a note on the quadratic exponential binary distribution summary the joint distribution of p binary variables is studied in the quadratic exponential form containing only main effects and two factor interactions in the log probabilities approximate versions of marginalized forms of the distribution are studied based on taylor expansion and a number of conclusions drawn

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

robust tests for treatment effects based on censored recurrent event data observed over multiple periods summary we derive semiparametric methods for estimating and testing treatment effects when censored recurrent event data are available over multiple periods these methods are based on estimating functions motivated by a working mixed poisson assumption under which conditioning can eliminate subject specific random effects robust pseudoscore test statistics are obtained via sandwich variance estimation the relative efficiency of conditional versus marginal analyses is assessed analytically under a mixed time homogeneous poisson model the robustness and empirical power of the semiparametric approach are assessed through simulation adaptations to handle recurrent events arising in crossover trials are described and these methods are applied to data from a two period crossover trial of patients with bronchial asthma

autoregressive and cross lagged model for bivariate non commensurate outcomes autoregressive and cross lagged models have been widely used to understand the relationship between bivariate commensurate outcomes in social and behavioral sciences but not much work has been carried out in modeling bivariate non commensurate e g mixed binary and continuous outcomes simultaneously we develop a likelihood based methodology combining ordinary autoregressive and cross lagged models with a shared subject specific random effect in the mixed model framework to model two correlated longitudinal non commensurate outcomes the estimates of the cross lagged and the autoregressive effects from our model are shown to be consistent with smaller mean squared error than the estimates from the univariate generalized linear models inclusion of the subject specific random effects in the proposed model accounts for between subject variability arising from the omitted and or unobservable but possibly explanatory subject level predictors our model is not restricted to the case with equal number of events per subject and it can be extended to different types of bivariate outcomes we apply our model to an ecological momentary assessment study with complex dependence and sampling data structures specifically we study the dependence between the condom use and sexual satisfaction based on the data reported in a longitudinal study of sexually transmitted infections we find negative cross lagged effect between these two outcomes and positive autoregressive effect within each outcome copyright 2017 john wiley sons ltd

robust estimation of the variance in moment methods for extra binomial and extra poisson variation when faced with data in the form of overdispersed counts or proportions moment methods allow consistent parameter estimation when only the form of the mean and variance is specified if the variance form is misspecified these methods still yield consistent parameter estimates though with lower efficiency and the variances of the estimates will be inconsistent a variance correction is available that yields consistent variance estimates in these circumstances the asymptotic and small sample efficiencies of this correction are calculated and its performance under variance misspecification is studied a group randomized breast self examination prevention study that is now underway serves as a focal point for the study of these properties the use of the variance correction in modelling is illustrated on a teratology data set

the estimation of age period and cohort effects for vital rates in models for vital rates which include effects due to age period and cohort there is aliasing due to a linear dependence among these three factors this dependence arises both when age and period intervals are equal and when they are not one solution to the dependence is to set an arbitrary constraint on the parameters estimable functions of the parameters are invariant to the particular constraint applied for evenly spaced intervals deviations from linearity are estimable but only a linear function of the three slopes is estimable when age and period intervals have different widths further aliasing occurs it is assumed that the number of deaths in the numerator of the rate equation has a poisson distribution the calculations are illustrated with data on mortality from prostate cancer among nonwhites in the u s

pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data abstract we show how the dynamic logit model for binary panel data may be approximated by a quadratic exponential model under the approximating model simple sufficient statistics exist for the subject specific parameters introduced to capture the unobserved heterogeneity between subjects the latter must be distinguished from the state dependence which is accounted for by including the lagged response variable among the regressors by conditioning on the sufficient statistics we derive a pseudo conditional likelihood estimator of the structural parameters of the dynamic logit model which is simple to compute asymptotic properties of this estimator are studied in detail simulation results show that the estimator is competitive in terms of efficiency with estimators recently proposed in the econometric literature

correlated binary regression using a quadratic exponential model summary a model of quadratic exponential form is parameterized in terms of marginal means and pairwise correlations for the regression analysis of correlated binary data pseudo maximum likelihood methods using a special case termed the multiplicative model are proposed but are noted to be computationally unattractive if the blocks of correlated responses are at all large on the other hand score estimating functions for mean and correlation parameters are shown to be of a particularly simple form under the quadratic exponential family special cases of such estimating functions having attractive computational properties are identified and illustrated

binary models for marginal independence summary log linear models are a classical tool for the analysis of contingency tables in particular the subclass of graphical log linear models provides a general framework for modelling conditional independences however with the exception of special structures marginal independence hypotheses cannot be accommodated by these traditional models focusing on binary variables we present a model class that provides a framework for modelling marginal independences in contingency tables the approach that is taken is graphical and draws on analogies with multivariate gaussian models for marginal independence for the graphical model representation we use bidirected graphs which are in the tradition of path diagrams we show how the models can be parameterized in a simple fashion and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm finally we consider combining these models with symmetry restrictions

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

on reductants in the framework of multi adjoint logic programming reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties as it has been reported when interpreted on a partially ordered structure a multi adjoint logic program has to include all its reductants in order to preserve the approximate completeness property after a short survey of the different notions of reductant that have been developed for multi adjoint logic programs we introduce a new and more adequate notion of reductant in the multi adjoint framework we study some of its properties and its relationships with other notions of reductants and provide an algorithm for computing all the reductants associated with a multi adjoint logic program

the notion of weak contradiction definition and measures in this paper we present a way to represent contradiction between fuzzy sets this representation is given in terms of the notion of f weak contradiction unlike other approaches we do not define contradiction just by using one of the relations of f weak contradiction but by considering the whole set of relations this consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets as a result we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties symmetry antitonicity if the intersection is empty then the measure is one and if there is an element in the intersection with degree of membership hbox 1 then the measure is zero

analysis of two way layout of count data involving multiple counts in each cell abstract multiple counts may occur in each cell of an a b two way layout balanced or unbalanced of two fixed factors a and b standard log linear model analysis based on a poisson distribution assumption of the cell counts is not applicable here because of the unbalanced nature of the table or because the poisson distribution assumption is not valid we develop c tests for interaction and main effects assuming data to be poisson distributed and also assuming that data within the cells have extra over under dispersion beyond that explained by a poisson distribution for this we consider an extended negative binominal distribution and a semiparametric model using the quasi likelihood we show that in all situations the c tests for interaction are of very simple forms for c tests for the main effect in presence of no interaction such simplification is possible only under certain conditions a score test for detecting extra dispersion in presence of interaction is also obtained and is of sim

quantum deformation of kdv hierarchies and their infinitely many conservation laws a reasonable q deformed differential is defined a set of operation rules are constructed for the q deformed formal pseudo differential operators the complete procedure of constructing the q deformed kdv hierarchies and their infinite conservation laws is given as an important example he obtains a detailed structure of the simplest 3 2 system i e the q deformed kdv equations

recursion operators and conservation laws for discrete lax equations in this paper a method for constructing recursion operator of discrete lax equations is proposed to illustrate the method recursion operators for discrete boussinesq equation and discrete kdv equation are obtained then the recursion operators of continuous boussinesq equation and kdv equation are successfully recovered by the discrete ones infinitely many conservation laws of discrete boussinesq equation are constructed by the discrete residue formula and the first three conserved quantities are given explicitly and verified numerically existence of recursion operators and infinite number of conservation laws proves the integrability of the discrete lax equations

conservation laws of discrete lax equations based on the pseudodifference operators ring and lax pair we present a residue formula to calculate the conservation laws of discrete lax equations the details are explained with two illustrative examples furthermore some numerical results are given to verify the method

exponential mixtures and quadratic exponential families summary conditions are derived under which quadratic and polynomial exponential models can be generated as mixtures of linear exponential models the conditions are highly restrictive for continuous sample spaces but less restrictive in the discrete case some properties of binary quadratic exponential models are explored with a view towards finding models that have properties suitable for epidemiological applications

testing covariance structure in multivariate models application to family disease data abstract recent interest in modeling multivariate responses for members of groups has emphasized the need for testing goodness of fit here we describe a way to test the covariance structure of a multivariate distribution parameterized by a vector the idea is to extend this distribution the null distribution to a more general distribution that depends on an additional scalar and a specific quadratic function of the response vector chosen to capture features of an alternative covariance structure when 0 the more general distribution reduces to the null one standard likelihood theory yields a score test for 0 that is a test of fit of the null distribution the score statistic is the standardized difference between observed and expected values of the quadratic function where the expectation is taken with respect to the null distribution with replaced by its maximum likelihood estimate applying the methods to case control data on familial cancers of the ovary and breast we illu

statistical testing of genetic linkage under heterogeneity summary recent advances in human genetics have led to a renewed interest in statistical methods for the detection of linkage from family data for example between marker loci and disease traits statistical analysis of linkage between two loci is carried out almost exclusively by means of the lod log odds score test equivalent to a likelihood ratio test the current practice is to declare genetic linkage between loci when the maximum lod score exceeds 3 as will be discussed here the lod score approach is not appropriate for the detection of linkage from heterogeneous data e g when families consist of a mixture of linked and unlinked types heterogeneity may arise for example when rare mutations at different genetic loci are responsible for the same disease trait as an alternative approach to account for possible heterogeneity in the detection of linkage we propose the application of largesample test statistics that are members of neyman s class of c av or partial score tests the convergence of the proposed test statistics to their asymptotic distributions is investigated via monte carlo simulation for typical study designs applicable in human genetics

segregation analysis of case control data using generalized estimating equations generalized estimating equations gees liang and zeger 1986 biometrika 73 13 22 are used to fit genetic models to binary disease data for families of subjects in case control studies the gees include model specification of both the disease probabilities and the two way and possibly three way correlation coefficients of the family disease data these quantities are modelled as nonlinear functions of unobserved genotypes observed environmental covariates and the unknown parameters the functions reflect the method used to ascertain the family data goodness of fit is tested by allowing more flexible forms for the correlation coefficients regressing them against covariates specific to the relevant pair or triple of family members the approach is applied to family data obtained from simulated and real case control studies this semiparametric approach is less dependent on unverifiable assumptions and more computationally tractable than other methods for segregation analysis

econometric models for count data with an application to the patents r d relationship this paper focuses on developing and adapting statistical models of counts nonnegative integers in the context of panel data and using them to analyze the relationship between patents and r d expenditures since a variety of other economic data come in the form of repeated counts of some individual actions or events the methodology should have wide applications the statistical models we develop are applications and generalizations of the poisson distribution two important issues are i given the panel nature of our data how can we allow for separate persistent individual fixed or random effects ii how does one introduce the equivalent of disturbances in the equation into the analysis of poisson and other discrete probability functions the first problem is solved by conditioning on the total sum of outcomes over the observed years while the second problem is solved by introducing an additional source of randomness allowing the poisson parameter to be itself randomly distributed and compounding the two distributions lastly we develop a test statistic for the presence of serial correlation when fixed effects estimators are used in nonlinear conditional models

algebraic structure of fuzzy signatures abstract fuzzy signatures have been used for various applications including medical diagnosis communication of robots based on intention guessing and residential building evaluation however there exist many questions about this research topic which have not been addressed in the literature one of the most important aims is to formally define a family of fuzzy signatures from which an algebraic structure can be obtained allowing to make computations among fuzzy signatures this paper studies this family and defines suitable meet and join operators satisfying the properties of a lattice as an algebraic structure a partial ordering relation the least and greatest elements are also defined on the family of fuzzy signatures as a consequence fuzzy signatures can be used as truth values of fuzzy sets which provides a great level of representativity completely different from the interval valued and type 2 fuzzy sets among others

a semiparametric model for the analysis of recurrent event panel data summary in many longitudinal studies interest focuses on the occurrence rate of some phenomenon for the subjects in the study when the phenomenon is nonterminating and possibly recurring the result is a recurrent event data set examples include epileptic seizures and recurrent cancers when the recurring event is detectable only by an expensive or invasive examination only the number of events occurring between follow up times may be available this article presents a semiparametric model for such data based on a multiplicative intensity model paired with a fully flexible nonparametric baseline intensity function a random subject specific effect is included in the intensity model to account for the overdispersion frequently displayed in count data estimators are determined from quasi likelihood estimating functions because only first and second moment assumptions are required for quasi likelihood the method is more robust than those based on the specification of a full parametric likelihood consistency of the estimators depends only on the assumption of the proportional intensity model the semiparametric estimators are shown to be highly efficient compared with the usual parametric estimators as with semiparametric methods in survival analysis the method provides useful diagnostics for specific parametric models including a quasi score statistic for testing specific baseline intensity functions the techniques are used to analyze cancer recurrences and a pheromone based mating disruption experiment in moths a simulation study confirms that for many practical situations the estimators possess appropriate small sample characteristics

an extended quasi likelihood function summary wedderburn s original definition of quasi likelihood for generalized linear models is extended to allow the comparison of variance functions as well as those of linear predictors and link functions the relationship between generalized linear models and the use of transformations of the response variable is explored and the ideas are illustrated by three examples generalized linear models by allowing the full distributional assumption about the random component in the model to be replaced by a much weaker assumption in which only the first and second moments were defined in making this extension wedderburn widened the scope of generalized linear models in a way very similar to that of gauss when he replaced the assumption of normality in classical linear models by that of equal variance for generalized linear models with distributions in the exponential family likelihood ratio and score tests are used for testing hypotheses concerning nested subsets of covariates in the linear predictor and for assessing hypothesized link functions these methods are also applicable with wedderburn s form of quasi likelihood however neither of these methods is suitable for the comparison of different variance functions in this paper we introduce an extended quasi likelihood function which allows for the comparison of various forms of all the components of a generalized linear model i e the linear predictor the link function and the variance function we then apply the ideas to the analysis of several sets of data

the q deformation of akns d hierarchy in this paper we have considered the q deformation of the akns d hierarchy proved the bilinear identity and obtained the function of the q deformed akns d hierarchy

a variance components approach to categorical data models with heterogeneous cell populations analysis of spatial gradients in lung cancer mortality rates in north carolina counties a mixed categorical continuous variable model is proposed for the analysis of mortality rates this model differs from other available models such as weighted least squares and loglinear models in that the within cell populations are assumed to be heterogeneous in their levels of mortality risk heterogeneity implies that in addition to the sampling variance considered in other available models there will be a second component of variance due solely to within cell heterogeneity maximum likelihood procedures are presented for the estimation of the model parameters these procedures are based on the assumption that the distribution function for each cell death count is the negative binomial probability function this assumption is shown to be equivalent to assuming a mixture of poisson processes with the differential risk levels among individuals within each cell being governed by a two parameter gamma distribution the model is applied to data on lung cancer mortality for 1970 1975 for the 100 counties of north carolina the analysis shows that though a gradient in lung cancer mortality rates exist in space the gradient is restricted to specific demographic categories identified by race age and sex

diagnostics for overdispersion abstract diagnostic tools are proposed for assessing the dependence of extrabinomial or extra poisson variation on explanatory variables and for comparing several common models for overdispersion these tools are based on tests for regression terms in the dispersion parameter of a generalized linear model using double exponential family and pseudolikelihood formulations score tests do not require the full fitting of models for variation and lead to easy graphical and numerical procedures based on squared residuals deviance or pearson robust modifications of these are motivated by levene s test in linear models the diagnostic tools are intended primarily to ensure prudent modeling of the variance to make correct inferences about parameters in the mean

on marginal and conditional parameters in logistic regression models a fundamental research question is how much a variation in a covariate influences a binary response variable in a logistic regression model both directly or through mediators we derive the exact formula linking the parameters of marginal and conditional regression models with binary mediators when no conditional independence assumptions can be made the formula has the appealing property of being the sum of terms that vanish whenever parameters of the conditional models vanish thereby recovering well known results as particular cases it also permits to quantify the distortion induced by omission of some relevant covariates opening the way to sensitivity analysis also in this case as the parameters of the conditional models are multiplied by terms that are always positive or bounded the formula may be used to construct reasonable bounds on the parameters of interest we assume that conditionally on a set of covariates the data generating process can be represented by a directed acyclic graph we also show how the results here presented lead to the extension of path analysis to a system of binary random variables

measuring inconsistency in fuzzy answer set semantics recent approaches have shown that the measurement of the amount of inconsistent information contained in a logic theory can be useful to infer positive information this paper deals with the definition of measures of inconsistency in the residuated logic programming paradigm under the fuzzy answer set semantics this fuzzy framework provides a soft mechanism to control the amount of information inferred and thus controlling the inconsistencies by modifying slightly the truth values of some rules

a likelihood based method for analysing longitudinal binary responses summary in this paper we discuss a likelihood based method for analysing correlated binary responses based on a multivariate model it is related to the pseudo maximum likelihood approach suggested recently by zhao prentice 1990 their parameterization results in a simple pairwise model in which the association between responses is modelled in terms of correlations while the present paper uses conditional log odds ratios with this approach higher order associations can be incorporated in a natural way one important advantage of this parameterization is that the maximum likelihood estimates of the marginal mean parameters are robust to misspecification of the time dependence we describe an iterative two stage procedure for obtaining the maximum likelihood estimates two examples are presented to illustrate this methodology

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

a note on pseudolikelihood constructed from marginal densities for likelihood based inference involving distributions in which high dimensional dependencies are present it may be useful to use approximate likelihoods based for example on the univariate or bivariate marginal distributions the asymptotic properties of formal maximum likelihood estimators in such cases are outlined in particular applications in which only a single q x i vector of observations is observed are examined conditions under which consistent estimators of parameters result from the approximate likelihood using only pairwise joint distributions are studied some examples are analysed in detail

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

extended multi adjoint logic programming abstract extended multi adjoint logic programming arises as an extension of multi adjoint normal logic programming where constraints and a special type of aggregator operator have been included the use of this general aggregator operator permits to consider for example different negation operators in the body of the rules of a logic program we have introduced the syntax and the semantics of this new paradigm as well as an interesting mechanism for obtaining a multi adjoint normal logic program from an extended multi adjoint logic program this mechanism will allow us to establish technical properties relating the different stable models of both logic programming frameworks moreover it makes possible that the already developed and future theory associated with stable models of multi adjoint normal logic programs can be applied to extended multi adjoint logic programs

symmetries conserved quantities and hierarchies for some lattice systems with soliton structure basic invariants such as conserved quantities symmetries mastersymmetries and recursion operators are explicitly constructed for the following nonlinear lattice systems the modified korteweg de vries lattice the ablowitz ladik lattice the brusci ragnisco lattice the ragnisco tu lattice and some cases of the class of integrable systems introduced by bogoyavlensky the algorithmic basis for obtaining these quantities is described and the interrelation between the underlying mastersymmetry approach and the lax pair analysis is discussed by explicit presentation of the higher order members of the corresponding hierarchies new completely integrable lattice flows are found for all systems multi hamiltonian formulations are given

syntax and semantics of multi adjoint normal logic programming abstract multi adjoint logic programming is a general framework with interesting features which involves other positive logic programming frameworks such as monotonic and residuated logic programming generalized annotated logic programs fuzzy logic programming and possibilistic logic programming one of the most interesting extensions of this framework is the possibility of considering a negation operator in the logic programs which will improve its flexibility and the range of real applications this paper introduces multi adjoint normal logic programming which is an extension of multi adjoint logic programming including a negation operator in the underlying lattice beside the introduction of the syntax and semantics of this paradigm we will provide sufficient conditions for the existence of stable models defined on a convex compact set of an euclidean space finally we will consider a particular algebraic structure in which sufficient conditions can be given in order to ensure the unicity of stable models of multi adjoint normal logic programs

goodness of fit tests for censored survival data the problem of testing the underlying distribution in a general regression model is considered when the data are right censored it is proposed that tests be based on efficient scores from a certain class of parametric alternatives the connection between tests based on the scores and more traditional approaches using empirical distribution functions is explored neyman s smooth test is extended to allow for censored data

an improved reductant calculus using fuzzy partial evaluation techniques partial evaluation pe is an automatic program transformation technique aiming to obtain among other advantages the optimization of a program with respect to parts of its input hence it is also known as program specialization this paper introduces the subject of pe into the field of fuzzy logic programming we define the concept of pe for multi adjoint logic programs and goals and apart from discussing the benefits achieved by this technique we also introduce in the fuzzy setting a completely novel application of pe which allows us the computation of reductants guaranteeing completeness properties without harming the computational efficiency reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties as observed in the specialized literature a multi adjoint logic program when interpreted on a partially ordered lattice has to include all its reductants in order to preserve the approximate completeness property this introduces severe penalties in the implementation of efficient multi adjoint logic programming systems not only the size of programs increases but also their execution time in this paper we define a refinement to the notion of reductant based on pe techniques that we call pe reductant we establish the main properties of pe reductants i e the classical concept of reductant and the new notion of pe reductant are both semantically and operationally equivalent and what is the best we demonstrate that our refined notion of pe reductant is even able to increase the efficiency of multi adjoint logic programs

martingale based residuals for survival models summary graphical methods based on the analysis of residuals are considered for the setting of the highly used cox 1972 regression model and for the andersen gill 1982 generalization of that model we start with a class of martingale based residuals as proposed by barlow prentice 1988 these residuals and or their transforms are useful for investigating the functional form of a covariate the proportional hazards assumption the leverage of each subject upon the estimates of 13 and the lack of model fit to a given subject 1 1 model consider a set of n independent subjects such that the counting process ni ni t t o for the ith subject in the set indicates the number of observed events experienced over time t the sample paths of the ni are step functions with jumps of size 1 and with ni 0 0 we assume that the intensity function for ni t is given by yi t da t zi t yi t ep z t dao t 1 where yi t is a 0 1 process indicating whether the ith subject is a risk at time t 13 is a vector of regression coefficients zi t is a p dimensional vector of covariate processes and ao is the baseline cumulative hazard function several familar survival models fit into this framework the andersen gill 1982 generalization of the cox 1972 model arises when ao t is completely unspecified the further restriction that yi t 1 until the first event or censoring and is 0 thereafter yields the cox model the parametric form ao t t yields a poisson model or an exponential if restricted to a single event per subject and ao t tp a weibull model our attention will focus primarily on the andersen gill and cox models however the

comparison of methods for the analysis of longitudinal interval count data longitudinal studies are often concerned with estimating the recurrence rate of a non fatal event in many cases only the total number of events occurring during successive time intervals is known we compared a mixed poisson gamma regression method proposed by thall and a quasi likelihood method proposed by zeger and liang for the analysis of such data in the case where the mean was correctly specified using simulation techniques with large samples both methods produced similar standard errors in most situations except in the case of time dependent covariates with non poisson gamma data where they were seriously underestimated by the thall method a simple method for discriminating between the variance forms of the two methods is described the findings are applied to the analyses of clinical trials of non melanoma skin cancer and familial polyposis this study extends the findings of breslow concerning variance misspecification in overdispersed poisson and quasi likelihood models to the longitudinal setting

on the approximation of the quadratic exponential distribution in a latent variable context summary following cox wermuth 1994 2002 we show that the distribution of a set of binary observable variables induced by a certain discrete latent variable model may be approximated by a quadratic exponential distribution this discrete latent variable model is equivalent to the latent class version of the two parameter logistic model of birnbaum 1968 which may be seen as a generalized version of the rasch model rasch 1960 1961 on the basis of this result we develop an approximate maximum likelihood estimator of the item parameters of the two parameter logistic model which is very simply implemented the proposed approach is illustrated through an example based on a dataset on educational assessment

pseudolikelihood modeling of multivariate outcomes in developmental toxicology abstract the primary goal of this article is to determine benchmark doses based on the ethylene glycol study which comprises data from a developmental toxicity study in mice because the data involve a vector of malformation indicators a flexible model for multivariate clustered data is required an exponential family model is considered and pseudolikelihood based inferential tools are proposed hence avoiding excessive computational requirements

robust estimation in heteroscedastic linear models we consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter theta we propose robust estimates for the regression parameter beta and show that as long as a reasonable starting estimate of theta is available our estimates of beta are asymptotically equivalent to the natural estimate obtained with known variances a particular method for estimating theta is proposed and shown by monte carlo to work quite well especially in power and exponential models for the variances we also briefly discuss a feedback estimate of beta

fuzzy logic programming in this paper we consider the theory of fuzzy logic programming without negation our results cover logical systems with a wide variety of connectives ranging from t norm and conorms through conjunctors and disjunctors and their residuals to aggregation operators rules of our programs are many valued implications we emphasize that in contrast to other approaches our logic is truth functional i e according to p hajek we work in fuzzy logic in narrow sense we prove the soundness and the completeness of our formal model we deal with applications to threshold computation abduction fuzzy unification based on similarity we show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying

an approximation to maximum likelihood estimates in reduced models summary an approximation to the maximum likelihood estimates of the parameters in a model can be obtained from the corresponding estimates and information matrices in an extended model i e a model with additional parameters the approximation is close provided that the data are consistent with the first model applications are described to log linear models for discrete data to models for multivariate normal distributions with special covariance matrices and to mixed discrete continuous models

vertex operator solutions to the discrete kp hierarchy vertex operators which are disguised darboux maps transform solutions of the kp equation into new ones in this paper we show that the bi infinite sequence obtained by darboux transforming an arbitrary kp solution recursively forward and backwards yields a solution to the discrete kp hierarchy the latter is a kp hierarchy where the continuous space x variable gets replaced by a discrete n variable the fact that these sequences satisfy the discrete kp hierarchy is tantamount to certain bilinear relations connecting the consecutive kp solutions in the sequence at the grassmannian level these relations are equivalent to a very simple fact which is the nesting of the associated infinite dimensional planes flag the discrete kp hierarchy can thus be viewed as a container for an entire ensemble of vertex or darboux generated kp solutions it turns out that many new and old systems lead to such discrete semi infinite solutions like sequences of soliton solutions with more and more solitons sequences of calogero moser systems having more and more particles just to mention a few examples this is developed in 3 in this paper as another example we show that the q kp hierarchy maps via a kind of fourier transform into the discrete kp hierarchy enabling us to write down a very large class of solutions to the q kp hierarchy this was also reported in a brief note 4

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures