tableau algorithms for factor analysis by instrumental variable methods simple tableau algorithms are given for the noniterative instrumental variable fabin 2 and two stage regression fabin 3 factor loading estimates of hagglund corresponding generalized least squares estimates of factor covariances and unique variances are introduced an example is given for the purpose of illustration and comparison

a numerical study of an ill posed boussinesq equation arising in water waves and nonlinear lattices filtering and regularization techniques1this research was supported by nsf grants no dms 9208061 and by the office of the vice president for research and associate provost for graduate studies at texas a m university 1 we consider an ill posed boussinesq equation which arises in shallow water waves and nonlinear lattices this equation has growing and decaying modes in the linear as well as nonlinear regimes and its linearized growth rate s for short waves of wavenumber k is given by s k 2 previous numerical studies have addressed numerical difficulties and construction of approximate solutions for ill posed problems with short wave instability up to s k e g kelvin helmholtz s k and rayleigh taylor s k instabilities these same issues are addressed and critically examined here for the present problem which has more severe short wave instability in order to develop numerical techniques for constructing good approximate solutions of this equation we use a finite difference scheme to investigate the effect of this short wave instability on the numerical accuracy of the exact solitary wave solution of this equation computational evidence is presented which indicates that numerical accuracy of the solutions is lost very quickly due to severe growth of numerical errors roundoff as well as truncation we use both filtering and regularization techniques to control growth of these errors and to provide better approximate solutions of this equation in the filtering technique numerical experiments with three types of spectral filters of increasing order of regularity are performed we examine the role of regularity of these filters on the accuracy of the numerical solutions numerical evidence is provided which indicates that the regularity of a filter plays an important role in improving the accuracy of the solutions in the regularization technique the ill posed equation is regularized by adding a higher order term to the equation two types of higher order terms are discussed i one that diminishes the growth rate of all modes below a cutoff wavenumber and sets the growth rate of all modes above it to zero and ii the other one diminishes the growth rate of all modes and the growth rate asymptotically approaches to zero as the wavenumber approaches infinity we have argued in favor of the first type of regularization and numerical results using a finite difference scheme are presented numerical evidence is provided which suggests that regularization in combination with the most regular c 2 here spectral filter for small values of the regularization parameter can provide good approximate solutions of the ill posed boussinesq equation for longer time than possible otherwise some of the ideas presented here can possibly be utilized for solving other ill posed problems with severe short wave instabilities and may have an important role to play in numerical studies of their solutions

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

factor analysis by instrumental variables methods three alternative estimation procedures for factor analysis based on the instrumental variables method are presented these procedures are justified by the method of least squares formulas for asymptotic standard errors of factor loadings are derived the procedures are empirically compared to the method of maximum likelihood the conclusion based on the data used in this study is that two of the procedures seem to work well

a bifurcation problem governed by the boundary condition ii we deal with positive solutions of u a x up in a bounded smooth domain omega subset mathbb r n subject to the boundary condition u v u a parameter p 1 we prove that this problem has a unique positive solution if and only if 0 0 and coincides with the first eigenvalue of an associated eigenvalue problem moreover we find the limit profile of the solution as 1

a polychoric instrumental variable piv estimator for structural equation models with categorical variables this paper presents a new polychoric instrumental variable piv estimator to use in structural equation models sems with categorical observed variables the piv estimator is a generalization of bollen s psychometrika 61 109 121 1996 2sls iv estimator for continuous variables to categorical endogenous variables we derive the piv estimator and its asymptotic standard errors for the regression coefficients in the latent variable and measurement models we also provide an estimator of the variance and covariance parameters of the model asymptotic standard errors for these and test statistics of overall model fit we examine this estimator via an empirical study and also via a small simulation study our results illustrate the greater robustness of the piv estimator to structural misspecifications than the system wide estimators that are commonly applied in sems

model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable models the common maximum likelihood ml estimator for structural equation models sems has optimal asymptotic properties under ideal conditions e g correct structure no excess kurtosis etc that are rarely met in practice this paper proposes model implied instrumental variable generalized method of moments miiv gmm estimators for latent variable sems that are more robust than ml to violations of both the model structure and distributional assumptions under less demanding assumptions the miiv gmm estimators are consistent asymptotically unbiased asymptotically normal and have an asymptotic covariance matrix they are distribution free robust to heteroscedasticity and have overidentification goodness of fit j tests with asymptotic chi square distributions in addition miiv gmm estimators are scalable in that they can estimate and test the full model or any subset of equations and hence allow better pinpointing of those parts of the model that fit and do not fit the data an empirical example illustrates miiv gmm estimators two simulation studies explore their finite sample properties and find that they perform well across a range of sample sizes

positive solutions of an elliptic partial differential equation on rn abstract in this paper we discuss the existence nonexistence and uniqueness of positive solutions of a one parameter family of elliptic partial differential equations on r n n 2 these equations are of interests in mathematical biology and riemannian geometry our approach are based on variational arguments and comparison principles

conjugate gradient acceleration of the em algorithm the em algorithm is a very popular and widely applicable algorithm for the computation of maximum likelihood estimates although its implementation is generally simple the em algorithm often exhibits slow convergence and is costly in some areas of application past attempts to accelerate the em algorithm have most commonly been based on some form of aitken acceleration here we propose an alternative method based on conjugate gradients the key as we show is that the em step can be viewed approximately at least as a generalized gradient making it natural to apply generalized conjugate gradient methods in an attempt to accelerate the em algorithm the proposed method is relatively simple to implement and can handle problems with a large number of parameters an important feature of most em algorithms to demonstrate the effectiveness of the proposed acceleration method we consider its application to several problems in each of the following areas estimation of a covariance matrix from incomplete mu

nonconvergence improper solutions and starting values in lisrel maximum likelihood estimation in the framework of a robustness study on maximum likelihood estimation with lisrel three types of problems are dealt with nonconvergence improper solutions and choice of starting values the purpose of the paper is to illustrate why and to what extent these problems are of importance for users of lisrel the ways in which these issues may affect the design and conclusions of robustness research is also discussed

some contributions to efficient statistics in structural models specification and estimation of moment structures current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments e g means and covariances and to distribution theory based on multivariate normality in psychometrics the multinormality assumption is often incorrect so that statistical tests on parameters or model goodness of fit will frequently be incorrect as well it is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary structural representations are developed for generalizations of the bentler weeks joreskog keesling wiley and factor analytic models some asymptotically distribution free efficient estimators for such arbitrary structural models are developed limited information estimators are obtained as well the special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail the argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds many open research areas are described

large conformal metrics with prescribed scalar curvature abstract let m g be an n dimensional compact riemannian manifold let h be a smooth function on m and assume that it has a critical point m such that h 0 and which satisfies a suitable flatness assumption we are interested in finding conformal metrics g u 4 n 2 g with u 0 whose scalar curvature is the prescribed function h 2 h where is a small parameter in the positive case i e when the scalar curvature r g is strictly positive we find a family of bubbling metrics g where u blows up at the point and approaches zero far from as goes to zero in the general case if in addition we assume that there exists a non degenerate conformal metric g 0 u 0 4 n 2 g with u 0 0 whose scalar curvature is equal to h then there exists a bounded family of conformal metrics g 0 u 0 4 n 2 g with u 0 0 which satisfies u 0 u 0 uniformly as 0 here we build a second family of bubbling metrics g where u blows up at the point and approaches u 0 far from as goes to zero in particular this shows that this problem admits more than one solution

variational approach for a class of cooperative systems abstract the aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non local equation through classical variational methods thanks to those results we are able to obtain the blow up behavior of the solutions in the whole domain for certain values of the main continuation parameter

analytic studies and numerical simulations of the generalized boussinesq equation the modified adomian decomposition method is used to solve the generalized boussinesq equation the equation commonly describes the propagation of small amplitude long waves in several physical contents the analytic solution of the equation is obtained in the form of a convergent series with easily computable components for comparison purposes a numerical algorithm based on chebyshev polynomials is developed and simulated numerical results show that the modified adomian decomposition method proves to be more accurate and computationally more efficient than the galerkin chebyshev method

multiple solutions for a semilinear elliptic equation let ql be a bounded smooth domain in rn n 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem au au h x iuip lu in q u 0 onoq where h 0 h 0 is holder continuous on q and p 1 a are constants let qlo denote the interior of the set where h vanishes in q we assume h 0 a e on q k1o and consider the eigenvalues ai k2 and ai 0o of the dirichlet problem in q and qlo respectively we prove that no nontrivial solution of the equation exists if a satisfies for some k 1 ak 90 k 1 a satisfies as ql 1 we consider the problem of finding nontrivial solutions to the elliptic boundary value problem 0 1 au au h x iuip u in q 0 2 u 0 on aq where h is a nonnegative not identically zero holder continuous function defined on q and p 1 a are constants ouyang 5 studied existence and uniqueness of positive solutions to problem 0 1 0 2 and also of its corresponding analogue on a compact riemannian manifold that paper mainly focused on studying the effect of vanishing of the received by the editors october 13 1993 and in revised form october 24 1994 1991 mathematics subject classification primary 35j25 35j20

a lattice boltzmann model for the generalized boussinesq equation a lattice boltzmann model is developed for the simulation of the generalized nonlinear boussinesq equation through adding a differential operator of the diffusion term as a source term to the evolution equation the macroscopic equation is recovered with higher order truncation error detailed numerical simulations for the motion of the soliton solutions of the boussinesq equation are performed and the numerical results agree well with the exact solutions the results show that the lattice boltzmann method is an efficient algorithm with excellent long time numerical behaviors for the motion of the soliton solutions

varying bifurcation diagrams of positive solutions for a class of indefinite superlinear boundary value problems in this work we analyze the existence multiplicity and stability of positive solutions for a class of indefinite superlinear elliptic boundary value problems the main contribution of this paper consists in the change of mind inherent to the fact of adding the superlinear amplitude e as an unfolding parameter this change of mind allows us to unify many previous results obtained separately in the literature it helps us to realize the global structure of the set of positive steady states and provides us with a great variety of new general results our techniques can be applied to much more general equations and systems

the boundary blow up rate of large solutions abstract in this paper we ascertain the blow up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain at different rates according to the point of the boundary x all previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of this hypothesis substantially simplified the mathematical analysis of the problem as it allowed constructing global sub and supersolutions in an open neighborhood of obtaining general results requires localizing at each particular point of the boundary making particularly involved the mathematical analysis of the problem

analytical and numerical studies of a singularly perturbed boussinesq equation we study the singularly perturbed sixth order boussinesq equation recently introduced by daripa and hua appl math comput 101 1999 159 motivated by their work we formally derive this equation from two dimensional potential flow equations governing the small amplitude long capillary gravity waves on the surface of shallow water for bond number very close to but less than 1 3 on the basis of far field analyses and heuristic arguments we show that the traveling wave solutions of this equation are weakly non local solitary waves characterized by small amplitude fast oscillations in the far field we review various analytical and numerical methods originally devised to obtain this type of weakly non local solitary wave solutions of the singularly perturbed fifth order kdv equation using these methods we obtain weakly non local solitary wave solutions of the singularly perturbed sixth order boussinesq equation and provide estimates of the amplitude of oscillations which persist in the far field

simultaneous equation systems as moment structure models with an introduction to latent variable models abstract an introduction to latent variable covariance structure models is provided estimation and testing of such models with normal and non normal variables is reviewed and a relatively inexpensive asymptotically distribution free estimator is introduced the traditional econometric simultaneous equation system is reconceptualized as a random vector structural equation model extensions of the model to deal with latent variables and a wider variety of structural phenomena are made via the joreskog keesling wiley lisrel approach and a simpler approach due to bentler and weeks these representation systems are extended via first and second moments about the origin of measured variables explained in terms of the structural coefficients and the moments of explanatory variables citations to further literature are provided

on the positive solutions of semilinear equations δ ℎ 0 on the compact manifolds in this paper we study the existence nonexistence and uniqueness of positive solutions of semilinear equations u u hu p 0 on compact riemannian manifolds as well as on bounded smooth domains in r n with homogeneous dirichlet or neumann boundary conditions

a gauss newton algorithm for exploratory factor analysis it is shown that the scoring algorithm for maximum likelihood estimation in exploratory factor analysis can be developed in a way that is many times more efficient than a direct development based on information matrices and score vectors the algorithm offers a simple alternative to current algorithms and when used in one step mode provides the simplest and fastest method presently available for moving from consistent to efficient estimates perhaps of greater importance is its potential for extension to the confirmatory model the algorithm is developed as a gauss newton algorithm to facilitate its application to generalized least squares and to maximum likelihood estimation

growing up positive solutions of semilinear elliptic boundary value problems this paper is devoted to the study of the existence uniqueness and asymptotic behavior of positive solutions of a class of degenerate boundary value problems for semilinear second order elliptic differential operators which originates from the so called yamabe problem in riemannian geometry our approach is based on the super sub solution method adapted to the degenerate case

the decomposition method for solving 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation we study the solitary wave solutions of the 2 1 dimensional boussinesq equation u t t u x x u y y u 2 x x u x x x x 0 and 3 1 dimensional kp equation u x t 6u x 2 6uu x x u x x x x u y y u z z 0 in this paper by considering the decomposition scheme we first obtain the exact solitary wave solutions of the 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation for the initial conditions without using any classical transformations and then its numerical solutions are constructed without using any discretization technique the numerical solutions are compared with the known analytical solutions its remarkable accuracy is finally demonstrated in the study of 2 1 dimensional boussinesq equation and 3 1 dimensional kp equation