positive loadings and factor correlations from positive covariance matrices in many instances it is reasonable to assume that the population covariance matrix has positive elements this assumption implies for the single factor analysis model that the loadings and regression weights for best linear factor prediction are positive for the multiple factor analysis model where each variable loads on a single factor and a hierarchical factor model it implies that the loadings and the factor correlations are positive for the latter model it also implies that the regression weights for first and second order factor prediction are positive

discrete time stochastic adaptive control this paper establishes global convergence of a stochastic adaptive control algorithm for discrete time linear systems it is shown that with probability one the algorithm will ensure the system inputs and outputs are sample mean square bounded and the conditional mean square output tracking error achieves its global minimum possible value for linear feedback control thus asymptotically the adaptive control algorithm achieves the same performance as could be achieved if the system parameters were known

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

identifiability of factor analysis some results and open problems abstract identifiability of the factor analysis model is discussed and some recent results and their relation to previous work are surveyed sufficient conditions for local identifiability are presented a counterexample shows that these conditions are not necessary in general a simple counting rule for local identifiability of the factor analysis model is given generically finally some open problems are formulated

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

parameter identification of wiener systems with discontinuous nonlinearities abstract the paper deals with modeling and parameter identification of wiener type nonlinear dynamic systems having discontinuous asymmetric piecewise linear characteristics with preloads and dead zones multiple application of a decomposition technique provides a special form of static nonlinearity description its incorporation into the wiener model leads to an input output equation where all the model parameters are separated and can be estimated iteratively using input output data and internal variable estimates more illustrative examples are included to demonstrate the feasibility of the proposed approach

minimum modelling retrospective cost adaptive control of uncertain hammerstein systems using auxiliary nonlinearities we augment retrospective cost adaptive control rcac with auxiliary nonlinearities to address a command following problem for uncertain hammerstein systems with possibly non monotonic input nonlinearities we assume that only one markov parameter of the linear plant is known and that the input nonlinearity is uncertain auxiliary nonlinearities are used within rcac to create a globally non decreasing composite input nonlinearity the required modelling information for the input nonlinearity includes the intervals of monotonicity as well as values of the nonlinearity that determine overlapping segments of the range of the nonlinearity within each interval of monotonicity

modeling and parameter identification of systems with multisegment piecewise linear characteristics this paper deals with the modeling and parameter identification of nonlinear systems having multi segment piecewise linear characteristics the decomposition of the corresponding mapping provides a new form of multi segment nonlinearity representation leading to an output equation where all the parameters to be estimated are separated hence an iterative method with internal variable estimation can be applied for parameter identification using input output data records the only required a priori knowledge of the nonlinear characteristic represents the limits for the domain partition the proposed model of given static nonlinearity is also incorporated into the hammerstein model examples of parameter identification for static and dynamic systems with multi segment piecewise linear characteristics are presented

generic global indentification in factor analysis abstract the paper proves global indentification of the unique variances in factor analysis for almost all parameter points if the number of factors is smaller than the ledermann bound it also shows how to compute using a closed form representation the second solution in the case of six variables and three factors

lord wingersky algorithm version 2 0 for hierarchical item factor models with applications in test scoring scale alignment and model fit testing lord and wingersky s appl psychol meas 8 453 461 1984 recursive algorithm for creating summed score based likelihoods and posteriors has a proven track record in unidimensional item response theory irt applications extending the recursive algorithm to handle multidimensionality is relatively simple especially with fixed quadrature because the recursions can be defined on a grid formed by direct products of quadrature points however the increase in computational burden remains exponential in the number of dimensions making the implementation of the recursive algorithm cumbersome for truly high dimensional models in this paper a dimension reduction method that is specific to the lord wingersky recursions is developed this method can take advantage of the restrictions implied by hierarchical item factor models e g the bifactor model the testlet model or the two tier model such that a version of the lord wingersky recursive algorithm can operate on a dramatically reduced set of quadrature points for instance in a bifactor model the dimension of integration is always equal to 2 regardless of the number of factors the new algorithm not only provides an effective mechanism to produce summed score to irt scaled score translation tables properly adjusted for residual dependence but leads to new applications in test scoring linking and model fit checking as well simulated and empirical examples are used to illustrate the new applications

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

direct schmid leiman transformations and rank deficient loadings matrices the schmid leiman s l psychometrika 22 53 61 1957 transformation is a popular method for conducting exploratory bifactor analysis that has been used in hundreds of studies of individual differences variables to perform a two level s l transformation it is generally believed that two separate factor analyses are required a first level analysis in which k obliquely rotated factors are extracted from an observed variable correlation matrix and a second level analysis in which a general factor is extracted from the correlations of the first level factors in this article i demonstrate that the s l loadings matrix is necessarily rank deficient i then show how this feature of the s l transformation can be used to obtain a direct s l solution from an unrotated first level factor structure next i reanalyze two examples from mansolf and reise multivar behav res 51 698 717 2016 to illustrate the utility of best fitting s l rotations when gauging the ability of hierarchical factor models to recover known bifactor structures finally i show how to compute direct bifactor solutions for non hierarchical bifactor structures an online supplement includes r code to reproduce all of the analyses that are reported in the article

nonparametric identification of hammerstein systems a discrete time nonlinear hammerstein system is identified and the correlation and frequency domain methods for identification of its linear subsystem are presented the main results concern the estimation of the nonlinear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data it is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable pointwise as well as global consistencies are established for lipschitz characteristics the rate of the convergence in probability is o n sup 1 3

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

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

a general structural equation model with dichotomous ordered categorical and continuous latent variable indicators a structural equation model is proposed with a generalized measurement part allowing for dichotomous and ordered categorical variables indicators in addition to continuous ones a computationally feasible three stage estimator is proposed for any combination of observed variable types this approach provides large sample chi square tests of fit and standard errors of estimates for situations not previously covered two multiple indicator modeling examples are given one is a simultaneous analysis of two groups with a structural equation model underlying skewed likert variables the second is a longitudinal model with a structural model for multivariate probit regressions

discrete time adaptive control of linear dynamic systems with a two segment piecewise linear asymmetric nonlinearity in this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a two segment piecewise linear asymmetric nonlinearity followed by a linear system a switching gain sequence is introduced to make the parameter identification time invariant the algorithm will ensure that the closed loop system is globally convergent and stable for both the deterministic and stochastic cases

on estimation of a class of nonlinear systems by the kernel regression estimate the estimation of a multiple input single output discrete hammerstein system is studied such a system contains a nonlinear memoryless subsystem followed by a dynamic linear subsystem the impulse response of the dynamic linear subsystem is obtained by the correlation method the main results concern the estimation of the nonlinear memoryless subsystem no conditions are imposed on the functional form of the nonlinear subsystem and the nonlinearity is recovered using the kernel regression estimate the distribution free pointwise and global convergence of the estimate is demonstrated that is no conditions are imposed on the input distribution and convergence is proven for virtually all nonlinearities the rates of pointwise as well as global convergence are obtained for all input distributions and for lipschitz type nonlinearities

on the relationship between the higher order factor model and the hierarchical factor model the relationship between the higher order factor model and the hierarchical factor model is explored formally we show that the schmid leiman transformation produces constrained hierarchical factor solutions using a generalized schmid leiman transformation and its inverse we show that for any unconstrained hierarchical factor model there is an equivalent higher order factor model with direct effects loadings on the manifest variables from the higher order factors therefore the class of higher order factor models without direct effects of higher order factors is nested within the class of unconstrained hierarchical factor models in light of these formal results we discuss some implications for testing the higher order factor model and the issue of general factor an interesting aspect concerning the efficient fitting of the higher order factor model with direct effects is noted

cfa models with a general factor and multiple sets of secondary factors we propose a class of confirmatory factor analysis models that include multiple sets of secondary or specific factors and a general factor the general factor accounts for the common variance among manifest variables whereas multiple sets of secondary factors account for the remaining source specific dependency among subsets of manifest variables a special case of the model is further proposed which constrains the specific factor loadings to be proportional to the general factor loadings this proportional model substantially reduces the number of model parameters while preserving the essential structure of the general model furthermore the proportional model allows for the interpretation of latent variables as the expected values of the observed manifest variables decomposition of the variances and the inclusion of interactions similar to generalizability theory we provide two applications to illustrate the utility of the proposed class of models

nonmetric maximum likelihood multidimensional scaling from directional rankings of similarities a maximum likelihood estimation procedure is developed for multidimensional scaling when dis similarity measures are taken by ranking procedures such as the method of conditional rank orders or the method of triadic combinations the central feature of these procedures may be termed directionality of ranking processes that is rank orderings are performed in a prescribed order by successive first choices those data have conventionally been analyzed by shepard kruskal type of nonmetric multidimensional scaling procedures we propose as a more appropriate alternative a maximum likelihood method specifically designed for this type of data a broader perspective on the present approach is given which encompasses a wide variety of experimental methods for collecting dissimilarity data including pair comparison methods such as the method of tetrads and the pick m method of similarities an example is given to illustrate various advantages of nonmetric maximum likelihood multidimensional scaling as a statistical method at the moment the approach is limited to the case of one mode two way proximity data but could be extended in a relatively straightforward way to two mode two way two mode three way or even three mode three way data under the assumption of such models as indscal or the two or three way unfolding models

modeling within subject dependencies in ordinal paired comparison data this paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments it is argued that a core assumption of latent class choice models independence of individual decisions may not be well suited for the analysis of paired comparison data instead the analysis and interpretation of paired comparison data may be much simplified by allowing for within person dependencies that result from repeated evaluations of the same options in different pairs moreover by relating dependencies among the individual level responses to in consistencies in the judgmental process we show that the proposed graded paired comparison models reduce to ranking models under certain conditions three applications are presented to illustrate the approach

reconstruction of complex obstacles with generalized impedance boundary conditions from far field data this paper is concerned with the inverse problem of scattering of time harmonic acoustic plane waves from a complex obstacle in the sense that a so called generalized impedance boundary condition gibc is satisfied on the boundary of the obstacle the factorization method is established to reconstruct the complex obstacle from the far field data at a fixed frequency numerical examples are also provided to illustrate the practicability of the inversion algorithm

nonparametric estimation of nonlinear dynamic systems using semirecursive regression estimates abstract in the paper we apply semirecursive nonparametric estimation techniques for the estimation of dynamic systems we investigate in detail the estimation of hammerstein dynamic systems using kernel and partitioning regression estimates in particular we propose estimation algorithms and study their convergence for all distributions of the data

recursive identification of hammerstein systems with discontinuous nonlinearities containing dead zones this note deals with the recursive parameter identification of hammerstein systems with discontinuous nonlinearities i e two segment piecewise linear with dead zones and preloads a special form of the hammerstein model with this type of nonlinearity is incorporated into the recursive least squares identification scheme supplemented with the estimation of model internal variables the proposed method is illustrated by examples

simultaneous factor analysis of dichotomous variables in several groups a new method is proposed for a simultaneous factor analysis of dichotomous responses from several groups of individuals the method makes it possible to compare factor loading pattern factor variances and covariances and factor means over groups the method uses information from first and second order proportions and estimates the model by generalized least squares hypotheses regarding different degrees of invariance over groups may be evaluated by a large sample chi square test

on modified green functions in exterior problems for the helmholtz equation the question of non uniqueness in boundary integral equation formulations of exterior problems for the helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the green function the present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of coefficients of the added terms that is optimal in the sense of minimizing the least squares difference between the modified and exact green functions

confidence regions for indscal using the jackknife and bootstrap techniques bootstrap and jackknife techniques are used to estimate ellipsoidal confidence regions of group stimulus points derived from indscal the validity of these estimates is assessed through monte carlo analysis asymptotic estimates of confidence regions based on a multiscale solution are also evaluated our findings suggest that the bootstrap and jackknife techniques may be used to provide statements regarding the accuracy of the relative locations of points in space our findings also suggest that multiscale asymptotic estimates of confidence regions based on small samples provide an optimistic view of the actual statistical reliability of the solution

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

brief paper discrete time adaptive control of linear systems with preload nonlinearity in this note a method is presented for doing discrete time adaptive control of a nonlinear system which is given by a cascade connection of a preload nonlinearity followed by a linear system it is shown that the algorithm will ensure that the closed loop system is globally convergent with a specific residue and stable for both the deterministic and stochastic cases

parameter identification of wiener systems with multisegment piecewise linear nonlinearities the paper deals with the identification of wiener systems having multisegment piecewise linear nonlinearities a special form of nonlinearity representation is used in the wiener system description the resulting output equation contains the least possible number of parameters required for the blocks of given system the proposed iterative method enables simultaneous estimation of both the linear block parameters and all the parameters characterizing the nonlinearity i e the slopes of linear segments and the constants determining the partition of domain limits for the constants are the only a priori knowledge required

global identification of nonlinear hammerstein systems by recursive kernel approach abstract in this paper we discuss identification of hammerstein systems by the recursive kernel regression estimate we propose the identification algorithm and study its global convergence and the rate of convergence

partial identification of latent correlations with binary data the tetrachoric correlation is a popular measure of association for binary data and estimates the correlation of an underlying normal latent vector however when the underlying vector is not normal the tetrachoric correlation will be different from the underlying correlation since assuming underlying normality is often done on pragmatic and not substantial grounds the estimated tetrachoric correlation may therefore be quite different from the true underlying correlation that is modeled in structural equation modeling this motivates studying the range of latent correlations that are compatible with given binary data when the distribution of the latent vector is partly or completely unknown we show that nothing can be said about the latent correlations unless we know more than what can be derived from the data we identify an interval constituting all latent correlations compatible with observed data when the marginals of the latent variables are known also we quantify how partial knowledge of the dependence structure of the latent variables affect the range of compatible latent correlations implications for tests of underlying normality are briefly discussed

hammerstein system identification by non parametric regression estimation a discrete time multiple input non linear hammerstein system is identified the dynamical subsystem is recovered using the standard correlation method the main results concern estimation of the non linear memoryless subsystem no conditions concerning the functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is given the algorithm is simply a non parametric kernel estimate of the regression function calculated from the dependent data it is shown that the algorithm converges to the characteristic of the subsystem in the pointwise as well as the global sense for sufficiently smooth characteristics the rate of convergence is o n 1 2 d in probability where d is the dimension of the input variable

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

the two dimensional direct and inverse scattering problems with generalized oblique derivative boundary condition consider the two dimensional exterior problem for the helmholtz equation with a generalized oblique derivative boundary condition which arises in some new scattering problems such as the scattering of tidal waves by islands under suitable assumptions different from the well studied scattering problems with dirichlet neumann and impedance boundary conditions the boundary condition in our new model involves a linear combination of the normal and tangential derivatives of the wave field with complex coefficient compared with the classical scattering models the tangential derivative on the obstacle boundary leads to some essential differences such as the symmetric property of the green function and the reciprocity principle of the scattering data both the direct and inverse scattering problems are studied in this paper first based on the lax phillips method we show the unique solvability of the direct scattering problem and the analyticity of the solution on the wave number second we investigate

commentary on coefficient alpha a cautionary tale the general use of coefficient alpha to assess reliability should be discouraged on a number of grounds the assumptions underlying coefficient alpha are unlikely to hold in practice and violation of these assumptions can result in nontrivial negative or positive bias structural equation modeling was discussed as an informative process both to assess the assumptions underlying coefficient alpha and to estimate reliability

identification of nonlinear systems using a piecewise linear hammerstein model abstract in the paper a method for nonlinear system identification is proposed it is based on a piecewise linear hammerstein model which is linear in the parameters the model and the identification algorithm are adapted to allow the parameter identification in the presence of a special form of the excitation signal the identification method is derived from a recursive least squares algorithm which is properly adapted to take into account the proposed model structure and the properties of the identification signal the applicability of the approach is illustrated by an example in which a discontinuous nonlinear static function is connected to a dynamic block

parameter identification of discontinuous hammerstein systems the paper deals with the parameter identification of hammerstein systems having discontinuous asymmetric nonlinearities two segment piecewise linear with preload and dead zone application of a simple decomposition technique provides a special form of hammerstein model with a minimum number of parameters the identification is carried out with only one record of measured input output data despite the dead zone to demonstrate the feasibility of the identification method some illustrative examples are included

thurstonian modeling of ranking data via mean and covariance structure analysis although thurstonian models provide an attractive representation of choice behavior they have not been extensively used in ranking applications since only recently efficient estimation methods for these models have been developed these however require the use of special purpose estimation programs which limits their applicability here we introduce a formulation of thurstonian ranking models that turns an idiosyncratic estimation problem into an estimation problem involving mean and covariance structures with dichotomous indicators well known standard solutions for the latter can be readily applied to this specific problem and as a result any thurstonian model for ranking data can be fitted using existing general purpose software for mean and covariance structure analysis although the most popular programs for covariance structure analysis e g lisrel and eqs cannot be presently used to estimate thurstonian ranking models other programs such as mecosa already exist that can be straightforwardly used to estimate these models

a maximum likelihood method for fitting the wandering vector model after introducing some extensions of a recently proposed probabilistic vector model for representing paired comparisons choice data an iterative procedure for obtaining maximum likelihood estimates of the model parameters is developed the possibility of testing various hypotheses by means of likelihood ratio tests is discussed finally the algorithm is applied to some existing data sets for illustrative purposes

latent variable models for ordered categorical data abstract the multivariate analysis of ordered categorical data is an important growth point in statistics especially as applied to the social sciences this paper is concerned with the situation in which the associations between a set of categorical variables are assumed to arise from their dependence on a small number of latent variables the problem of modelling this relationship is first posed in very general terms and then specialized to particular cases for which statistical methods are available or in course of development such models can be viewed as tools for data reduction or for scaling and both aspects are reviewed the possible relevance of the method in economics and their relationship to other methods for categorical variables is briefly discussed

global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation an improved exponential bound on the l sub 1 error for the recursive kernel regression estimates is derived it is shown using the martingale device that weak strong and complete l sub 1 consistencies are equivalent consequently the conditions on a certain smoothing sequence are necessary and sufficient for strong l sub 1 consistency of the recursive kernel regression estimate the rates of global convergence are also given obtained results are applied to recursive classification rules and to nonlinear time series estimation

iterative algorithm for parameter identification of hammerstein systems with two segment nonlinearities this paper deals with parameter identification of hammerstein systems having two segment polynomial nonlinearities the application of a simple decomposition technique and using switching sequences provide a special form of a hammerstein model that is linear in parameters this model is used in an iterative algorithm enabling simultaneous estimation of all of the model parameters to demonstrate the feasibility of the identification method more illustrative examples are included

discrete time adaptive control of systems with multisegment piecewise linear nonlinearities inverse schemes are constructed for multisegment piecewise linear nonlinearities adaptive laws are proposed to update the inverse to cancel the effect of the unknown characteristic of such a nonlinearity which appears at the input of a linear part two adaptive control schemes using an adaptive inverse and a linear controller structure are developed one for the linear part known and the other for the linear part unknown different adaptive designs are given based on different a priori nonlinearity knowledge necessary for the construction of an adaptive inverse the adaptive inverse controllers ensure closed loop signal boundedness and lead to significant improvements of system tracking performance