a latent class approach to fitting the weighted euclidean model clascal a weighted euclidean distance model for analyzing three way proximity data is proposed that incorporates a latent class approach in this latent class weighted euclidean model the contribution to the distance function between two stimuli is per dimension weighted identically by all subjects in the same latent class this model removes the rotational invariance of the classical multidimensional scaling model retaining psychologically meaningful dimensions and drastically reduces the number of parameters in the traditional indscal model the probability density function for the data of a subject is posited to be a finite mixture of spherical multivariate normal densities the maximum likelihood function is optimized by means of an em algorithm a modified fisher scoring method is used to update the parameters in the m step a model selection strategy is proposed and illustrated on both real and artificial data

monotonicity of entropy for real multimodal maps in 16 milnor posed the monotonicity conjecture that the set of parameters within a family of real multimodal polynomial interval maps for which the topological entropy is constant is connected this conjecture was proved for quadratic by milnor thurston 17 and for cubic maps by milnor tresser see 18 and also 5 in this paper we will prove the general case

model selection and akaike s information criterion aic the general theory and its analytical extensions during the last fifteen years akaike s entropy based information criterion aic has had a fundamental impact in statistical model evaluation problems this paper studies the general theory of the aic procedure and provides its analytical extensions in two ways without violating akaike s main principles these extensions make aic asymptotically consistent and penalize overparameterization more stringently to pick only the simplest of the true models these selection criteria are called caic and caicf asymptotic properties of aic and its extensions are investigated and empirical performances of these criteria are studied in choosing the correct degree of a polynomial model in two different monte carlo experiments under different conditions

uniqueness and nonuniqueness for positive radial solutions of δu f u r 0 on considere le probleme de l unicite pour les solutions positives du probleme de dirichlet non lineaire u f u x 0 dans u 0 est une boule ou un anneau de r n et f 0 est superlineaire en u et satisfaisait f 0 x 0

a nonparametric approach for assessing latent trait unidimensionality assuming a nonparametric family of item response theory models a theory based procedure for testing the hypothesis of unidimensionality of the latent space is proposed the asymptotic distribution of the test statistic is derived assuming unidimensionality thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait based upon a new notion of dimensionality the test is shown to have asymptotic power 1 a 6300 trial monte carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice

estimating latent distributions in recurrent choice data this paper introduces a flexible class of stochastic mixture models for the analysis and interpretation of individual differences in recurrent choice and other types of count data these choice models are derived by specifying elements of the choice process at the individual level probability distributions are introduced to describe variations in the choice process among individuals and to obtain a representation of the aggregate choice behavior due to the explicit consideration of random effect sources the choice models are parsimonious and readily interpretable an easy to implement em algorithm is presented for parameter estimation two applications illustrate the proposed approach

hierarchical classes models for three way three mode binary data interrelations and model selection several hierarchical classes models can be considered for the modeling of three way three mode binary data including the indclas model leenen van mechelen de boeck and rosenberg 1999 the tucker3 hiclas model ceulemans van mechelen and leenen 2003 the tucker2 hiclas model ceulemans and van mechelen 2004 and the tucker1 hiclas model that is introduced in this paper two questions then may be raised 1 how are these models interrelated and 2 given a specific data set which of these models should be selected and in which rank in the present paper we deal with these questions by 1 showing that the distinct hierarchical classes models for three way three mode binary data can be organized into a partially ordered hierarchy and 2 by presenting model selection strategies based on extensions of the well known scree test and on the akaike information criterion the latter strategies are evaluated by means of an extensive simulation study and are illustrated with an application to interpersonal emotion data finally the presented hierarchy and model selection strategies are related to corresponding work by kiers 1991 for principal component models for three way three mode real valued data

regular or stochastic dynamics in real analytic families of unimodal maps in this paper we prove that in any non trivial real analytic family of quasiquadratic maps almost any map is either regular i e it has an attracting cycle or stochastic i e it has an absolutely continuous invariant measure to this end we show that the space of analytic maps is foliated by codimension one analytic submanifolds hybrid classes this allows us to transfer the regular or stochastic property of the quadratic family to any non trivial real analytic family

global hyperbolicity of renormalization for c r unimodal mappings in this paper we extend m lyubichi s recent results on the global hyperbolicity of renormalization of quadratic like germs to the space of cr unimodal maps with quadratic critical point we show that in this space the boundedtype limit sets of the renormalization operator have an invariant hyperbolic structure provided r i 2 a with a close to one as an intermediate step between lyubichi s results and ours we prove that the renormalization operator is hyperbolic in a banach space of real analytic maps we construct the local stable manifolds and prove that they form a continuous lamination whose leaves are c1 codimension one banach submanifolds of the ambient space and whose holonomy is c1 for some 0 we also prove that the global stable sets are c1 immersed codimension one submanifolds as well provided r i 3 a with a close to one as a corollary we deduce that in generic oneparameter families of cr unimodal maps the set of parameters corresponding to infinitely renormalizable maps of bounded combinatorial type is a cantor set with hausdorff dimension less than one

complex bounds for real maps in this paper we prove complex bounds also referred to as a priori bounds for c 3 and in particular for analytic maps of the interval any c 3 mapping of the interval has an asymptotically holomorphic extension to a neighbourhood of the interval we associate to such a map a complex box mapping which provides a kind of markov structure for the dynamics moreover we prove universal geometric bounds on the shape of the domains and on the moduli between components of the range and domain such bounds show that the first return maps to these domains are well controlled and consequently such bounds form one of the corner stones in many recent results in one dimensional dynamics for example renormalization theory rigidity density of hyperbolicity and local connectivity of julia sets

cluster number selection for a small set of samples using the bayesian ying yang model one major problem in cluster analysis is the determination of the number of clusters in this paper we describe both theoretical and experimental results in determining the cluster number for a small set of samples using the bayesian kullback ying yang byy model selection criterion under the second order approximation we derive a new equation for estimating the smoothing parameter in the cost function finally we propose a gradient descent smoothing parameter estimation approach that avoids complicated integration procedure and gives the same optimal result

a response model for multiple choice items in the mid 1960s samejima initiated the development of item response models that involve separate response functions for all of the alternatives in the multiple choice and likert type formats her work in this area began at the educational testing service and continued during a visit to the l l thurstone psychometric laboratory at the university of north carolina both samejima s 1969 this volume original model for graded item responses and bock s 1972 this volume model for nominal responses were originally intended to produce response functions for all of the alternatives of multiple choice items for various reasons neither model has proved entirely satisfactory for that purpose although both have been applied in other contexts using a combination of ideas suggested by bock 1972 and samejima 1968 1979 a multiple choice model was developed that produces response functions that fit unidimensional multiple choice tests better thissen and steinberg 1984 that model is the subject of this chapter

multiple solutions for a semilinear boundary value problem a computational multiplicity proof abstract we prove the first genuine partial differential equation result on a conjecture concerning the number of solutions of second order elliptic boundary value problems with a nonlinearity which grows superlinearly at the proof makes massive use of computer assistance after approximate solutions have been computed by a numerical mountain pass algorithm combined with a newton iteration to improve accuracy a fixed point argument is used to show the existence of exact solutions close to the approximations

range image segmentation using surface selection criterion in this paper we address the problem of recovering the true underlying model of a surface while performing the segmentation first and in order to solve the model selection problem we introduce a novel criterion which is based on minimising strain energy of fitted surfaces we then evaluate its performance and compare it with many other existing model selection techniques using this criterion we then present a robust range data segmentation algorithm capable of segmenting complex objects with planar and curved surfaces the presented algorithm simultaneously identifies the type order and geometric shape of each surface and separates all the points that are part of that surface this paper includes the segmentation results of a large collection of range images obtained from objects with planar and curved surfaces the resulting segmentation algorithm successfully segments various possible types of curved objects more importantly the new technique is capable of detecting the association between separated parts of a surface which has the same cartesian equation while segmenting a scene this aspect is very useful in some industrial applications of range data analysis

deriving ultrametric tree structures from proximity data confounded by differential stimulus familiarity this paper presents a new procedure called treefam for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity the objective of the proposed treefam procedure is to quantitatively filter out the effects of stimulus unfamiliarity in the estimation of an ultrametric tree a conditional alternating maximum likelihood procedure is formulated to simultaneously estimate an ultrametric tree under the unobserved condition of complete stimulus familiarity and subject specific parameters capturing the adjustments due to differential unfamiliarity we demonstrate the performance of the treefam procedure under a variety of alternative conditions via a modest monte carlo experimental study an empirical application provides evidence that the treefam outperforms traditional models that ignore the effects of unfamiliarity in terms of superior tree recovery and overall goodness of fit

application of model selection criteria to some problems in multivariate analysis a review of model selection criteria is presented with a view toward showing their similarities it is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model selection criteria consideration is given to application of model selection criteria to some problems of multivariate analysis especially the clustering of variables factor analysis and more generally describing a complex of variables

binomial regression with monotone splines a psychometric application abstract a binomial regression function p x models the probability of rj successes in nj trials as a function of the values of an observed covariate xj and or a latent variable j j 1 j this article explores the use of monotone regression splines to define p and applies them to the representation of test items as functions of examinee ability some illustrative data suggest that the flexibility of monotone splines permits the detection of item characteristics not observable using logistic based or log linear approaches a simulation study indicates that estimates of both item characteristic curves and ability are reasonably precise for numbers of items and examinees typical of large university lectures given a set of such binomial regression functions it can be useful to study the principal components of functional variation the extension of multivariate principal components analysis to permit the analysis of many item characteristic curves is described

on entropy and monotonicity for real cubic maps consider real cubic maps of the interval onto itself either with positive or with negative leading coefficient this paper completes the proof of the monotonicity conjecture which asserts that each locus of constant topological entropy in parameter space is a connected set the proof makes essential use of the thesis of christopher heckman and is based on the study of bones in the parameter triangle as defined by tresser and r mackay

a model based approach for visualizing the dimensional structure of ordered successive categories preference data a cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two or three way dominance data e g preference choice consideration measured on ordered successive category rating scales the technical description of the proposed model and estimation procedure are discussed as well as the rather unique joint spaces derived we then conduct a modest monte carlo simulation to demonstrate the parameter recovery of the proposed methodology as well as investigate the performance of various information heuristics for dimension selection a consumer psychology application is provided where the spatial results of the proposed model are compared to solutions derived from various traditional multidimensional unfolding procedures this application deals with consumers intending to buy new luxury sport utility vehicles suvs finally directions for future research are discussed

location estimation of a random signal source based on correlated sensor observations the problem of location estimation of a source of random signals using a network of sensors is considered a novel maximum likelihood estimation mle based approach using copula functions is proposed the measurements received at the sensors are often spatially correlated and characterized by a multivariate distribution using the theory of copulas the joint parametric density of sensor observations joint likelihood is approximated assuming only the knowledge of the marginal likelihood functions of the sensor observations the problem of selecting the best copula function to model the joint likelihood is approached as one of model selection and a model fusion strategy is used to reduce the effect of selection bias an example involving source localization of a poisson source is presented to illustrate the proposed approach and demonstrate its performance

weighted likelihood estimation of ability in item response theory applications of item response theory which depend upon its parameter invariance property require that parameter estimates be unbiased a new method weighted likelihood estimation wle is derived and proved to be less biased than maximum likelihood estimation mle with the same asymptotic variance and normal distribution wle removes the first order bias term from mle two monte carlo studies compare wle with mle and bayesian modal estimation bme of ability in conventional tests and tailored tests assuming the item parameters are known constants the monte carlo studies favor wle over mle and bme on several criteria over a wide range of the ability scale

on the unboundedness of the number of solutions of a dirichlet problem in an informative article 11 lazer and mckenna proposed a modified mathematical model for the onset of large amplitude oscillations in suspension bridges by wind with specific velocities the study was motivated by the inadequacy of older theories to explain the collapse of the tacoma narrows bridge of seattle in 1941 in the lazer mckenna model the motion of the bridge is as usual governed by a system of differential equations more specifically semilinear elliptic differential equations the complexity of which depends on the degree of approximation and simplifications one is willing to accept one of the new ideas introduced is the asymmetry of the restoring force from a cable with respect to expansion and compression the author s basic assumption is that the cable strongly resists expansion but does not resist compression the study of elliptic equations involving a nonlinear restoring force term of this type is still largely unexplored in the same article lazer and mckenna posed many interesting open questions some of these have not been answered even in the one dimensional case when the elliptic equation becomes a second order nonlinear ordinary differential equation in an earlier article 5 we gave a counterexample to their problem 4 in this article we take up another one of these questions problem 2 concerning a nonlinear function that grows very fast at infinity the boundary value problem we are interested in is

a characterization of monotone unidimensional latent variable models recently the problem of characterizing monotone unidimensional latent variable models for binary repeated measures was studied by ellis and van den wollenberg and by junker we generalize their work with a de finetti like characterization of the distribution of repeated measures x x 1 x 2 that can be represented with mixtures of likelihoods of independent but not identically distributed random variables where the data satisfy a stochastic ordering property with respect to the mixing variable the random variables x j may be arbitrary real valued random variables we show that the distribution of x can be given a monotone unidimensional latent variable representation that is useful in the sense of junker if and only if this distribution satisfies conditional association ca and a vanishing conditional dependence vcd condition which asserts that finite subsets of the variables in x become independent as we condition on a larger and larger segment of the remaining variables in x it is also interesting that the mixture representation is in a certain ordinal sense unique when ca and vcd hold the characterization theorem extends and simplifies the main result of junker and generalizes methods of ellis and van den wollenberg to a much broader class of models exchangeable sequences of binary random variables also satisfy both ca and vcd as do exchangeable sequences arising as location mixtures in the same way that de finetti s theorem provides a path toward justifying standard i i d mixture components in hierarchical models on the basis of our intuitions about the exchangeability of observations this theorem justifies one dimensional latent variable components in hierarchical models in terms of our intuitions about positive association and redundancy between observations because these conditions are on the joint distribution of the observable data x they may also be used to construct asymptotically power 1 tests for unidimensional latent variable models

feigenbaum coullet tresser universality and milnor s hairiness conjecture we prove the feigenbaum coullet tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type this gives the first computer free proof of the original feigenbaum observation of the universal parameter scaling laws we use the hyperbolicity theorem to prove milnor s conjectures on self similarity and hairiness of the mandelbrot set near the corresponding parameter values we also conclude that the set of real infinitely renormalizable quadratics of type bounded by some n 1 has hausdorff dimension strictly between 0 and 1 in the course of getting these results we supply the space of quadratic like germs with a complex analytic structure and demonstrate that the hybrid classes form a complex codimension one foliation of the connectedness locus

data model conclusion doing it again this paper explores the robustness of conclusions from a statistical model against variations in model choice rather than variations in random sampling and random assignment to treatments which are the usual variations covered by inferential statistics after the problem formulation in section 1 section 2 presents an example from box and tiao in which variation in parent distribution is modeled for a one sample location problem an adaptive bayesian procedure permits to use a weighted mixture of parent distributions rather than choosing just one such as a normal or a uniform distribution in section 3 similar considerations are applied to an event history model for the influence of education and gender on age at first marriage but here the conclusions are hardly influenced by the choice of the duration distribution in section 4 a brief discussion of model choice in factor analysis and structural equation models is followed by a more elaborate treatment of the choice of integer valued slopes for item response functions in the oplm model which is an extension of the rasch model a modest simulation study suggests that adaptive bayesian modeling with a mixture of sets of slopes works better than fixing one set of postulated slopes the paper concludes with some remarks on the roles and sources of prior distributions followed by a short epilogue which argues that simultaneous consideration of a class of models for the same data is sometimes superior to exclusively analyzing the data under one specific model chosen from such a class

a similarity based smoothing approach to nondimensional item analysis the probability that an examinee chooses a particular option within an item is estimated by averaging over the responses to that item of examinees with similar response patterns for the whole test the approach does not presume any latent variable structure or any dimensionality but simulated and actual data analyses are presented to show that when the responses are determined by a latent ability variable this similarity based smoothing procedure can reveal the dimensionality of ability very satisfactorily

transition to topological chaos for circle maps abstract many biperiodic flows can be modelled by maps of a circle to itself for such maps the transition from zero to positive topological entropy can be achieved in several ways we describe all the possible routes for smooth circle maps and discuss the relevance of our results to the transition to chaos for two frequency systems

on the choice of a model to fit data from an exponential family let x 1 cdots x n be iid observations coming from an exponential family the problem of interest is this given a finite number of models m j smoothly curved manifolds in mathbb r k choose the best model to fit the observations with some penalty for choosing models with dimensions which are too large a result of schwarz is made more specific and is extended to the case where the models are curved manifolds if s y n j is up to a constant c n independent of the model the log of the posterior probability of the j th model where the sample mean y n 1 n sum n i 1 x i has been replaced by y schwarz suggested an asymptotic expansion of s y n j whose leading terms are gamma y n j n sup psi in m j cap theta y psi b psi frac 1 2 k j log n in the case where the models are affine subspaces of mathbb r k we establish a similar asymptotic expansion including the next term with uniform bounds for y in a compact neighborhood of nabla b theta where theta is the true value of the parameter we suggest a criterion for the choice of the best model that consists of maximizing the three leading terms in the expansion s y n j we show that the criterion gives the correct model with probabilities p n theta rightarrow 1 as n rightarrow infty

tail measurability in monotone latent variable models we consider latent variable models for an infinite sequence or universe of manifest observable variables that may be discrete continuous or some combination of these the main theorem is a general characterization by empirical conditions of when it is possible to construct latent variable models that satisfy unidimensionality monotonicity conditional independence andtail measurability tail measurability means that the latent variable can be estimated consistently from the sequence of manifest variables even though an arbitrary finite subsequence has been removed the characterizing necessary and sufficient conditions that the manifest variables must satisfy for these models are conditional association and vanishing conditional dependence as one conditions upon successively more other manifest variables our main theorem considerably generalizes and sharpens earlier results of ellis and van den wollenberg 1993 holland and rosenbaum 1986 and junker 1993 it is also related to the work of stout 1990 the main theorem is preceded by many results for latent variable modelsin general not necessarily unidimensional and monotone they pertain to the uniqueness of latent variables and are connected with the conditional independence theorem of suppes and zanotti 1981 we discuss new definitions of the concepts of true score and subpopulation which generalize these notions from the stochastic subject random sampling and domain sampling formulations of latent variable models e g holland 1990 lord novick 1968 these definitions do not require the a priori specification of a latent variable model

global complexity and essential simplicity a conjectural picture of the boundary of chaos for smooth endomorphisms of the interval abstract mixing a symbolic approach to the dynamics of the period doubling operators recent results by sullivan on the renormalization for real analytic maps and some confidence a global picture emerges for the structure of the boundary of positive topological entropy in spaces of smooth endomorphisms of the interval

rigidity for real polynomials we prove the topological or combinatorial rigidity property for real polynomials with all critical points real and nondegenerate which completes the last step in solving the density of axiom a conjecture in real one dimensional dynamics

facaic model selection algorithm for the orthogonal factor model using aic and caic this paper describes the authors fortran algorithm facaic for choosing the number of factors for an orthogonal factor model using akaike s information criterion facaic utilizes the imsl subroutine ofcomm

admissible selection of an accurate and parsimonious normal linear regression model let mo be a normal linear regression model and let m1 mk be distinct proper linear submodels of mo let k e 0 k be a model selection rule based on observed data from the true model given k let the unknown parameters of the selected model ms be fitted by the maximum likelihood method a loss function is introduced which depends additively on two parts i a measure of the difference between the fitted model ms and the true model and ii a measure cs of the complexity of the selected model a natural model selection rule k which minimizes an empirical version of this loss is shown to be admissible and very nearly bayes

a new item response theory modeling approach with applications to unidimensionality assessment and ability estimation using an infinite item test framework it is argued that the usual assumption of local independence be replaced by a weaker assumption essential independence a fortiori the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality essential unidimennsionnality implies the existence of a unique unidimensional latent ability essential unidimensionality is equivalent to the consistent estimation of this latnet ability in an ordinal scaling sense using anybalanced empirical scaling a variation of this estimation approach allows consistent estimation of ability on the given latent ability scale

filter order selection in adaptive maximum likelihood estimation the choice of the number of parameters is an important problem in adaptive filtering in the general ground of maximum likelihood ml parameter estimation akaike criterion has proved to be a very useful tool significant results and the importance of the kullback information measure as the implicit measure of distance associated with ml estimation are discussed application of these results to adaptive filtering is then considered for time invariant and time varying parametric models the corresponding practical forms of akaike criterion are given in the time varying case this criterion may be used as a way to fit the model into the nonstationarity of an exact filter the possible generalization of the akaike criterion to non ml estimation is discussed and application is made for weighted least squares estimation a more general approach to the nonstationary case is given by assuming a linear stochastic model for the vector of the filter coefficients in which case the ml estimate is computed recursively using the kalman filtering equation then the random sequence of kalman gains is close to a deterministic average sequence this sequence may be precomputed and gives an optimal choice for the gain matrices in an adaptive gradient type filter

bayesian estimation in the three parameter logistic model a bayesian procedure is developed for the estimation of parameters in the two parameter logistic item response model joint modal estimates of the parameters are obtained and procedures for the specification of prior information are described through simulation studies it is shown that bayesian estimates of the parameters are superior to maximum likelihood estimates in the sense that they are a more meaningful since they do not drift out of range and b more accurate in that they result in smaller mean squared differences between estimates and true values

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

on model selection and the arc sine laws generalizations of the arc sine laws are shown to provide insight into the operating characteristics of certain techniques for selecting models to fit a given data set when the available models are nested as a corollary one sees that a popular technique may be expected to include about one superfluous parameter even if the sample size is large

the boundary of chaos for interval mappings a goal in the study of dynamics on the interval is to understand the transition to positive topological entropy there is a conjecture from the 1980s that the only route to positive topological entropy is through a cascade of period doubling bifurcations we prove this conjecture in natural families of smooth interval maps and use it to study the structure of the boundary of mappings with positive entropy in particular we show that in families of mappings with a fixed number of critical points the boundary is locally connected and for analytic mappings that it is a cellular set

the iteration of cubic polynomials part i the global topology of parameter space fonctions univalentes en dynamique analytique complexe torsion de la structure complexe topologie globale de l espace parametre

biclustering models for two mode ordinal data the work in this paper introduces finite mixture models that can be used to simultaneously cluster the rows and columns of two mode ordinal categorical response data such as those resulting from likert scale responses we use the popular proportional odds parameterisation and propose models which provide insights into major patterns in the data model fitting is performed using the em algorithm and a fuzzy allocation of rows and columns to corresponding clusters is obtained the clustering ability of the models is evaluated in a simulation study and demonstrated using two real data sets

period doubling forc2 mappings the rigorous treatment of period doubling cascades developed by lanford for analytic families is extended to coverc2 families for any 0 this requires spectral analysis of the linearised doubling operator on spaces of differentiable mappings and a version of stable manifold theory which takes account of the non differentiability of the doubling operator on these spaces

on the superlinear lazer mckenna conjecture abstract we prove the lazer mckenna conjecture for a superlinear elliptic problem of ambrosetti prodi type by constructing solutions with sharp peaks

on the metric properties of multimodal interval maps and c 2 density of axiom a in this paper we shall prove that axiom a maps are dense in the space of c 2 interval maps endowed with the c 2 topology as a step of the proof we shall prove real and complex a priori bounds for first return maps to certain small neighborhoods of the critical points of real analytic multimodal interval maps with non degenerate critical points we shall also discuss rigidity for interval maps without large bounds

the chic model a global model for coupled binary data often problems result in the collection of coupled data which consist of different n way n mode data blocks that have one or more modes in common to reveal the structure underlying such data an integrated modeling strategy with a single set of parameters for the common mode s that is estimated based on the information in all data blocks may be most appropriate such a strategy implies a global model consisting of different n way n mode submodels and a global loss function that is a weighted sum of the partial loss functions associated with the different submodels in this paper such a global model for an integrated analysis of a three way three mode binary data array and a two way two mode binary data matrix that have one mode in common is presented a simulated annealing algorithm to estimate the model parameters is described and evaluated in a simulation study an application of the model to real psychological data is discussed

a multidimensional item response model constrained latent class analysis using the gibbs sampler and posterior predictive checks in this paper it will be shown that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models the parameters of this latent class model will be estimated using an application of the gibbs sampler it will be illustrated that the gibbs sampler is an excellent tool if inequality constraints have to be taken into consideration when making inferences model fit will be investigated using posterior predictive checks checks for manifest monotonicity the agreement between the observed and expected conditional association structure marginal local homogeneity and the number of latent classes will be presented

factor analysis and aic the information criterion aic was introduced to extend the method of maximum likelihood to the multimodel situation it was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis the use of the aic criterion in the factor analysis is particularly interesting when it is viewed as the choice of a bayesian model this observation shows that the area of application of aic can be much wider than the conventional i i d type models on which the original derivation of the criterion was based the observation of the bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings

optimal product positioning based on paired comparison data a new approach for analyzing paired comparison data is proposed which combines a probabilistic ideal point model with product positioning issues unlike traditional approaches based on paired comparison data the same formulation is used for estimating a joint space representation of consumer segments and products as well as for determining optimal new product positioning options in a relevant product market a monte carlo experiment is presented and real world coffee market data are used to show advantages of the new approach

decay of geometry for unimodal maps negative schwarzian case we show that decay of geometry holds for unimodal maps of the interval which have negative schwarzian derivative sufficient finite smoothness and a nondegenerate critical point the proof is based on pseudo analytic extensions of order at least 2 they allow us to modify sullivan s principle that rescaled high iterates of one dimensional maps tend to analytic limits in such a way that no passage to a limit is actually needed but the maps are shown to approach the analytic class in a well defined sense as a technical improvement this method yields a uniform estimate in the case of renormalizable maps