period or practice effects a numerical illustration using data initially collected by nesselroade and baltes is presented

on deriving the inverse of a sum of matrices available expressions are reviewed and new ones derived for the inverse of the sum of two matrices one of them being nonsingular particular attention is given to text bf a text bf ubv 1 where textbf a is nonsingular and textbf u b and textbf v may be rectangular generalized inverses of textbf a textbf ubv are also considered several statistical applications are discussed

prediction functions for categorical panel data prediction of categorical responses in panel studies is considered prediction functions based on general conditional log linear models are investigated for statistical properties both from a population perspective and a sampling perspective problems such as existence and uniqueness of optimal prediction functions are addressed and basic properties of measures of prediction quality are examined estimation consistency and asymptotic normality are studied for the proposed parameter estimates and measures of prediction quality

paradoxical results and item bundles hooker finkelman and schwartzman psychometrika 2009 in press defined a paradoxical result as the attainment of a higher test score by changing answers from correct to incorrect and demonstrated that such results are unavoidable for maximum likelihood estimates in multidimensional item response theory the potential for these results to occur leads to the undesirable possibility of a subject s best answer being detrimental to them this paper considers the existence of paradoxical results in tests composed of item bundles when compensatory models are used we demonstrate that paradoxical results can occur when bundle effects are modeled as nuisance parameters for each subject however when these nuisance parameters are modeled as random effects or used in a bayesian analysis it is possible to design tests comprised of many short bundles that avoid paradoxical results and we provide an algorithm for doing so we also examine alternative models for handling dependence between item bundles and show that using fixed dependency effects is always guaranteed to avoid paradoxical results

cronbach s α revelle s β and mcdonald s ωh their relations with each other and two alternative conceptualizations of reliability we make theoretical comparisons among five coefficients cronbach s revelle s mcdonald s h and two alternative conceptualizations of reliability though many end users and psychometricians alike may not distinguish among these five coefficients we demonstrate formally their nonequivalence specifically whereas there are conditions under which and h are equivalent to each other and to one of the two conceptualizations of reliability considered here we show that equality with this conceptualization of reliability and between and h holds only under a highly restrictive set of conditions and that the conditions under which equals h are only somewhat more general the nonequivalence of and h suggests that important information about the psychometric properties of a scale may be missing when scale developers and users only report as is almost always the case

on green best linear composites with a specified structure and oblique estimates of factor scores green solved the problem of least squares estimation of several criteria subject to the constraint that the estimates have an arbitrary fixed covariance or correlation matrix in the present paper an omission in green s proof is discussed and resolved furthermore it is shown that some recently published solutions for estimating oblique factor scores are special cases of green s solution for the case of fixed covariance matrices

conditions for factor in determinacy in factor analysis the subject of factor indeterminacy has a vast history in factor analysis guttman 1955 lederman 1938 wilson 1928 it has lead to strong differences in opinion steiger 1979 the current paper gives necessary and sufficient conditions for observability of factors in terms of the parameter matrices and a finite number of variables five conditions are given which rigorously define indeterminacy it is shown that un observable factors are in determinate specifically the indeterminacy proof by guttman is extended to heywood cases the results are illustrated by two examples and implications for indeterminacy are discussed

weil representations associated with finite quadratic modules to any finite quadratic module that is a finite abelian group together with a non degenerate quadratic form it is possible to associate a representation of mathrm mp 2 mathbb z the metaplectic cover of the modular group this representation is usually referred to as a weil representation and our main result is a general explicit formula for its matrix coefficients this result completes earlier work by scheithauer in the case when the representation factors through mathrm sl 2 mathbb z furthermore our formula is given in a such a way that it is easy to implement efficiently on a computer

on separable tests correlated priors and paradoxical results in multidimensional item response theory this paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee we demonstrate that when three or more ability dimensions are being used paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent in the case of separable tests we demonstrate the mathematical causes of paradoxical results develop a computationally feasible means to check whether they can occur in any given test and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them

on the construction of all factors of the model for factor analysis a construction method is given for all factors that satisfy the assumptions of the model for factor analysis including partially determined factors where certain error variances are zero various criteria for the seriousness of indeterminacy are related it is shown that green s 1976 conjecture holds for a linear factor predictor the mean squared error of prediction is constant over all possible factors a simple and general geometric interpretation of factor indeterminacy is given on the basis of the distance between multiple factors it is illustrated that variable elimination can have a large effect on the seriousness of factor indeterminacy a simulation study reveals that if the mean square error of factor prediction equals 5 then two thirds of the persons are correctly selected by the best linear factor predictor

computations of siegel modular forms of genus two we explain the basic notions and theorems for doing computations in the theory of siegel modular forms of degree two on the full modular group and of even weight this synopsis concludes with a handy and computationally realistic algorithm for tabulating the fourier coefficients of such forms and the euler factors of their spinor zeta functions in the second part of this paper we present and discuss some of the results of actual computations which we performed following this algorithm we point out two theoretically striking phenomena that are implied by the results of these computations

computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis in the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum trace communality solution in factor analysis have been developed in this paper convergence properties of these methods are examined instead of using lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be gramian whereas computational pitfalls for two methods suggested by woodhouse and jackson can be constructed it is shown that a slightly modified version of one method suggested by bentler and woodward can safely be applied to any set of data a uniqueness proof for the solution desired is offered

a generalization of kristofs theorem on the trace of certain matrix products kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form x 1 hat gamma 1 x 2 hat gamma 2 cdots x n hat gamma n where the matrices hat gamma i are diagonal and fixed and thex i vary unrestrictedly and independently over the set of orthonormal matrices the theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints the present paper contains a generalization of kristof s theorem to the case where thex i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank the generalized theorem contains the schwarz inequality as a special case various examples from the psychometric literature illustrating the practical use of the generalized theorem are discussed

some new results on correlation preserving factor scores prediction methods anderson and rubin and mcdonald have proposed a correlation preserving method of factor scores prediction which minimizes the trace of a residual covariance matrix for variables green has proposed a correlation preserving method which minimizes the trace of a residual covariance matrix for factors krijnen wansbeek and ten berge have proposed minimizing the determinant rather than the trace of the latter covariance matrix and offered an iterative procedure to that effect in the present paper it is shown that the iterative procedure can be replaced by a closed form solution when all unique variances are strictly positive this solution is the same as mcdonald s the solution coincides with green s solution in certain special cases for instance when the factors are orthogonal

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

dispersion of categorical variables and penalty functions derivation estimation and comparability abstract measures of dispersion for categorical random variables based on penalty functions play a central role in establishing relevant measures of association between such variables the literature concerning these measures provides little systematic treatment of such aspects of these measures as comparability efficient estimation and large sample properties this article provides a systematic and rigorous construction of dispersion measures based on penalty functions efficient estimation procedures and asymptotic properties of estimates are examined conditions from majorization theory that ensure a meaningful comparability of dispersion measures based on penalty functions are discussed a large class of familiar dispersion measures is then given a new interpretation using these conditions

some results on mean square error for factor score prediction for the confirmatory factor model a series of inequalities is given with respect to the mean square error mse of three main factor score predictors the eigenvalues of these mse matrices are a monotonic function of the eigenvalues of the matrix p 1 2 p p 1 p 1 2 this matrix increases with the number of observable variables p a necessary and sufficient condition for mean square convergence of predictors is divergence of the smallest eigenvalue of p or equivalently divergence of signal to noise schneeweiss mathes 1995 the same condition is necessary and sufficient for convergence to zero of the positive definite mse differences of factor predictors convergence to zero of the distance between factor predictors and convergence to the unit value of the relative efficiencies of predictors various illustrations and examples of the convergence are given as well as explicit recommendations on the problem of choosing between the three main factor score predictors

exact tracking using backstepping control design and high order sliding modes in this technical note a controller ensuring exponential exact tracking in the presence of matched and unmatched disturbances for the nonlinear systems in the block controllable form is proposed the controller is designed using the backstepping procedure and combines the feedback linearization technique with the high order sliding modes the matched and unmatched disturbances are compensated by the injection of a continuous term generated by the robust exact high order sliding modes differentiator the obtained control law is differentiable and can be applied directly to the system simulations verify the performance of the proposed controller

observer design for uncertain nonlinear systems with unmodeled dynamics this paper is concerned with the observer design problem for a class of multi input multi output nonlinear systems with the unmodeled dynamics unknown parameters and external disturbance a dynamic signal which can dominate the unmodeled dynamics is firstly constructed then two types of observer schemes that is adaptive observer and robust observer are respectively proposed the observation error in the two schemes can be made arbitrarily small by choosing the appropriate design parameters an illustrative example is provided to demonstrate the validity of the proposed design methods

adaptive robust stabilisation of uncertain nonlinear dynamical systems an improved backstepping approach abstractthe main purpose of this paper is to propose a design approach by which some simple adaptive robust controllers can be synthesised for a class of uncertain nonlinear dynamical systems which can be transformed into uncertain strict feedback nonlinear systems in this paper an improved backstepping design approach is presented to synthesising a class of continuous adaptive robust state feedback controllers with a rather simple structure the improved backstepping design approach can avoid the repeated differentiation problem which appears in using the conventional backstepping algorithm in particular it is not required to know the nonlinear upper bound functions of uncertainties in the light of the presented approach the state feedback controllers can be constructed to be linear in the state with the time varying control gains which can be self tuned by the adaptive laws similar to the conventional backstepping algorithm the improved backstepping approach can be extended to a rather large cl

in spite of indeterminacy many common factor score estimates yield an identical reproduced covariance matrix it was investigated whether commonly used factor score estimates lead to the same reproduced covariance matrix of observed variables this was achieved by means of schonemann and steiger s 1976 regression component analysis since it is possible to compute the reproduced covariance matrices of the regression components corresponding to different factor score estimates it was shown that thurstone s ledermann s bartlett s anderson rubin s mcdonald s krijnen wansbeek and ten berge s as well as takeuchi yanai and mukherjee s score estimates reproduce the same covariance matrix in contrast harman s ideal variables score estimates lead to a different reproduced covariance matrix