building an identifiable latent class model with covariate effects on underlying and measured variables in recent years latent class models have proven useful for analyzing relationships between measured multiple indicators and covariates of interest such models summarize shared features of the multiple indicators as an underlying categorical variable and the indicators substantive associations with predictors are built directly and indirectly in unique model parameters in this paper we provide a detailed study on the theory and application of building models that allow mediated relationships between primary predictors and latent class membership but that also allow direct effects of secondary covariates on the indicators themselves theory for model identification is developed we detail an expectation maximization algorithm for parameter estimation standard error calculation and convergent properties comparison of the proposed model with models underlying existing latent class modeling software is provided a detailed analysis of how visual impairments affect older persons functioning requiring distance vision is used for illustration

c 1 conformal field theories on riemann surfaces we study the theory ofc 1 torus and 2 orbifold models on general riemann surfaces the operator content and occurrence of multi critical points in this class of theories is discussed the partition functions and correlation functions of vertex operators and twist fields are calculated using the theory of double covered riemann surfaces it is shown that orbifold partition functions are sensitive to the torelli group we give an algebraic construction of the operator formulation of these nonchiral theories on higher genus surfaces modular transformations are naturally incorporated as canonical transformations in the hilbert space

latent structure analysis of a set of multidimensional contingency tables abstract statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables three basic classes of models are considered a models that assume complete homogeneity across tables b models that allow partial homogeneity across tables and c models that allow complete heterogeneity methods are presented for testing whether these models are congruent with the data in the tables and for assessing the significance of differences among the tables in the estimated parameters to illustrate the wide applicability of these models and methods we present analyses of two quite different sets of data

on the solution of the minimal rational interpolation problem it is shown that the reachability and the observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational bitangen tial interpolation problem

latent class analysis of two way contingency tables by bayesian methods summary latent class analysis in two way contingency tables usually suffers from unidentifiability problems these can be overcome by using bayesian techniques in which prior distributions are assumed on the latent parameters application of these techniques however involves some unusual computational difficulties bayesian techniques suitable for latent class analyses together with a remedy to the computational difficulties are discussed in this paper

continued fraction decomposition of linear systems in the state space abstract various results pertaining to a continued fraction decomposition of matrix formal power series and in particular of multi input multi output linear constant systems are presented from a state space point of view

new results on the algebraic theory of linear systems the solution of the cover problems abstract we give the complete solution of a large class of problems in linear system theory the so called cover problems these problems are formulated and solved both in the state space and in the input output frameworks the key concept which allows the effective parametrization of all solutions of the cover problems is that of the partial realizations of a sequence of matrices it is shown that the solutions of the state space cover problems can be expressed as state spaces of the partial realizations of appropriately defined sequences of matrices and the solution of the input output cover problems can be expressed as a simple function of the functions of the partial realizations of the sequences of mentioned above

fixed distance latent class models for the analysis of sets of two way contingency tables this paper develops and describes the application of modified latent class models for analyzing sets of two way contingency tables the proposed fixed distance models differ from traditional latent class models in that the assumption of local stochastic independence is superseded by allowing interactions of the manifest variables within each class which can be represented by a single association parameter as an example two data sets on eye color by hair color collected in caithness n1 5 387 and aberdeen n2 22 361 and fixed distance models with up to six classes three classes per data set are considered finally leading to satisfactory fit and rather simple interpretation

partiallyu 1 compactified scalar massless field on the compact riemann surface and the bosonic string amplitudes the theory of the partiallyu 1 compactified scalar massless field on the compact riemann surface with nambu goto action is defined the partition function is determined completely by a choice of the finite dimensional approximations the correlation functions are the only correctly defined objects of the theory the averages of the correlation function asymptotic values provide the amplitudes for the compact riemann surfaces of any genus the usual bosonic string amplitudes are the special cases of the above amplitudes

mixed inar 1 poisson regression models analyzing heterogeneity and serial dependencies in longitudinal count data this paper presents finite mixture versions of integer valued autoregressive inar poisson regression models for investigating regularity and predictability of purchase behavior over time the approach facilitates the analysis of heterogeneity and serial correlation effects as well as conditional and marginal analyses of the effects of covariates an application to scanner panel data of detergents yields substantive insights into sources of autodependencies in individual category purchases

analysis of sets of two way contingency tables using association models abstract a class of models is introduced for the analysis of group differences in the association between two discrete variables the rc m association model for two way tables is reviewed and alternative weighting systems for identifying interaction parameters are presented this model is generalized for the setting where a two way contingency table is available for two or more groups various restricted models can be used to examine possible sources of intergroup heterogeneity in the association these sources pertain to heterogeneity in the intrinsic association and or in the scores for the row and column variables the importance of weights used to identify the row and column scores is emphasized a classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here

semiparametric estimation in the rasch model and related exponential response models including a simple latent class model for item analysis abstract the rasch model for item analysis is an important member of the class of exponential response models in which the number of nuisance parameters increases with the number of subjects leading to the failure of the usual likelihood methodology both conditional likelihood methods and mixture model techniques have been used to circumvent these problems in this article we show that these seemingly unrelated analyses are in fact closely linked to each other despite dramatic structural differences between the classes of models implied by each approach we show that the finite mixture model for j dichotomous items having t latent classes gives the same estimates of item parameters as conditional likelihood on a set whose probability approaches one if t j 1 2 unconditional maximum likelihood estimators for the finite mixture model can be viewed as keifer wolfowitz estimators for the random effects version of the rasch model latent class versions of the model are especially attractive when t is

latent class model diagnosis summary in many areas of medical research such as psychiatry and gerontology latent class variables are used to classify individuals into disease categories often with the intention of hierarchical modeling problems arise when it is not clear how many disease classes are appropriate creating a need for model selection and diagnostic techniques previous work has shown that the pearson 2 statistic and the log likelihood ratio g2 statistic are not valid test statistics for evaluating latent class models other methods such as information criteria provide decision rules without providing explicit information about where discrepancies occur between a model and the data identifiability issues further complicate these problems this paper develops procedures for assessing markov chain monte carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using markov chain monte carlo techniques simulations and a psychiatric example are presented to demonstrate the effective use of these methods

a maximum likelihood method for latent class regression involving a censored dependent variable the standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored this model is generalized by developing a conditional mixture maximum likelihood method for latent class censored regression the proposed method simultaneously estimates separate regression functions and subject membership in k latent classes or groups given a censored dependent variable for a cross section of subjects maximum likelihood estimates are obtained using an em algorithm the proposed method is illustrated via a consumer psychology application

flat output characterization for linear systems using polynomial matrices this paper is devoted to the study of linear flat outputs for linear controllable time invariant systems in polynomial matrix form we characterize the transformations expressing the system variables in terms of a linear flat output and derivatives called defining matrices as the kernel of a polynomial matrix an application to trajectory planning is presented showing the usefulness of the present characterization

linear logistic latent class analysis for polytomous data abstract for latent class analysis a widely known statistical method for the unmixing of an observed frequency table into several unobservable ones a flexible model is presented in order to restrain the unknown class sizes mixing weights and the unknown latent response probabilities two systems of basic equations are stated such that they simultaneously allow parameter fixations the equality of certain parameters as well as linear logistic constraints of each of the original parameters the maximum likelihood equations for the parameters of this linear logistic latent class analysis are given and their estimation by means of the em algorithm is described further the criteria for their local identifiability and statistical tests pearson and likelihood ratio 2 for goodness of fit are outlined the practical applicability of linear logistic latent class analysis is demonstrated by three examples mixed logistic regression a mixed bradley terry model for paired comparisons with ties and a lo

column reduced rational matrix functions with given null pole data in the complex plane abstract explicit formulas are given for rational matrix functions which have a prescribed null pole structure in the complex plane and are column reduced at infinity a full parametrization of such functions is obtained the results are specified and developed further for matrix polynomials

bayesian inferences of latent class models with an unknown number of classes this paper focuses on analyzing data collected in situations where investigators use multiple discrete indicators as surrogates for example a set of questionnaires a very flexible latent class model is used for analysis we propose a bayesian framework to perform the joint estimation of the number of latent classes and model parameters the proposed approach applies the reversible jump markov chain monte carlo to analyze finite mixtures of multivariate multinomial distributions in the paper we also develop a procedure for the unique labeling of the classes we have carried out a detailed sensitivity analysis for various hyperparameter specifications which leads us to make standard default recommendations for the choice of priors the usefulness of the proposed method is demonstrated through computer simulations and a study on subtypes of schizophrenia using the positive and negative syndrome scale panss

latent class analysis of complex sample survey data application to dietary data high fruit and vegetable intake is associated with decreased cancer risk however dietary recall data from national surveys suggest that on any given day intake falls below the recommended minima of three daily servings of vegetables and two daily servings of fruit there is no single widely accepted measure of usual intake one approach is to regard the distribution of intake as a mixture of regular relatively frequent and nonregular relatively infrequent consumers using an indicator of whether an individual consumed the food of interest on the recall day we use a new approach to summarizing dietary data latent class analysis lca to estimate usual intake of vegetables the data consist of four 24 hour dietary recalls from the 1985 continuing survey of intakes by individuals collected from 1 028 women traditional lca based on simple random sampling was extended to complex survey data by introducing sample weights into the latent class estimation algorithm and by accounting for the co

optimization based model fitting for latent class and latent profile analyses statisticians typically estimate the parameters of latent class and latent profile models using the expectation maximization algorithm this paper proposes an alternative two stage approach to model fitting the first stage uses the modified k means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model the second stage then uses mixture modeling treating the class membership as known the proposed approach is theoretically justifiable directly checks the conditional independence assumption and converges much faster than the full likelihood approach when analyzing high dimensional data this paper also develops a new classification rule based on latent variable models the proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease which makes it perfect for analyzing high throughput genomic data simulation studies and real data analysis demonstrate the advantages of the proposed method

calculus on arithmetic surfaces in a2 and a3 arakelov introduces an intersection calculus for arithmetic surfaces that is for stable models of curves over a number field in this paper we intend to show that his intersection product has a lot of useful properties more precisely we show that the following properties from the theory of algebraic surfaces have an analogue in our situation

the mumford form and the polyakov measure in string theory an explicit formula is derived for the mumford form on the moduli space of algebraic curves according to the belavin knizhnik theorem this gives a formula for the polyakov bosonic string measure

concomitant variable latent class models abstract this article introduces and illustrates a new type of latent class model in which the probability of latent class membership is functionally related to concomitant variables with known distribution the function or so called submodel may be logistic exponential or another suitable form concomitant variable models supplement latent class models incorporating grouping by providing more parsimonious representations of data for some cases also concomitant variable models are useful when grouping models involve a greater number of parameters than can be meaningfully fit to existing data sets although parameter estimates may be calculated using standard iterative procedures such as the newton raphson method sample analyses presented here employ a derivative free approach known as the simplex method a general procedure for imposing linear constraints on the parameter estimates is introduced a data set involving arithmetic test items in a mastery testing context is used to illustrate fitting a

collapsibility and response variables in contingency tables summary various definitions of the collapsibility of a hierarchical log linear model for a multidimensional contingency table are considered and shown to be equivalent necessary and sufficient conditions for collapsibility are found in terms of the generating class it is shown that log linear models are appropriate for tables with response and explanatory variables if and only if they are collapsible onto the explanatory variables some key word8 collapsibility contingency table graphical model interaction graph log linear model response variable s sufficiency shown to be closely related some models have the property that relations between a set of the classifying factors may be studied by examination of the table of marginal totals formed by summing over the remaining factors such models are said to be collapsible onto the given set of factors collapsibility has important consequences for hypothesis testing and model selection and can be useful in data reduction we consider various definitions of collapsibility and show their equivalence furthermore necessary and sufficient conditions for collapsi bility are found in terms of the generating class many tables analysed in practice involve response variables simple examples one of which is given in 3 suffice to show the importance of distinguishing between response and explanatory variables first that inappropriate models may be avoided and second that natural and relevant models that are not log linear may be considered this paper characterizes appropriate and inappropriate log linear models for tables with response variables and some alternative approaches for the analysis of such tables are briefly considered we consider a multidimensional contingency table n based on a set of classifying factors f for a given subset a of f we are interested in the table of marginal totals na that is to say the table of cell counts summed over the remaining factors ac that is the complement of a in f we identify a hierarchical log linear model l that is the set of probabilities p e l with its generating class whose elements generators are given in square brackets thus for example the model ab bcd for a 4 way table corresponds

on scaling models applied to data from several groups statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups these methods can be used to a compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups b compare the corresponding estimated item reliabilities or item response error rates for the different groups and c test whether the scaling model applied to the several groups can be replaced by a more parsimonious scaling model that includes various homogeneity constraints i e constraints that describe which parameters in the model are the same for the several groups various kinds of scaling models are considered here in the multiple group context

matrix fractions and strict system equivalence unimodular equivalence ue is defined for matrix fraction decompositions mfds it is shown that if an mfd is regarded as a quadruple d s n s i then uni modular equivalence and fuhrmann strict system equivalence coincide it is thus established that ue for mfds and system similarity for state space representations are exact counterparts a brief discussion on extended unimodular equivalence eue of polynomial matrices is included and a short polynomial matrix proof that the invariant factors of the smith form are preserved under eue is given

the application of latent class models in adaptive testing this paper provides a description of a new adaptive testing algorithm based on a latent class modeling framework the algorithm incorporates a four stage iterative procedure that conditionally minimizes expected loss in classification of respondents across different content domains the classification decisions relate to the membership of a person in a category of a latent variable for each of the separate domains considered the algorithm appears to be particularly effective when latent class membership is related across the various domains of interest since classification decisions on domains assessed early in the process are used to revise the probabilities for latent class membership on domains for which classification decisions have not yet been made to assess the effectiveness of the proposed algorithm a simulation based upon real data was conducted for this example the algorithm proved to be relatively efficient requiring only 40 of the number of items needed under a nonadaptive approach in addition the algorithm provided classification decisions which in 96 of the cases were consistent with decisions based upon all available items when the maximum acceptable classification error rate was set at 5

a hierarchical finite mixture model that accommodates zero inflated counts non independence and heterogeneity a number of mixture modeling approaches assume both normality and independent observations however these two assumptions are at odds with the reality of many data sets which are often characterized by an abundance of zero valued or highly skewed observations as well as observations from biologically related i e non independent subjects we present here a finite mixture model with a zero inflated poisson regression component that may be applied to both types of data this flexible approach allows the use of covariates to model both the poisson mean and rate of zero inflation and can incorporate random effects to accommodate non independent observations we demonstrate the utility of this approach by applying these models to a candidate endophenotype for schizophrenia but the same methods are applicable to other types of data characterized by zero inflation and non independence

bivariate modelling of clustered continuous and ordered categorical outcomes simultaneous observation of continuous and ordered categorical outcomes for each subject is common in biomedical research but multivariate analysis of the data is complicated by the multiple data types here we construct a model for the joint distribution of bivariate continuous and ordinal outcomes by applying the concept of latent variables to a multivariate normal distribution the approach is then extended to allow for clustering of the bivariate outcomes the model can be parameterized in a way that allows writing the joint distribution as a product of a standard random effects model for the continuous variable and a correlated cumulative probit model for the ordinal outcome this factorization suggests convenient parameter estimation using estimating equations foetal weight and malformation data from a developmental toxicity experiment illustrate the results

predicting latent class scores for subsequent analysis latent class regression models relate covariates and latent constructs such as psychiatric disorders though full maximum likelihood estimation is available estimation is often in three steps i a latent class model is fitted without covariates ii latent class scores are predicted and iii the scores are regressed on covariates we propose a new method for predicting class scores that in contrast to posterior probability based methods yields consistent estimators of the parameters in the third step additionally in simulation studies the new methodology exhibited only a minor loss of efficiency finally the new and the posterior probability based methods are compared in an analysis of mobility exercise

on recursiveness and related topics in linear systems a decomposition of matrix formal power series linear systems is developed the interconnections between formal power series realization pade approximation recursiveness berlekamp massey algorithm feedback interconnections matrix linear fractional representations matrix continued fractions and the matrix euclidean algorithm are thereby revealed

selecting the number of classes under latent class regression a factor analytic analogue recently the regression extension of latent class analysis rlca model has received much attention in the field of medical research the basic rlca model summarizes shared features of measured multiple indicators as an underlying categorical variable and incorporates the covariate information in modeling both latent class membership and multiple indicators themselves to reduce complexity and enhance interpretability one usually fixes the number of classes in a given rlca often goodness of fit methods comparing various estimated models are used as a criterion to select the number of classes in this paper we propose a new method that is based on an analogous method used in factor analysis and does not require repeated fitting two ideas with application to many settings other than ours are synthesized in deriving the method a connection between latent class models and factor analysis and techniques of covariate marginalization and elimination a monte carlo simulation study is presented to evaluate the behavior of the selection procedure and compare to alternative approaches data from a study of how measured visual impairments affect older persons functioning are used for illustration

mixed effects analyses of rank ordered data this paper presents a synthesis of bock s 1972 nominal categories model and luce s 1959 choice model for mixed effects analyses of rank ordered data it is shown that the proposed ranking model is both parsimonious and flexible in accounting for preference heterogeneity as well as fixed and random effects of covariates relationships to other approaches including takane s 1987 ideal point discriminant model and croon s 1989 latent class version of luce s ranking model are also discussed the application focuses on a ranking study of behavioral traits that parents find desirable in children

multilevel and latent variable modeling with composite links and exploded likelihoods composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models applications considered include survival or duration models models for rankings small area estimation with census information models for ordinal responses item response models with guessing randomized response models unfolding models latent class models with random effects multilevel latent class models models with log normal latent variables and zero inflated poisson models with random effects some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation

two step estimation of models between latent classes and external variables we consider models which combine latent class measurement models for categorical latent variables with structural regression models for the relationships between the latent classes and observed explanatory and response variables we propose a two step method of estimating such models in its first step the measurement model is estimated alone and in the second step the parameters of this measurement model are held fixed when the structural model is estimated simulation studies and applied examples suggest that the two step method is an attractive alternative to existing one step and three step methods we derive estimated standard errors for the two step estimates of the structural model which account for the uncertainty from both steps of the estimation and show how the method can be implemented in existing software for latent variable modelling

on canonical forms for linear constant systems let f 0 h be a reachable system we introduce the notion of a nice selection and that of a minimal nice selection of column vectors of the reachability matrix g fg these notions lead to a unified treatment and a parametrization of all the and all the t canonical forms of f 0 h which are sometimes called first and second control canonical forms this global approach shows that the and the canonical forms are local coordinates of the quasi projeetive algebraic variety of all reachable systems of fixed dimension modulo basis change in the state space more over the canonical forms of f g h we mentioned above are in bijective correspondence with the so called and and matrix fraction representations of its transfer function finally we investigate a canonical form for proper rational matrix fractions which turns out to be a matrix fraction representation