points of view analysis revisited fitting multidimensional structures to optimal distance components with cluster restrictions on the variables points of view analysis pva proposed by tucker and messick in 1963 was one of the first methods to deal explicitly with individual differences in multidimensional scaling but at some point was apparently superceded by the weighted euclidean model well known as the carroll and chang indscal model this paper argues that the idea behind points of view analysis deserves new attention especially as a technique to analyze group differences a procedure is proposed that can be viewed as a streamlined integrated version of the tucker and messick process which consisted of a number of separate steps at the same time our procedure can be regarded as a particularly constrained weighted euclidean model while fitting the model two types of nonlinear data transformations are feasible either for given dissimilarities or for variables from which the dissimilarities are derived various applications are discussed where the two types of transformation can be mixed in the same analysis a quadratic assignment framework is used to evaluate the results

overcoming scale usage heterogeneity questions that use a discrete ratings scale are commonplace in survey research examples in marketing include customer satisfaction measurement and purchase intention survey research practitioners have long commented that respondents vary in their usage of the scale common patterns include using only the middle of the scale or using the upper or lower end these differences in scale usage can impart biases to correlation and regression analyses to capture scale usage differences we developed a new model with individual scale and location effects and a discrete outcome variable we model the joint distribution of all ratings scale responses rather than specific univariate conditional distributions as in the ordinal probit model we apply our model to a customer satisfaction survey and show that the correlation inferences are much different once proper adjustments are made for the discreteness of the data and scale usage we also show that our adjusted or latent ratings scale is more closely related to

a note on partitioned determinants a formula for the determinant of a partitioned matrix possibly with singular submatrices is derived and applied to some psychometric and numerical problems

the integration of multidimensional scaling and multivariate analysis with optimal transformations the recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines in multidimensional scaling mds the available data typically describe the relationships among a set of objects in terms of similarity dissimilarity or pseudo distances in multivariate analysis mva data usually result from observation on a collection of variables over a common set of objects this paper starts from a very general multidimensional scaling task defined on distances between objects derived from one or more sets of multivariate data particular special cases of the general problem following familiar notions from mva will be discussed that encompass a variety of analysis techniques including the possible use of optimal variable transformation throughout it will be noted how certain data analysis approaches are equivalent to familiar mva solutions when particular problem specifications are combined with particular distance approximations

guessing under source uncertainty this paper considers the problem of guessing the realization of a finite alphabet source when some side information is provided the only knowledge the guesser has about the source and the correlated side information is that the joint source is one among a family a notion of redundancy is first defined and a new divergence quantity that measures this redundancy is identified this divergence quantity shares the pythagorean property with the kullback leibler divergence good guessing strategies that minimize the supremum redundancy over the family are then identified the min sup value measures the richness of the uncertainty set the min sup redundancies for two examples the families of discrete memoryless sources and finite state arbitrarily varying sources are then determined

improved bounds on lossless source coding and guessing moments via renyi measures this paper provides upper and lower bounds on the optimal guessing moments of a random variable taking values on a finite set when side information may be available these moments quantify the number of guesses required for correctly identifying the unknown object and similarly to arikan s bounds they are expressed in terms of the arimoto renyi conditional entropy although arikan s bounds are asymptotically tight the improvement of the bounds in this paper is significant in the non asymptotic regime relationships between moments of the optimal guessing function and the map error probability are also established characterizing the exact locus of their attainable values the bounds on optimal guessing moments serve to improve non asymptotic bounds on the cumulant generating function of the codeword lengths for fixed to variable optimal lossless source coding without prefix constraints non asymptotic bounds on the reliability function of discrete memoryless sources are derived as well relying on these techniques lower bounds on the cumulant generating function of the codeword lengths are derived by means of the smooth renyi entropy for source codes that allow decoding errors

canonical analysis of two convex polyhedral cones and applications canonical analysis of two convex polyhedral cones consists in looking for two vectors one in each cone whose square cosine is a maximum this paper presents new results about the properties of the optimal solution to this problem and also discusses in detail the convergence of an alternating least squares algorithm the set of scalings of an ordinal variable is a convex polyhedral cone which thus plays an important role in optimal scaling methods for the analysis of ordinal data monotone analysis of variance and correspondence analysis subject to an ordinal constraint on one of the factors are both canonical analyses of a convex polyhedral cone and a subspace optimal multiple regression of a dependent ordinal variable on a set of independent ordinal variables is a canonical analysis of two convex polyhedral cones as long as the signs of the regression coefficients are given we discuss these three situations and illustrate them by examples

generalized structured component analysis we propose an alternative method to partial least squares for path analysis with components called generalized structured component analysis the proposed method replaces factors by exact linear combinations of observed variables it employs a well defined least squares criterion to estimate model parameters as a result the proposed method avoids the principal limitation of partial least squares i e the lack of a global optimization procedure while fully retaining all the advantages of partial least squares e g less restricted distributional assumptions and no improper solutions the method is also versatile enough to capture complex relationships among variables including higher order components and multi group comparisons a straightforward estimation algorithm is developed to minimize the criterion

component analysis with different sets of constraints on different dimensions many of the classical multivariate data analysis and multidimensional scaling techniques call for approximations by lower dimensional configurations a model is proposed in which different sets of linear constraints are imposed on different dimensions in component analysis and classical multidimensional scaling frameworks a simple efficient and monotonically convergent algorithm is presented for fitting the model to the data by least squares the basic algorithm is extended to cover across dimension constraints imposed in addition to the dimensionwise constraints and to the case of a symmetric data matrix examples are given to demonstrate the use of the method

assessing influence on regression coefficients in generalized linear models summary suggested diagnostics for influence on the estimated regression coefficients in a generalized linear model have generally approximated the effect of deleting a single case we apply the local influence method of cook 1986 to assess the effect of small perturbations of the data including the vector of responses case weights explanatory variables and the components of one case the resulting diagnostics allow one to check for different kinds of influence and may give insight into its workings two examples illustrate some of the diagnostics

diagnostics in linear discriminant analysis abstract some new diagnostic measures in discriminant analysis are proposed they can be expressed in terms of the two fundamental influence statistics in discriminant analysis d i 2 and i a theorem on the asymptotic distributions of the fundamental statistics is derived based on the theorem the proposed measures can be shown to be asymptotically distributed as functions of independent chi squared and standard normal random variables critical values and expected quantiles of the measures can then be constructed hence influential observations are detected using q q plots and significance tests two measures have analogous forms in regression the theorem is also useful for getting the asymptotic distributions of existing measures that are functions of d i 2 and i a comparison of the diagnostics in linear discriminant analysis linear regression and linear logistic regression discriminant analysis is made although discriminant coefficients can be determined under a regression model regress

monotone spline transformations for dimension reduction consider a set of data consisting of measurements ofn objects with respect top variables displayed in ann p matrix a monotone transformation of the values in each column represented as a linear combination of integrated basis splines is assumed determined by a linear combination of a new set of values characterizing each row object two different models are used one an eckart young decomposition model and the other a multivariate normal model examples for artificial and real data are presented the results indicate that both methods are helpful in choosing dimensionality and that the eckart young model is also helpful in displaying the relationships among the objects and the variables also results suggest that the resulting transformations are themselves illuminating

interpreting canonical correlation analysis through biplots of structure correlations and weights this paper extends the biplot technique to canonical correlation analysis and redundancy analysis the plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second the link between multivariate regression and canonical correlation analysis redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients this plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables an example is used to show how the proposed biplots may be interpreted

redundancy analysis for qualitative variables redundancy analysis also called principal components analysis of instrumental variables is a technique for two sets of variables one set being dependent of the other its aim is maximization of the explained variance of the dependent variables by a linear combination of the explanatory variables the technique is generalized to qualitative variables it then gives implicitly a simultaneous optimal scaling of the dependent qualitative variables examples are taken from the dutch life situation survey 1977 using satisfaction with life and happiness as dependent variables the analysis leads to one well being scale defined by the explanatory variables marital status schooling income and activity

canonical primal dual algorithm for solving fourth order polynomial minimization problems this paper focuses on implementation of a general canonical primal dual algorithm for solving a class of fourth order polynomial minimization problems a critical issue in the canonical duality theory has been addressed i e in the case that the canonical dual problem has no interior critical point in its feasible space s a a quadratic perturbation method is introduced to recover the global solution through a primal dual iterative approach and a gradient based method is further used to refine the solution a series of test problems including the benchmark polynomials and several instances of the sensor network localization problems have been used to testify the effectiveness of the proposed algorithm

statistical significance of the contribution of variables to the pca solution an alternative permutation strategy in this paper the statistical significance of the contribution of variables to the principal components in principal components analysis pca is assessed nonparametrically by the use of permutation tests we compare a new strategy to a strategy used in previous research consisting of permuting the columns variables of a data matrix independently and concurrently thus destroying the entire correlational structure of the data this strategy is considered appropriate for assessing the significance of the pca solution as a whole but is not suitable for assessing the significance of the contribution of single variables alternatively we propose a strategy involving permutation of one variable at a time while keeping the other variables fixed we compare the two approaches in a simulation study considering proportions of type i and type ii error we use two corrections for multiple testing the bonferroni correction and controlling the false discovery rate fdr to assess the significance of the variance accounted for by the variables permuting one variable at a time combined with fdr correction yields the most favorable results this optimal strategy is applied to an empirical data set and results are compared with bootstrap confidence intervals

robust canonical discriminant analysis a method for robust canonical discriminant analysis via two robust objective loss functions is discussed these functions are useful to reduce the influence of outliers in the data majorization is used at several stages of the minimization procedure to obtain a monotonically convergent algorithm an advantage of the proposed method is that it allows for optimal scaling of the variables in a simulation study it is shown that under the presence of outliers the robust functions outperform the ordinary least squares function both when the underlying structure is linear in the variables as when it is nonlinear furthermore the method is illustrated with empirical data

multivariate methods for quantitative and qualitative data abstract in this paper several multivariate analysis methods are analyzed by means of the errors in variables model two specifications viz the principal relations and the principal factors model for the set of unobserved latent variables are introduced and shown to be complementary for particular choices of the error covariance matrix the general model reduces to several well known multivariate techniques including ordinary least squares principal components orthogonal regression and canonical correlations the same apparatus is used to arrive at a set of multivariate techniques in case the data is qualitative instead of quantitative the relationship with optimal scaling techniques for qualitative data is shown an empirical example is given of a regression involving a dependent latent variable having two ordered categorical indicator variables

variational methods for non differentiable functionals and their applications to partial differential equations the interest in extending the theory of nonlinear partial differential equations pde to pde with discontinuous nonlinearities dnde has been increasing daily the reasons are twofold 1 many free boundary problems may be reduced to boundary value problems of dnde cf chang 16 71 chang and jiang 9 and fleishman and mahar 121 2 sometimes in dealing with a pde problem it is beneficial to put the original pde into a large category for instance dnde cf chang 7 simply speaking a dnde is as follows

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

forced classification a simple application of a quantification method this study formulates a property of a quantification method the principle of equivalent partitioning pep when the pep is used together with guttman s principle of internal consistency pic in a simple way the combination offers an interesting way of analyzing categorical data in terms of the variate s chosen by the investigator a type of canonical analysis the study discusses applications of the technique to multiple choice rank order and paired comparison data

convergence analysis of nonmonotone levenberg marquardt algorithms for complementarity problem this paper addresses the convergence of two nonmonotone levenberg marquardt algorithms for nonlinear complementarity problem under some mild assumptions and requiring only the solution of a linear system at each iteration the nonmonotone levenberg marquardt algorithms are shown to be globally convergent

global optimization by canonical dual function in this paper the canonical dual function gao 2004 4 is used to solve a global optimization we find global minimizers by backward differential flows the backward flow is created by the local solution to the initial value problem of an ordinary differential equation some examples and applications are presented

reducing guesswork via an unreliable oracle alice holds a random variable x and bob is trying to guess its value by asking questions of the form is x x alice answers truthfully and the game terminates once bob guesses correctly before the game begins bob is allowed to reach out to an oracle carole and ask her any yes no question i e a question of the form is x in a carole is known to lie with a given probability p what should bob ask carole if he would like to minimize his expected guessing time when carole is always truthful p 0 it is not difficult to check that bob should order the symbol probabilities in descending order and ask carole whether the index of x with respect to this order is even or odd we show that this strategy is almost optimal for any lying probability p up to a small additive constant upper bounded by 1 4 we discuss a connection to the cutoff rate of the bsc with feedback

the influence of observations on misclassification probability estimates in linear discriminant analysis summary the influence of observations upon misclassification probability estimates in linear discriminant analysis is examined for a single observation an exact expression is given confirming two surprising results of campbell 1978 it also shows that the influence of an observation is governed by two quantities a the difference between its linear discriminant score and that for its sample mean and b its atypicality estimate for its own population this is analogous to linear model results where an observation s influence depends upon its residual and its leverage however important differences from the regression situation are noted contours of this one at a time influence can be superimposed on the plot introduced by critchley ford 1985 examining the joint influence of several observations is complicated by the computational burden and by possible masking effects a quadratic approximation is developed for this problem using pregibon s 1981 case weights scheme this approximation has an error of order n 3 where n denotes the assumed common order of the sample sizes an example is given

multi scale modelling and canonical dual finite element method in phase transitions of solids this paper presents a multi scale model in phase transitions of solid materials with both macro and micro effects this model is governed by a semi linear nonconvex partial differential equation which can be converted into a coupled quadratic mixed variational problem by the canonical dual transformation method the extremality conditions of this variational problem are controlled by a triality theory which reveals the multi scale effects in phase transitions therefore a potentially useful canonical dual finite element method is proposed for the first time to solve the nonconvex variational problems in multi scale phase transitions of solids applications are illustrated results shown that the canonical duality theory developed by the first author in nonconvex mechanics can be used to model complicated physical phenomena and to solve certain difficult nonconvex variational problems in an easy way the canonical dual finite element method brings some new insights into computational mechanics

an analysis and synthesis of multiple correspondence analysis optimal scaling dual scaling homogeneity analysis and other methods for quantifying categorical multivariate data we discuss a variety of methods for quantifying categorical multivariate data these methods have been proposed in many different countries by many different authors under many different names in the first major section of the paper we analyze the many different methods and show that they all lead to the same equations for analyzing the same data in the second major section of the paper we introduce the notion of a duality diagram and use this diagram to synthesize the many superficially different methods into a single method

a multivariate reduced rank growth curve model with unbalanced data a multivariate reduced rank growth curve model is proposed that extends the univariate reducedrank growth curve model to the multivariate case in which several response variables are measured over multiple time points the proposed model allows us to investigate the relationships among a number of response variables in a more parsimonious way than the traditional growth curve model in addition the method is more flexible than the traditional growth curve model for example response variables do not have to be measured at the same time points nor the same number of time points it is also possible to apply various kinds of basis function matrices with different ranks across response variables it is not necessary to specify an entire set of basis functions in advance examples are given for illustration

minimum guesswork with an unreliable oracle we study a guessing game where alice holds a discrete random variable x and bob tries to sequentially guess its value before the game begins bob can obtain side information about x by asking an oracle carole any binary question of his choosing carole s answer is however unreliable and is incorrect with probability epsilon we show that bob should always ask carole whether the index of x is odd or even with respect to a descending order of probabilities this question simultaneously minimizes all the guessing moments for any value of epsilon in particular this result settles a conjecture of burin and shayevitz we further consider a more general setup where bob can ask a multiple choice m ary question and then observe carole s answer through a noisy channel when the channel is completely symmetric i e when carole decides whether to lie regardless of bob s question and has no preference when she lies a similar question about the ordered index of x modulo m is optimal interestingly however the problem of testing whether a given question is optimal appears to be generally difficult in other symmetric channels we provide supporting evidence for this difficulty by showing that a core property required in our proofs becomes np hard to test in the general m ary case we establish this hardness result via a reduction from the problem of testing whether a system of modular difference disequations has a solution which we prove to be np hard for m geq 3

optimal scaling by alternating length constrained nonnegative least squares with application to distance based analysis an important feature of distance based principal components analysis is that the variables can be optimally transformed for monotone spline transformation a nonnegative least squares problem with a length constraint has to be solved in each iteration as an alternative algorithm to lawson and hanson 1974 we propose the alternating length constrained non negative least squares alc nnls algorithm which minimizes the nonnegative least squares loss function over the parameters under a length constraint by alternatingly minimizing over one parameter while keeping the others fixed several properties of the new algorithm are discussed a monte carlo study is presented which shows that for most cases in distance based principal components analysis alc nnls performs as good as the method of lawson and hanson or sometimes even better in terms of the quality of the solution

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

interval estimation in discrimination the multivariate normal equal covariance case summary a general approach to discrimination problems is described which emphasizes the viewpoint of individual cases and expresses the uncertainty with which individual decisions are made it is applied to the particular case of two multivariate normal distributions with a common covariance matrix an affine transformation to which the key quantities are invariant simplifies discussion of the distribution of the estimated log odds ratio and suggests a practically useful plot which generalizes the usual display of discriminant scores and has several attractive features an illustration is given two approximate interval estimation techniques for the true log odds ratio are described and evaluated in a range of practical situations by a simulation study some further applications of our general approach are briefly indicated

an improvement of the harman fukuda method for the minres solution in factor analysis the method proposed by harman and fukuda to treat the so called heywood case in the minres method in factor analysis i e the case where the resulting communalities are greater than one involves the frequent solution of eigenvalue problems a simple method to treat this problem requiring less computing time and enjoying higher numerical stability is described in this paper

quantitative analysis of qualitative data this paper presents an overview of an approach to the quantitative analysis of qualitative data with theoretical and methodological explanations of the two cornerstones of the approach alternating least squares and optimal scaling using these two principles my colleagues and i have extended a variety of analysis procedures originally proposed for quantitative interval or ratio data to qualitative nominal or ordinal data including additivity analysis and analysis of variance multiple and canonical regression principal components common factor and three mode factor analysis and multidimensional scaling the approach has two advantages a if a least squares procedure is known for analyzing quantitative data it can be extended to qualitative data and b the resulting algorithm will be convergent three completely worked through examples of the additivity analysis procedure and the steps involved in the regression procedures are presented

multivariate analysis with linearizable regressions we study the class of multivariate distributions in which all bivariate regressions can be linearized by separate transformation of each of the variables this class seems more realistic than the multivariate normal or the elliptical distributions and at the same time its study allows us to combine the results from multivariate analysis with optimal scaling and classical multivariate analysis in particular a two stage procedure which first scales the variables optimally and then fits a simultaneous equations model is studied in detail and is shown to have some desirable properties

bounds on a probability for the heavy tailed distribution and the probability of deficient decoding in sequential decoding although sequential decoding of convolutional codes gives a very small decoding error probability the overall reliability is limited by the probability pg of deficient decoding the term introduced by jelinek to refer to decoding failures caused mainly by buffer overflow the number of computational efforts in sequential decoding has the pareto distribution and it is this heavy tailed distribution that characterizes pg the heavy tailed distribution appears in many fields and buffer overflow is a typical example of the behaviors in which the heavy tailed distribution plays an important role in this paper we give a new bound on a probability in the tail of the heavy tailed distribution and using the bound prove the long standing conjecture on pg that is pg ap constanttimes1 sigmarhonrho 1 for a large speed factor sigma of the decoder and for a large receive buffer size n whenever the coding rate r and rho satisfy e rho rhor for 0 les rho les 1

clustering n objects into k groups under optimal scaling of variables we propose a method to reduce many categorical variables to one variable withk categories or stated otherwise to classifyn objects intok groups objects are measured on a set of nominal ordinal or numerical variables or any mix of these and they are represented asn points inp dimensional euclidean space starting from homogeneity analysis also called multiple correspondence analysis the essential feature of our approach is that these object points are restricted to lie at only one ofk locations it follows that thesek locations must be equal to the centroids of all objects belonging to the same group which corresponds to a sum of squared distances clustering criterion the problem is not only to estimate the group allocation but also to obtain an optimal transformation of the data matrix an alternating least squares algorithm and an example are given

reduced rank models for multiple time series summary this paper is concerned with the investigation of reduced rank coefficient models for multiple time series in particular autoregressive processes which have a structure to their coefficient matrices similar to that of classical multivariate reduced rank regression are studied in detail the estimation of parameters and associated asymptotic theory are derived the exact correspondence between the reduced rank regression procedure for multiple autoregressive processes and the canonical analysis of box tiao 1977 is briefly indicated to illustrate the methods u s hog data are considered

fuzzy clustering with squared minkowski distances abstract this paper presents a new fuzzy clustering model based on a root of the squared minkowski distance which includes squared and unsquared euclidean distances and the l 1 distance an algorithm is presented that is based on iterative majorization and yields a convergent series of monotone nonincreasing loss function values this algorithm coincides under some condition with the isodata algorithm of dunn j cybernet 3 1974 32 57 and the fuzzy c means algorithm of bezdek ph d thesis cornell university ithaca 1973 for squared euclidean distance and with an algorithm of jajuga fuzzy sets and systems 39 1991 43 50 for l 1 distances to find a global minimum we compare a special strategy called fuzzy steps with fuzzy kohonen clustering networks fkcn pattern recognition 27 1994 757 764 and multistart fuzzy steps and fkcn are based on finding updates for a decreasing weighting exponent which seems to work particularly well for hard clustering to assess the performance of the methods two numerical experiments and a simulation study are performed

homogeneity analysis with k sets of variables an alternating least squares method with optimal scaling features homogeneity analysis or multiple correspondence analysis is usually applied tok separate variables in this paper we apply it to sets of variables by using sums within sets the resulting technique is called overals it uses the notion of optimal scaling with transformations that can be multiple or single the single transformations consist of three types nominal ordinal and numerical the corresponding overals computer program minimizes a least squares loss function by using an alternating least squares algorithm many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of overals an application to data from an epidemiological survey is presented

an efficient algorithm for joint correspondence analysis joint correspondence analysis is a technique for constructing reduced dimensional representations of pairwise relationships among categorical variables the technique was proposed by greenacre as an alternative to multiple correspondence analysis joint correspondence analysis differs from multiple correspondence analysis in that it focuses solely on between variable relationships greenacre described one alternating least squares algorithm for conducting joint correspondence analysis another alternating least squares algorithm is described in this article the algorithm is guaranteed to converge and does so in fewer iterations than does the algorithm proposed by greenacre a modification of the algorithm for handling heywood cases is described the algorithm is illustrated on two data sets

the tunneling method for global optimization in multidimensional scaling this paper focuses on the problem of local minima of the stress function it turns out that unidimensional scaling is particularly prone to local minima whereas full dimensional scaling with euclidean distances has a local minimum that is global for intermediate dimensionality with euclidean distances it depends on the dissimilarities how severe the local minimum problem is for city block distances in any dimensionality many different local minima are found a simulation experiment is presented that indicates under what conditions local minima can be expected we introduce the tunneling method for global minimization and adjust it for multidimensional scaling with general minkowski distances the tunneling method alternates a local search step in which a local minimum is sought with a tunneling step in which a different configuration is sought with the same stress as the previous local minimum in this manner successively better local minima are obtained and experimentation so far shows that the last one is often a global minimum

canonical redundancy factoring analysis the interrelationships between two sets of measurements made on the same subjects can be studied by canonical correlation originally developed by hotelling 1936 the canonical correlation is the maximum correlation betweenlinear functions canonical factors of the two sets of variables an alternative statistic to investigate the interrelationships between two sets of variables is the redundancy measure developed by stewart and love 1968 van den wollenberg 1977 has developed a method of extracting factors which maximize redundancy as opposed to canonical correlation

logistic regression diagnostics a maximum likelihood fit of a logistic regression model and other similar models is extremely sensitive to outlying responses and extreme points in the design space we develop diagnostic measures to aid the analyst in detecting such observations and in quantifying their effect on various aspects of the maximum likelihood fit the elements of the fitting process which constitute the usual output parameter estimates standard errors residuals etc will be used for this purpose with a properly designed computing package for fitting the usual maximum likelihood model the diagnostics are essentially free for the asking in particular good data analysis for logistic regression models need not be expensive or time consuming

bi complementarity and duality a framework in nonlinear equilibria with applications to the contact problem of elastoplastic beam theory abstract nonlinear complementarity problems and variational inequalities in nonlinear equilibrium problems are studied within a unified framework based on the generalized rockafellar tonti diagram a bi complementarity problem with both internal and external nonlinear complementarity conditions is proposed a general duality theory in variational inequality is established and the mosco dual variational inequality has been generalized to the nonsmooth systems in order to study the frictional contact problem of beam theory a two dimensional elastoplastic beam model is proposed the external complementarity condition provides the free boundary of contact region while the internal complementarity condition gives the interface of the elastic plastic regions our results shown that in nonsmooth equilibrium problems the dual approaches are much easier than the primal problems

duality for non convex variational principles abstract this paper treats the construction of dual variational principles for non convex problems using lagrangian methods besides the well known saddle point theory there are dualities involving minimizing the lagrangian in both variables and dualities where one first maximizes and then minimizes the lagrangian in each variable when the primal problem has certain structure an associated canonical lagrangian is defined which leads to the appropriate dual variational principle and to a hamiltonian description the properties of and correspondence between the critical points are analyzed the last five sections are devoted to examples of these dual principles

extending multivariate distance matrix regression with an effect size measure and the asymptotic null distribution of the test statistic person centered methods are useful for studying individual differences in terms of dis similarities between response profiles on multivariate outcomes multivariate distance matrix regression mdmr tests the significance of associations of response profile dis similarities and a set of predictors using permutation tests this paper extends mdmr by deriving and empirically validating the asymptotic null distribution of its test statistic and by proposing an effect size for individual outcome variables which is shown to recover true associations these extensions alleviate the computational burden of permutation tests currently used in mdmr and render more informative results thus making mdmr accessible to new research domains

comments on an inequality on guessing and its application to sequential decoding in the above paper by e arikan see ibid vol 42 no 1 p 99 105 1996 an asymptotically tight upper bound on the spl rho th moment spl rho spl ges 0 of the minimal number of guesses required to determine the value of a random variable was derived we show that we can tighten this bound for the case of positive integer moments when spl rho 1 the bound is improved by a factor of 2 and that the new bound also applies to a class of nonminimal guessing sequences

analyzing rectangular tables by joint and constrained multidimensional scaling abstract this paper selectively discusses multidimensional scaling methods addressing both theory and applications most of the discussion is focussed upon the analysis of rectangular tables the term joint mds is introduced for an analysis which gives a meaningful joint representation of the set of row and the set of column objects of such a table so that the dissimilarities either within sets or between sets are optimally approximated from this perspective it is possible to give an unified account of the relationships between classical multidimensional scaling principal components analysis and correspondence analysis by imposing constraints the general model can be structurally changed in a number of ways for example it can be made discrete that is in principle it subsumes subset models and quadratic assignment as special cases it can also be made more flexible in the sense that external information may be used in order to tune the analysis to specific hypotheses finally an elegant joint mds model called multidimensional unfolding is discussed as a technique unfolding unfortunately suffers from being extremely sensitive to ill conditioned data a new way of coping with this problem is indicated and an application is given in which the bootstrap technique succesfully establishes the stability of the results

diagnosing influential observations in quadratic discriminant analysis we propose various diagnostic measures for the identification of observations that are influential for the estimation of probability density functions probabilities and log odds in quadratic discriminant analysis the quantile quantile q q plots together with simulated confidence envelopes are found to be useful for detecting influential observations in a data set of two species of biting flies that are so similar that they are difficult to discriminate morphologically we find that the omission of even one case in the data set can have a very great effect on the estimated probabilities that the observations belong to a particular group

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

linear relations among k sets of variables a family of solutions for linear relations amongk sets of variables is proposed it is shown how these solutions apply fork 2 and how they can be generalized from there tok 3

a distance based variety of nonlinear multivariate data analysis including weights for objects and variables in the distance approach to nonlinear multivariate data analysis the focus is on the optimal representation of the relationships between the objects in the analysis in this paper two methods are presented for including weights in distance based nonlinear multivariate data analysis in the first method weights are assigned to the objects while the second method is concerned with differential weighting of groups of variables when each analysis variable defines a group the latter method becomes a variable weighting method for objects the weights are assumed to be given for groups of variables they may be given or estimated these weighting schemes can also be combined and have several important applications for example they make it possible to perform efficient analyses of large data sets to use the distance based variety of nonlinear multivariate data analysis as an addition to loglinear analysis of multiway contingency tables and to do stability studies of the solutions by applying the bootstrap on the objects or the variables in the analysis these and other applications are discussed and an efficient algorithm is proposed to minimize the corresponding loss function