a large sample study of cox s regression model strong consistency and asymptotic normality are established for the maximum partial likelihood estimate of the regression parameter in cox s regression model estimates are also derived for the underlying cumulative hazard function and survival distribution we establish the asymptotic normality of these estimates and calculate the limiting variances

cox s regression model for counting processes a large sample study the cox regression model for censored survival data specifies that covariates have a proportional effect on the hazard function of the life time distribution of an individual in this paper we discuss how this model can be extended to a model where covariate processes have a proportional effect on the intensity process of a multivariate counting process this permits a statistical regression analysis of the intensity of a recurrent event allowing for complicated censoring patterns and time dependent covariates furthermore this formulation gives rise to proofs with very simple structure using martingale techniques for the asymptotic properties of the estimators from such a model finally an example of a statistical analysis is included

on crystal bases and enright s completions abstract we investigate the interplay of crystal bases and completions in the sense of enright on certain nonintegrable representations of quantum groups we define completions of crystal bases show that this notion of completion is compatible with enright s completion of modules prove that every module in our category has a crystal basis which can be completed and that a completion of the crystal lattice is unique furthermore we give two constructions of the completion of a crystal lattice

misspecified proportional hazard models summary the properties of an estimator based on a proportional hazards model are investigated when the model is incorrect the estimator from the partial likelihood is shown to be consistent for a parameter that is defined implicitly the results are used to investigate the effects on estimation if the true model is accelerated failure time or if covariates are omitted from the proportional hazards model

cumulative dominance and heuristic performance in binary multiattribute choice we study the effectiveness of simple heuristics in multiattribute decision making we consider the case of an additive separable utility function with nonnegative nonincreasing attribute weights in this case cumulative dominance ensures that the so called cumulative dominance compliant heuristics will choose a best alternative for the case of binary attribute values and under two probabilistic models of the decision environment generalizing a simple bernoulli model we obtain the probabilities of simple and cumulative dominance in contrast with the probability of simple dominance the probability of cumulative dominance is shown to be large in many cases explaining the effectiveness of cumulative dominance compliant heuristics in those cases additionally for the subclass of the so called fully cumulative dominance compliant heuristics we obtain an upper bound for the expected loss that only depends on the weights being nonnegative and nonincreasing the low values of the upper bound for cases in

the effect of attribute ranges on weights in multiattribute utility measurements multiattribute utility theory requires a specific relation between the range of outcomes of each attribute and the weight for that attribute the greater the range the greater the weight has to be experimental results show that subjects do not adjust their judgments properly if the range is varied for the two methods tested the adjustment is smaller than required by theory the bias was smaller for a regression procedure than for the direct ratio method weights based on an intuitive range were not found to be superior to those elicited over different ranges

survival models for heterogeneous populations derived from stable distributions summary a new three parameter family of distributions on the positive numbers is proposed it includes the stable distributions on the positive numbers the gamma the degenerate and the inverse gaussian distributions the family is characterized by the laplace transform from which moments convolutions infinite divisibility unimodality and other properties are derived the density is complicated but a simple saddlepoint approximation is provided weibull and gompertz distributions are naturally mixed over some of the distributions the family is natural exponential in one of the parameters the distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations desirable properties of such distributions are discussed as an example survival after myocardial infarction is considered

tests for no treatment effect in randomized clinical trials summary we propose a test of the null hypothesis of no treatment effect in a randomized clinical trial that is based on the randomization distribution of residuals these residuals result from regressing the response on covariates but not treatment in contrast to model based score tests this procedure maintains nominal size when the model is misspecified and in particular when relevant covariates are omitted from the regression the efficiency of the procedure is evaluated for regressions with some but not all required covariates for many generalized linear models and survival models conventional model based score tests are shown to have supranominal size when relevant covariates are omitted but logistic regression and the proportional hazards model are robust

considerations in psychometric modeling of response time semiparametric models express a set of distributions of event times in terms of a a single parameter which varies across distributions and b a single function which does not vary across distributions and which has an unspecified form these models appear to be attractive alternatives to parametric models of response times in psychometrics however our use of such models may require incorporating additional functions which do not vary across distributions and may require expressing the models in terms of the joint distribution of response class and response time

attribute conflict and preference uncertainty the randmau model this paper extends the behavioral results reported in fischer et al 2000 by developing a model addressing preference uncertainty in multiattribute evaluation the model is motivated by two hypotheses regarding properties of multiattribute profiles that lead to greater preference uncertainty our attribute conflict hypothesis predicts that greater within alternative conflict discrepancy among the attributes of an alternative leads to more preference uncertainty our attribute extremity hypothesis predicts that greater attribute extremity very high or low attribute values leads to less preference uncertainty to provide a deeper explanation of attribute conflict and extremity effects we develop randmau a family of additive randauf and multiplicative randmuf random weights multiattribute utility models in randmau models preference uncertainty is represented as random variation in both the weighting parameters governing trade offs among attributes and the curvature parameters governing single attribute evaluations simulation results show that randmuf successfully predicts both the attribute conflict and attribute extremity effects exhibited by the experimental participants in fischer et al 2000 it also predicts an outcome value effect on error whose form depends on the shape of single attribute functions and on the type of multiattribute combination rule

psychometrics psychonomics psychonometrics rejoinder to rouder and wenger given the psychometric focus of this journal and of my paper it is stimulating to have the comments of two experts in psychonomically oriented response time modeling who do make an explicit distinction between person and item parameters let me first of all express my gratitude for their thorough comments on my paper and my agreement with several of their suggestions i will of course elaborate on points of disagreement rouder 2005 focuses on my restriction to a lognormal rt model with two parameters a scale parameter and a shape parameter of which only the first one is treated as a function of person and item characteristics a shift parameter is lacking and rouder gives an example and references to show the need for such a parameter with respect to the shape parameter my focus on the scale parameter may have created a misunderstanding that the shape parameter was restricted to be the same for all persons and items i did explore effects of angle and same different on the within subject variance of the log rt by allowing their regression parameters to vary and or to covary with the intercept within persons for details see chapter 8 of snijders and bosker 1999 none of these co variance estimates was significant all p 0 10 and none was substantial all 10 of the within subject intercept variance this was stated very briefly in sections 5 3 and 6 1 of my paper with respect to the need for a shift parameter i agree however extension of a two parameter model to a three parameter model may greatly complicate estimation and testing this is well known in the context of logistic irt models the guessing parameter of the three parameter model plays a role similar to the role of a shift parameter in rt models because it imposes a lower bound this is considered to be a serious burden for irt models in the context of the lognormal model similar statistical complications may arise see e g cohen 1988 it is therefore with much interest that i have read rouder s work on bayesian inference for the three parameter weibull rt model by mcmc methods e g rouder sun speckman lu and zhou 2003 statistical and psychometric literature shows an increasing use of such methods and they do appear to become inevitable however i still remember cox s reaction to a lecture by rubin involving gibbs sampling 10 years ago saying that he liked to keep it simple and to understand a method by writing it out on the back of a cigar box for part of this discussion see cox 1998 old fashioned as this attitude may seem i have a similar one and i feel that even twenty first century science cannot do without some of it before embracing mcmc estimation of many parameter models for speed and accuracy i need to know more about their identifiability the behavior of mcmc estimation in studies with small numbers of items say 20 and their added value for person and item estimation in the context of intelligence testing independent of these philosophical considerations most of the present findings may remain almost unaltered upon adding a shift parameter for instance item effects are clear from fig 2 and caf estimation by logistic regression of response correctness on log rt does not require any assumption about the rt distribution for

biased estimates of treatment effect in randomized experiments with nonlinear regressions and omitted covariates summary certain important nonlinear regression models lead to biased estimates of treatment effect even in randomized experiments if needed covariates are omitted the asymptotic bias is determined both for estimates based on the method of moments and for maximum likelihood estimates the asymptotic bias from omitting covariates is shown to be zero if the regression of the response variable on treatment and covariates is linear or exponential and in regular cases this is a necessary condition for zero bias many commonly used models do have such exponential regressions thus randomization ensures unbiased treatment estimates in a large number of important nonlinear models for moderately censored exponential survival data analysis with the exponential survival model yields less biased estimates of treatment effect than analysis with the proportional hazards model of cox if needed covariates are omitted simulations confirm that calculations of asymptotic bias are in excellent agreement with the bias observed in experiments of modest size

dilatations and factorizable equations in this paper we show that the dilatation operator in one dimension can be used to enlarge the lie algebra generated by the raising and lowering operators for some classes of special functions as a result we are able to derive new recursion relations and addition formulae for these functions furthermore we derive generalized ladder operators for these functions under coordinate stretching and translations

properties of proportional hazards score tests under misspecified regression models the effects are investigated of misspecifying a proportional hazards regression model on the associated partial likelihood score test for comparing two randomized treatments in the presence of covariates the asymptotic efficiency of the proportional hazards score test relative to the optimal partial likelihood test declines slowly as the hazard functions for the two treatments deviate from proportionality the efficiency can be very low when the hazard functions cross or differ only at large survival times misspecification of the functional form of the regression portion of a proportional hazards model introduces a quantitative treatment covariate interaction in the situations that we examine based on a binary covariate this misspecification usually results in only a minor drop in efficiency the omission of a covariate that is balanced across treatments has a negligible effect on the size of the score test but can substantially reduce power when the covariate effect is strong the loss of power from mismodeling a balanced covariate is usually small

a comparison of three simple test theory models in very simple test theory models such as the rasch model a single parameter is used to represent the ability of any examinee or the difficulty of any item simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available and are themselves of real practical value for small or even medium samples they can also serve a normative role in test design as an alternative to the rasch model or the rasch model with a correction for guessing a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference this model provides a natural account of guessing and has other useful things to contribute as well it also offers an alternative to the rasch model with the usual correction for guessing the three models are compared in terms of statistical properties and fits to actual data the goal of the paper is to widen the range of minimal models available to test analysts

reliability of test scores in nonparametric item response theory three methods for estimating reliability are studied within the context of nonparametric item response theory two were proposed originally by mokken 1971 and a third is developed in this paper using a monte carlo strategy these three estimation methods are compared with four classical lower bounds to reliability finally recommendations are given concerning the use of these estimation methods

psychometric modeling of response speed and accuracy with mixed and conditional regression human performance in cognitive testing and experimental psychology is expressed in terms of response speed and accuracy data analysis is often limited to either speed or accuracy and or to crude summary measures like mean response time rt or the percentage correct responses this paper proposes the use of mixed regression for the psychometric modeling of response speed and accuracy in testing and experiments mixed logistic regression of response accuracy extends logistic item response theory modeling to multidimensional models with covariates and interactions mixed linear regression of response time extends mixed anova to unbalanced designs with covariates and heterogeneity of variance related to mixed regression is conditional regression which requires no normality assumption but is limited to unidimensional models mixed and conditional methods are both applied to an experimental study of mental rotation univariate and bivariate analyzes show how within subject correlation between response and rt can be distinguished from between subject correlation and how latent traits can be detected given careful item design or content analysis it is concluded that both response and rt must be recorded in cognitive testing and that mixed regression is a versatile method for analyzing test data

on a non proportional hazards regression model for repeated medical random counts a wholly parametric non proportional hazards survival model is introduced the model retains cox s constant of proportionality as the leading term in the relative risk but permits additional flexibility by modelling the relative risk as a function of time covariate effects are modelled on the log odds scale a choice which is more in keeping with the spirit of the multiple logistic function rather than on the logarithmic scale as in the proportional hazards model some basic properties of the model are described a special feature of the model is that when the proportional hazards model applies cox s regression coefficients are easily recovered and the computation of other time dependent quantities of interest is routine a semi markov version of the model is derived to analyse recurrent sequential state processes and this is applied to a study of valvotomies conducted in the regional medical cardiology centre in belfast northern ireland the results obtained are compared with those from the classical proportional hazards analysis

logistic latent trait models with linear constraints two linearly constrained logistic models which are based on the well known dichotomous rasch model the linear logistic test model lltm and the linear logistic model with relaxed assumptions llra are discussed necessary and sufficient conditions for the existence of unique conditional maximum likelihood estimates of the structural model parameters are derived methods for testing composite hypotheses within the framework of these models and a number of typical applications to real data are mentioned

multi attribute decision making a simulation comparison of select methods abstract several methods have been proposed for solving multi attribute decision making problems madm a major criticism of madm is that different techniques may yield different results when applied to the same problem the problem considered in this study consists of a decision matrix input of n criteria weights and ratings of l alternatives on each criterion the comparative performance of some methods has been investigated in a few mostly field studies in this simulation experiment we investigate the performance of eight methods electre topsis multiplicative exponential weighting mew simple additive weighting saw and four versions of ahp original vs geometric scale and right eigenvector vs mean transformation solution simulation parameters are the number of alternatives criteria and their distribution the solutions are analyzed using twelve measures of similarity of performance similarities and differences in the behavior of these methods are investigated dissimilarities in weights produced by these methods become stronger in problems with few alternatives however the corresponding final rankings of the alternatives vary across methods more in problems with many alternatives although less significant the distribution of criterion weights affects the methods differently in general all ahp versions behave similarly and closer to saw than the other methods electre is the least similar to saw except for closer matching the top ranked alternative followed by mew topsis behaves closer to ahp and differently from electre and mew except for problems with few criteria a similar rank reversal experiment produced the following performance order of methods saw and mew best followed by topsis ahps and electre it should be noted that the electre version used was adapted to the common madm problem and therefore it did not take advantage of the method s capabilities in handling problems with ordinal or imprecise information

an irt based model for dichotomous longitudinal data the llra linear logistic model with relaxed assumptions fischer 1974 1977a 1977b 1983a was developed within the framework of generalized rasch models for assessing change in dichotomous item score matrices between two points in time it allows to quantify change on latent trait dimensions and to explain change in terms of treatment effects treatment interactions and a trend effect a remarkable feature of the model is that unidimensionality of the item set is not required the present paper extends this model to designs with any number of time points and even with different sets of items presented on different occasions provided that one unidimensional subscale is available per latent trait thus unidimensionality assumptions within subscales are combined with multidimensionality of the item set conditional maximum likelihood methods for parameter estimation and hypothesis testing are developed and a necessary and sufficient condition for unique identification of the model given the data is derived finally a sample application is presented

a flexible latent trait model for response times in tests latent trait models for response times in tests have become popular recently one challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests in order to reduce the need for tailor made models a model is proposed that unifies two popular approaches to response time modeling proportional hazard models and the accelerated failure time model with log normally distributed response times this is accomplished by resorting to discrete time the categorization of response time allows the formulation of a response time model within the framework of generalized linear models by using a flexible link function item parameters of the proposed model can be estimated with marginal maximum likelihood estimation applicability of the proposed approach is demonstrated with a simulation study and an empirical application additionally means for the evaluation of model fit are suggested

a class of multivanate failure time distributions summary a class of continuous multivariate lifetime distributions is proposed the dependence between individuals in a group is modelled by a group specific quantity which can be interpreted as an unobserved covariate common to the individuals in the group and assumed to follow a positive stable distribution it is possible to include covariates in the model and discuss whether the dependence is still present after specific covariates are taken into account if the conditional hazards are proportional then the hazards in the marginal distributions are also proportional but with different constants of proportionality also the hazard for the minimum in a group is proportional to the marginal hazards if the conditional distributions given the group quantity are weibull then the marginal distributions are also weibull this class can be used to test the hypothesis of independence of litter mates in the proportional hazards model

separability of item and person parameters in response time models this paper discusses two forms of separability of item and person parameters in the context of response time rt models the first is separate sufficiency the existence of sufficient statistics for the item person parameters that do not depend on the person item parameters the second is ranking independence the likelihood of the item person ranking with respect to rts does not depend on the person item parameters for each form a theorem stating sufficient conditions is proved the two forms of separability are shown to include several special cases of models from psychometric and biometric literature ranking independence imposes no restrictions on the general distribution form but on its parametrization an estimation procedure based upon ranks and pseudolikelihood theory is discussed as well as the relation of ranking independence to the concept of double monotonicity

applying the principles of specific objectivity and of generalizability to the measurement of change a formal framework for measuring change in sets of dichotomous data is developed and implications of the principle of specific objectivity of results within this framework are investigated building upon the concept of specific objectivity as introduced by g rasch three equivalent formal definitions of that postulate are given and it is shown that they lead to latent additivity of the parametric structure if in addition the observations are assumed to be locally independent realizations of bernoulli variables a family of models follows necessarily which are isomorphic to a logistic model with additive parameters determining an interval scale for latent trait measurement and a ratio scale for quantifying change adding the further assumption of generalizability over subsets of items from a given universe yields a logistic model which allows a multidimensional description of individual differences and a quantitative assessment of treatment effects as a special case a unidimensional parameterization is introduced also and a unidimensional latent trait model for change is derived as a side result the relationship between specific objectivity and additive conjoint measurement is clarified

survival analysis 1982 1991 the second decade of the proportional hazards regression model a short review of the cox regression model and its development from publication to 1982 is given i discuss how the model is used and presented in medical journals and how improvement may be achieved finally some extensions of the model are outlined

further developments and tests of a progressive algorithm for multiple criteria decision making p korhonen h moskowitz and j wallenius 1986 developed a progressive algorithm and the supporting theory for modeling and solving multiple criteria decision problems with discrete alternatives a special feature of the algorithm is that it relaxes the usual assumption of a fixed set of available decision alternatives and complete knowledge of a decision maker s dm s preference structure or value function the algorithm is based on progressively sampling the decision space obtaining preference information from the dm determining the likelihood of finding possibly surely better alternatives and based on this information continuing the search or terminating it by making the final choice we describe a computerized implementation and extensive computational tests of the algorithm as well as some of our experiences in applying and field testing it in practice we also consider several improvements and developments of the algorithm to further facilitate its use in practice

additive and multiplicative models for gamma distributed random variables and their application as psychometric models for response times a class of models for gamma distributed random variables is presented these models are shown to be more flexible than the classical linear models with respect to the structure that can be imposed on the expected value in particular both additive multiplicative and combined additive multiplicative models can be formulated as a special case a class of psychometric models for reaction times is presented together with their psychological interpretation by means of a comparison with existing models this class of models is shown to offer some possibilities that are not available in existing methods parameter estimation by means of maximum likelihood ml is shown to have some attractive properties since the models belong to the exponential family then the results of a simulation study of the bias in the ml estimates are presented finally the application of these models is illustrated by an analysis of the data from a mental rotation experiment this analysis is preceded by an evaluation of the appropriateness of the gamma distribution for these data

bootstrap investigation of the stability of a cox regression model we describe a bootstrap investigation of the stability of a cox proportional hazards regression model resulting from the analysis of a clinical trial of azathioprine versus placebo in patients with primary biliary cirrhosis we have considered stability to refer both to the choice of variables included in the model and more importantly to the predictive ability of the model in stepwise cox regression analyses of 100 bootstrap samples using 17 candidate variables the most frequently selected variables were those selected in the original analysis and no other important variable was identified thus there was no reason to doubt the model obtained in the original analysis for each patient in the trial bootstrap confidence intervals were constructed for the estimated probability of surviving two years it is shown graphically that these intervals are markedly wider than those obtained from the original model

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

aggregation of utility based individual preferences for group decision making abstract multi attribute utility theory maut elicits an individual decision maker s preferences for single attributes and develops a utility function by mathematics formulation to add up the preferences of the entire set of attributes when assessing alternatives a common aggregation method of maut for group decisions is the simple additive weighting saw method which does not consider the different preferential levels and preferential ranks for individual decision makers assessments of alternatives in a decision group and thus seems too intuitive in achieving the consensus and commitment for group decision aggregation in this paper the preferential differences denoting the preference degrees among different alternatives and preferential priorities denoting the favorite ranking of the alternatives for each decision maker are both considered and aggregated to construct the utility discriminative values for assessing alternatives in a decision group a comparative analysis is performed to compare the proposed approach to the saw model and a satisfaction index is used to investigate the satisfaction levels of the final two resulting group decisions in addition a feedback interview is conducted to understand the subjective perceptions of decision makers while examining the results obtained from these two approaches for the second practical case both investigation results show that the proposed approach is able to achieve a more satisfying and agreeable group decision than that of the saw method

group decision making using bilateral agreement matrix abstract group decision making based on a bilateral agreement matrix is investigated in this paper to derive a group decision from the opinions of individual decision makers pairs of decision makers are allowed to negotiate with one another and provide their bilateral negotiation values two algorithms are provided to help pairs of decision makers reach bilateral agreements which enables the construction of the bilateral agreement matrix the definition of a consistent bilateral agreement matrix is introduced to measure the credibility of the final result and its properties are investigated based on which a method is provided to construct a consistent bilateral agreement matrix from an inconsistent one models are then given to derive the weight vector from the bilateral agreement matrix based on which a consistency index of the matrix is defined two algorithms are then given to improve the level of consistency of the bilateral agreement matrix the final group decision is obtained by aggregating individual opinions using the weight vector the proposed methods are further extended to deal with the problem of incomplete bilateral agreement matrices several examples are also given to illustrate the proposed approach

extremal projectors of two parameter kashiwara algebras we define a two parameter kashiwara algebra br s g associated to a semi simple lie algebra g and its extremal projector and study their basic properties applying their properties to the category o br s g whose objects are upper bounded br s g modules we obtain its semi simplicity and the classification of simple modules

measuring change in latent subgroups using dichotomous data unconditional conditional and semiparametric maximum likelihood estimation abstract changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra in contrast to models of the rasch type the llra allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter because generalizability of the treatment effects over subjects and criteria is scientifically desirable statistical tests for this desideratum play an important role in practical situations whereas generalizability over the criteria can easily be tested generalizability over subjects can be tested only by stratifying the sample according to some further observable subject variables however one cannot be sure to detect nongeneralizability over the subjects by this method with certainty therefore the mixture llra is proposed that allows directly unobservable types of subjects reacting differently on

extremal projectors of q boson algebras we define the extremal projector of the q boson kashiwara algebra and study their basic properties applying their properties to the representation theory of the category whose objects are upper bounded modules we obtain its semi simplicity and the classification of simple modules

isotonic ordinal probabilistic models isop the concept of an ordinal instrumental probabilistic comparison is introduced it relies on an ordinal scale given a priori and on the concept of stochastic dominance it is used to define a weakly independently ordered system or isotonic ordinal probabilistic isop model which allows the construction of separate sample free ordinal scales on a set of subjects and a set of items the isop model is a common nonparametric theoretical structure for unidimensional models for quantitative ordinal and dichotomous variables

testing for dif in a model with single peaked item characteristic curves the parella model the parella model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences the data analyzed are the dichotomous responses of persons to items with a one zero indicating agreement disagreement with the content of the item the model provides a unidimensional representation of persons and items the response probabilities are a function of the distance between person and item the smaller the distance the larger the probability that a person will agree with the content of the item this paper discusses how the approach to differential item functioning presented by thissen steinberg and wainer can be implemented for the parella model

psychometric and information processing properties of selected response time models this paper discusses the compatibility of some response time rt models with psychometric and with information processing approaches to response times first three psychometrically desirable properties of probabilistic models for binary data related to the principle of specific objectivity are adapted to the domain of rt models one of these is the separability of item and subject parameters and another is double monotonicity next the compatibility of these psychometric properties with one very popular information processing approach the serial additive model is discussed finally five rt models are analyzed with respect to their compatibility with the psychometric properties with serial additive processing and with some alternative types of processing it is concluded that a current psychometric models each satisfy one or more of the psychometric properties but are not easily compatible with serial additive processing b at least one serial additive processing model satisfies separability of item and subject parameters and c rt models will more easily satisfy double monotonicity than the other two psychometric properties

piecewise exponential survival trees with time dependent covariates survival trees methods are nonparametric alternatives to the semiparametric cox regression in survival analysis in this paper a tree based method for censored survival data with time dependent covariates is proposed the proposed method assumes a very general model for the hazard function and is fully nonparametric the recursive partitioning algorithm uses the likelihood estimation procedure to grow trees under a piecewise exponential structure that handles time dependent covariates in a parallel way to time independent covariates in general the estimated hazard at a node gives the risk for a group of individuals during a specific time period both cross validation and bootstrap resampling techniques are implemented in the tree selection procedure the performance of the proposed survival trees method is shown to be good through simulation and application to real data

some neglected problems in irt the paper addresses three neglected questions from irt in section 1 the properties of the measurement of ability or trait parameters and item difficulty parameters in the rasch model are discussed it is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe section 2 deals with the measurement of individual change or modifiability based on a rasch test a conditional likelihood approach is presented that yields a an ml estimator of modifiability for given item parameters b allows one to test hypotheses about change by means of a clopper pearson confidence interval for the modifiability parameter or c to estimate modifiability jointly with the item parameters uniqueness results for all three methods are also presented in section 3 the mantel haenszel method for detecting dif is discussed under a novel perspective what is the most general framework within which the mantel haenszel method correctly detects dif of a studied item the answer is that this is a 2pl model where however all discrimination parameters are known and the studied item has the same discrimination in both populations since these requirements would hardly be satisfied in practical applications the case of constant discrimination parameters that is the rasch model is the only realistic framework a simple pearsonx2 test for dif of one studied item is proposed as an alternative to the mantel haenszel test moreover this test is generalized to the case of two items simultaneously studied for dif

a note on the uncertainty of a survival probability estimated from cox s regression model a partir d un modele de cox pour des donnees de survie censurees il est possible d estimer la probabilite de survie a l annee t pour un individu de covariables z 0

multi criteria group decision making based on bilateral agreements abstract in multi criteria group decision making a key issue is aggregating individual preference into group one in this study we employ a bilateral agreement to conduct group evaluation of alternatives the bilateral agreement between a pair of individuals could be on the weight of a criterion a criterion evaluation function or willingness to pay any one of three types of bilateral agreements can derive the group utility to express the relationship between the bilateral agreement and individual evaluations the quasi arithmetic mean is used which can ensure the consistency property of the pairwise comparison matrices the minimum requirements are explored to obtain the group preference which shows that n 1 pairs of bilateral agreements are necessary finally several examples are provided to illustrate the proposed methods

a goodness of fit test for cox s proportional hazards model based on martingale residuals a goodness of fit test for cox s proportional hazards model is proposed on the basis of martingale residuals the test is derived as the score test for the presence of an extra random effect in the exponential part of the hazard function assumptions about the distribution of the random effects are not made only the correlation matrix must be specified this can be done on the basis of an existing division of individuals into groups such as families or on the basis of the distance between observed covariates the variance of the test statistic is derived using a counting process approach corrections for the estimation of parameters are available the test is demonstrated in a simulated data set as well as in a real data set on ovarian cancer

generalized q boson algebras and their integrable modules abstract we define the generalized q boson algebra b associated to a pair of nichols algebras and a skew pairing we study integrable b modules generalizing results by m kashiwara and t nakashima on integrable modules over a q boson kashiwara algebra

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

a latent trait model for dichotomous choice data the parella model is a probabilistic parallelogram model that can be used for the measurement of latent attitudes or latent preferences the data analyzed are the dichotomous responses of persons to stimuli with a one zero indicating agreement disagreement with the content of the stimulus the model provides a unidimensional representation of persons and items the response probabilities are a function of the distance between person and stimulus the smaller the distance the larger the probability that a person will agree with the content of the stimulus an estimation procedure based on expectation maximization and marginal maximum likelihood is developed and the quality of the resulting parameter estimates evaluated

loglinear rasch models for the analysis of stability and change loglinear unidimensional and multidimensional rasch models are considered for the analysis of repeated observations of polytomous indicators with ordered response categories reparameterizations and parameter restrictions are provided which facilitate specification of a variety of hypotheses about latent processes of change models of purely quantitative change in latent traits are proposed as well as models including structural change a conditional likelihood ratio test is presented for the comparison of unidimensional and multiple scales rasch models in the context of longitudinal research this renders possible the statistical test of homogeneity of change against subject specific change in latent traits applications to two empirical data sets illustrate the use of the models

effect of misspecification of regression models in the analysis of survival data the accelerated life and proportional hazards families of models are widely used in the analysis of survival data we examine the question if interest lies in the qualitative effect on failure of various explanatory variables how critical is the choice of model family in assessing the relative importance of the explanatory variables we consider small effects when censoring is independent of the explanatory variables to first order the regression parameters are proportional under the alternative models this is not true when the censoring varies appreciably with the explanatory variables some higherorder theory is examined for the special case of the two sample problem

a linear regression model for the analysis of life times a linear model is suggested for the influence of covariates on the intensity function this approach is less vulnerable than the cox model to problems of inconsistency when covariates are deleted or the precision of covariate measurements is changed a method of non parametric estimation of regression functions is presented this results in plots that may give information on the change over time in the influence of covariates a test method and two goodness of fit plots are also given the approach is illustrated by simulation as well as by data from a clinical trial of treatment of carcinoma of the oropharynx

multivariate methods in ophthalmology with application to other paired data situations methods are presented for performing multiple regression analyses and multiple logistic regression analyses on ophthalmologic data with normally and binomially distributed outcome variables while accounting for the intraclass correlation between eyes these methods are extended to more general nested data structures where a variable number of subunits are available for each primary unit of analysis as in familial data these methods can also be applied to other types of paired data as in matched studies with a variable matching ratio where one has a continuous outcome variable and wishes to control for other confounding variables while maintaining the matching examples are given of these methods with a group of over 400 patients with retinitis pigmentosa in which spherical refractive error and visual acuity are related to genetic type after the effects of age sex and the presence of cataract have been controlled

conditional logistic regression models for correlated binary data summary a class of conditional logistic regression models for clustered binary data is considered this includes the polychotomous logistic model of rosner 1984 as a special case properties such as the joint distribution and pairwise odds ratio are investigated a class of easily computed estimating functions is introduced which is shown to have high efficiency compared to the computationally intensive maximum likelihood approach an example on chronic obstructive pulmonary disease among sibs is presented for illustration

group decisions with multiple criteria we consider a decision problem where a group of individuals evaluates multiattribute alternatives we explore the minimal required agreements that are sufficient to specify the group utility function a surprising result is that under some conditions a bilateral agreement among pairs of individuals on a single attribute is sufficient to derive the multiattribute group utility the bilateral agreement between a pair of individuals could be on the weight of an attribute on an attribute evaluation function or on willingness to pay we focus on the case in which each individual s utility function is additive we show that the group utility can be represented as the weighted sum of group attribute weights and more remarkably of attribute evaluation functions these group attribute evaluation functions are in turn weighted sums of individual attribute evaluation functions

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

graphical methods for assessing logistic regression models abstract in ordinary linear regression graphical diagnostic displays can be very useful for detecting and examining anomalous features in the fit of a model to data for logistic regression models the discreteness of binary data makes it difficult to interpret such displays modifications and extensions of linear model displays lead to three methods for diagnostic checking of logistic regression models local mean deviance plots are useful for detecting overall lack of fit empirical probability plots help point out isolated departures from the fitted model partial residual plots when smoothed to show underlying structure help identify specific causes of lack of fit these methods are illustrated through the analyses of simulated and real data

on the regression analysis of multivariate failure time data summary the paper is concerned with the analysis of regression effects when individual study subjects may experience multiple failures the proposed methods are most likely to be useful when there are a fairly large number of study subjects two general classes of regression models are considered in order to relate the hazard or intensity function to covariates and to preceding failure time history both models are of a stratified proportional hazards type one model includes baseline intensity functions that are arbitrary as a function of time from the beginning of study while the other includes baseline intensity functions that are arbitrary as a function of time from the study subject s immediately preceding failure partial likelihood functions are derived for the regression coefficients generalizations and illustrations are given

maximum likelihood estimation of order m for stationary stochastic processes sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible to overcome this problem for inference from a stochastic process we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations for some m s 0 general results on the asymptotic properties of the associated estimates are given and numerical comparisons with other estimators are carried out in special cases

multiple criteria decision making multiattribute utility theory the next ten years management science and decision science have grown exponentially since midcentury two closely related fields central to this growth are multiple criteria decision making mcdm and multiattribute utility theory maut this paper comments on the history of mcdm and maut and discusses topics we believe are important in their continued development and usefulness to management science over the next decade our aim is to identify exciting directions and promising areas for future research

latent change classes in dichotomous data changes in dichotomous data caused by treatments can be analyzed by means of the so called linear logistic model with relaxed assumptions llra the llra does not require observable criteria representing a single underlying latent trait but it postulates the generalizability of the treatment effects over criteria and subjects to test this latter crucial assumption the mixture llra was proposed that allows directly unobservable types of subjects to have different treatment effects as the earlier methods for estimating the parameters of the mixture llra have specific drawbacks a further method based on the conditional maximum likelihood principle will be presented here in contrast to the earlier conditional methods it uses all of the dichotomous change data while having fewer parameters further its goodness of fit tests become more sensitive to a falsely specified number of change types even though the treatment effects are biased for typically occurring small to moderate sample sizes however parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests finally three applications of the new method to empirical data are described first about the effect of the so called trager psychophysical integration second about the effect of autogenic therapy on patients with psychosomatic symptoms and third about the effect of religious education on the attitude towards sects

rasch s model for reading speed with manifest explanatory variables in educational and psychological measurement we find the distinction between speed and power tests although most tests are partially speeded the speed element is usually neglected here we consider a latent trait model developed by rasch for the response time on a set of pure speed test s which is based on the assumption that the test response times are approximately gamma distributed with known shape parameters and scale parameters depending on subject ability and test difficulty parameters in our approach the subject parameters are treated as random variables having a common gamma distribution from this maximum marginal likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution this basic model can be extended in a number of ways explanatory variables for the latent subject parameters and for the test parameters can be incorporated in the model our methods are illustrated by the analysis of a simulated and an empirical data set

omitting covariates from the proportional hazards model the problem of omitting covariates from the proportional hazards model phm when comparing two treatment groups was considered by lagakos and schoenfeld 1984 the absolute value of the parameter estimate of treatment effect is decreased in expectation when covariates are omitted from the phm resulting in an inefficient test for treatment comparison based on the asymptotic distribution of the score statistic when the hazard functions for the two treatment groups are nonproportional the asymptotic relative efficiency are of the phm score test for treatment difference was derived comparing the correctly specified phm to the misspecified non phm they considered the following nonproportional treatment hazards treatment covariate interactions omitted covariates and mismodeled covariates although the basic results of lagakos and schoenfeld on the are for nonproportional models appear correct the extension of these results to the are of omitting covariates is incorrect

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

quantum r matrix and intertwiners for the kashiwara algebra we study the algebrab q g presented by kashiwara and introduce intertwiners similar toq vertex operators we show that a matrix determined by 2 point functions of the intertwiners coincides with a quantumr matrix up to a diagonal matrix and give the commutation relations of the intertwiners we also introduce an analogue of the universalr matrix for the kashiwara algebra

rasch representable reaction time distributions this article investigates properties of a representation based on the rasch test model for reaction times rt that was proposed by micko necessary and sufficient conditions for a set of rt distributions to be rasch representable are derived it is shown that independent serial and independent parallel processing models cannot be reconciled with the representation however random extreme models compatible with the reasch representation exist that assume rt is determined by the longest or he shortest processing time of a random number of independent paraloel channels nonparametric properties of rasch representable distributions are derived that can be used for testing the model and for estimating its parameters conditions are presented for rasch representable distributions to form a scale family finally rasch represent able distributions are characterized interms of their hazard functions