recognizing the efficiency weak efficiency and inefficiency of dmus with an epsilon independent linear program abstract one of the important problems in the ccr and bbc models is determining the non archimedean infinitesimal epsilon mehrabian et al s mehrabian g r jahanshahloo m r alirezaei g r amin an assurance interval for the non archimedean epsilon in dea models operations research 48 2 2000 344 347 presented a procedure for determining overall assurance interval of e they also showed that choosing e in this interval guarantees the feasibility boundedness of the multiplier envelopment side of ccr models in this paper we show that choosing e arbitrarily in the proposed overall assurance interval may not lead to correct recognition of the efficient and inefficient dmus then we propose a new model that can recognize the efficient and inefficient dmus without dependence on different values of e

super efficiency in stochastic data envelopment analysis an input relaxation approach this paper addresses super efficiency issue based on input relaxation model in stochastic data envelopment analysis the proposed model is not limited to using the input amounts of evaluating dmu and one can obtain a total ordering of units by using this method the input relaxation super efficiency model is developed in stochastic data envelopment analysis and its deterministic equivalent also is derived which is a nonlinear program moreover it is shown that the deterministic equivalent of the stochastic super efficiency model can be converted to a quadratic program as an empirical example the proposed method is applied to the data of textile industry of china to rank efficient units finally when allowable limits of data variations for evaluating dmu are permitted the sensitivity analysis of the proposed model is discussed

analysis of matched case control data with multiple ordered disease states possible choices and comparisons in an individually matched case control study effects of potential risk factors are ascertained through conditional logistic regression clr extension of clr to situations with multiple disease or reference categories has been made through polychotomous clr and is shown to be more efficient than carrying out separate clrs for each subgroup in this paper we consider matched case control studies where there is one control group but there are multiple disease states with a natural ordering among themselves this scenario can be observed when the cases can be further classified in terms of the seriousness or progression of the disease for example according to different stages of cancer we explore several popular models for ordered categorical data in this context we first adopt a cumulative logit or equivalently a proportional odds model to account for the ordinal nature of the data the important distinction of this model from a stratified dichotomous and polychotomous logistic regression model is that the stratum specific nuisance parameters cannot be eliminated in this model via the conditional likelihood approach we discuss a mantel haenszel approach for analysing such data we point out possible difficulties with standard likelihood based approaches with the cumulative logit model when applied to case control data we then consider an alternative conditional adjacent category logit model we illustrate the methods by analysing data from a matched case control study on low birthweight in newborns where infants are classified according to low and very low birthweight and a child with normal birthweight serves as a control a simulation study compares the different ordinal methods with methods ignoring sub classification of the ordered disease states

estimation of a common effect parameter from sparse follow up data breslow 1981 biometrika 68 73 84 has shown that the mantel haenszel odds ratio is a consistent estimator of a common odds ratio in sparse stratifications for cohort studies however estimation of a common risk ratio or risk difference can be of greater interest under a binomial sparse data model the mantel haenszel risk ratio and risk difference estimators are consistent in sparse stratifications while the maximum likelihood and weighted least squares estimators are biased under poisson sparse data models the mantel haenszel and maximum likelihood rate ratio estimators have equal asymptotic variances under the null hypothesis and are consistent while the weighted least squares estimators are again biased similarly of the common rate difference estimators the weighted least squares estimators are biased while the estimator employing mantel haenszel weights is consistent in sparse data variance estimators that are consistent in both sparse data and large strata can be derived for all the mantel haenszel estimators

assessing partial association between ordinal variables quantification visualization and hypothesis testing partial association refers to the relationship between variables y1 y2 yk while adjusting for a set of covariates x x1 xp to assess such an association when yk s are recorded on ordinal sca

a study of pattern forming systems with a fully nonlocal interaction kernel of possibly changing sign abstract a nonlocal model with a possibly sign changing kernel is proposed to study pattern formation problems in physical and biological systems with self organization properties one defines pre solutions of a related linear problem and gives sufficient conditions for pre solutions to be jump discontinuous solutions of the nonlocal model among a multitude of solutions a selection criterion is used to single out more significant critical solutions these solutions are further classified into minimizing solutions maximizing solutions and saddle solutions minimizing solutions are the most relevant for patterned states and they exist if the kernel changes sign a non negative kernel on the other hand behaves in some ways like the gradient term in the standard local model

generalization of the mantel haenszel estimator to nonconstant odds ratios nouvel estimateur issu de la generalisation de l estimateur de mantel haenszel etude de ses proprietes asymptotiques en fonction du nombre de tables fixe et du comptage des cellules

generalized mantel haenszel estimators for k 2 x j tables mickey and elashoff 1985 biometrics 41 623 635 gave an extension of mantel haenszel estimation to log linear models for 2 x j x k tables their extension yields two generalizations of the mantel haenszel odds ratio estimator to k 2 x j tables this paper provides variance and covariance estimators for these generalized mantel haenszel estimators that are dually consistent i e consistent in both large strata and sparse data and presents comparisons of the efficiency of the generalized mantel haenszel estimators

summary attributable risk estimation from unmatched case control data abstract we propose an alternative method to obtain summary estimators variances and confidence intervals for attributable risk measures this method combines weighted exposure prevalences for cases and controls across strata formed by the cross classification of relevant covariates to form estimates of attributable risk among the exposed and attributable risk in the target population the major benefit of this approach over those previously proposed in the literature is that it operates on data summed across strata rather than on estimation of statistics within each stratum this alternative method for attributable risk measures utilizes the mantel haenszel estimate of an average odds ratio and can be implemented using the matrix procedure in sas this method is appropriate even when the within stratum sample sizes are too small for other methods to be valid simulation results indicate that this method is superior to others with respect to bias and coverage probability for confidence intervals

a generalization of the mantel haenszel estimator of partial association for 2 x j x k tables summary a generalization of the mantel haenszel estimator of a common odds ratio for a series of 2 x 2 tables is proposed for the estimation of log linear partial association parameters for a series of 2 x j j 2 tables the assumption of no three way interaction among row column and stratifying variables is made two approximate covariance estimators are presented small sample properties of these estimators are investigated by simulation studies the results indicate that use of the proposed partial association technique produces estimates with negligible bias both covariance estimation techniques provide confidence intervals for functions of partial association parameters for example odds ratios or adjusted rates a test of no three way interaction results from these procedures

regularity theory for fully nonlinear integro differential equations we consider nonlinear integro differential equations like the ones that arise from stochastic control problems with purely jump levy processes we obtain a nonlocal version of the abp estimate harnack inequality and interior c 1 regularity for general fully nonlinear integro differential equations our estimates remain uniform as the degree of the equation approaches two so they can be seen as a natural extension of the regularity theory for elliptic partial differential equations

solving dea models in a single optimization stage can the non archimedean infinitesimal be replaced by a small finite epsilon abstract single stage dea models aim to assess the input or output radial efficiency of a decision making unit and potential mix inefficiency in a single optimization stage this is achieved by incorporating the sum of input and output slacks multiplied by a small theoretically non archimedean infinitesimal value epsilon in the envelopment model or equivalently by using this value as the lower bound on the input and output weights in the dual multiplier model when this approach is used it is common practice to select a very small value for epsilon this is based on the expectation that for a sufficiently small epsilon the radial efficiency and optimal slacks obtained by solving the single stage model should be approximately equal to their true values obtained by the two separate optimization stages however as well known selecting a small epsilon may lead to significant computational inaccuracies in this paper we prove that there exists a threshold value referred to as the effective bound such that if epsilon is smaller than this bound the solution to the single stage program is not approximate but precise exactly the same as in the two stage approach provided there are no computational errors

the overall assurance interval for the non archimedean epsilon in dea models a partition base algorithm this study presents an algorithm for determining overall assurance interval of epsilon in dea models in the previous studies in this regard solving n linear programs are needed for this propose where n is the number of decision making units dmu involved in the evaluation this paper based on a classification of dmu s proposes a partition base algorithm that can determine the overall assurance interval of epsilon by solving a few number of linear programs the proposed algorithm is illustrated by the 44 unit data set of power plant systems of iran

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

model improvement for computational difficulties of dea technique in the presence of special dmus abstract data envelopment analysis dea is a non parametric mathematical optimization technique which evaluates the relative efficiency of decision making units dmus with multiple inputs and outputs a major advantage cited in support of the use of dea in measuring efficiency is that this method does not make assumption about functional forms of production function in other words it makes a piecewise frontier efficient frontier with calculation of a maximal efficiency measure for each dmu relative to all other observed measures also it identifies a subset of efficient best practice dmus and for the remaining dmus the magnitude of their non efficiency is measured by comparing to a frontier constructed from the efficient dmus therefore in the evaluation of non efficient units by dea referenced dmus have an important role to play unfortunately dmus with extraordinary output can lead to a monopoly in reference set the fact that may call it abnormality due to outliers data in this paper we introduce a dea model for evaluating dmus under this circumstance also the model is employed to measure the bank branches efficiency of a large canadian bank the layer model can derive a ranking for dmus and obtain an improving strategy for moving toward a better layer

attributable risk estimation from matched case control data a methodology is proposed for obtaining summary estimators variances and confidence intervals for attributable risk measures from data obtained through a case control study design where one or more controls have been matched to each case the sampling design for obtaining these data is conceptualized as a simple random sample of cases being equivalent to a simple random sample of matched sets by combining information across the strata determined by the matched sets this approach provides all of the benefits associated with the mantel haenszel procedure for the estimators of attributable risk among the exposed and population attributable risk asymptotic variances are derived under the assumption that the frequencies of the unique response patterns follow the multinomial distribution simulation results indicate that these methods fare very well with respect to bias and coverage probability

a proportional odds model with subject specific effects for repeated ordered categorical responses summary suppose subjects make repeated responses on the same ordered categorical scale we propose a generalization of the rasch model that expresses the cumulative logit of the response distribution using subject parameters and a proportional odds structure for item effects parameters in the model describe subject specific rather than populationaveraged effects consistent estimation of the effects requires eliminating the subject parameters we accomplish this by simultaneous fitting of rasch models conditional on sufficient statistics for those parameters for the possible binary collapsings of the response the fitting process uses an improved newton raphson algorithm for fitting generalized loglinear models by maximum likelihood estimation subject to constraints for the case of two items we give simple expressions for an effect estimate and its standard error and suggest a test of marginal homogeneity for ordinal matched pairs

young measures in a nonlocal phase transition problem a nonlocal variational problem modelling phase transitions is studied in the framework of young measures the existence of global minimisers among functions with internal layers on an infinite tube is proved by combining a weak convergence result for young measures and the principle of concentration compactness the regularity of such global minimisers is discussed and the nonlocal variational problem is also considered on asymptotic tubes

the evans krylov theorem for nonlocal fully nonlinear equations we prove a regularity result for solutions of a purely integro differential bellman equation this regularity is enough for the solutions to be understood in the classical sense if we let the order of the equation approach two we recover the theorem of evans and krylov about the regularity of solutions to concave uniformly elliptic partial differential equations

a one model approach based on relaxed combinations of inputs for evaluating input congestion in dea this paper provides a one model approach of input congestion based on input relaxation model developed in data envelopment analysis e g g r jahanshahloo m khodabakhshi suitable combination of inputs for improving outputs in dea with determining input congestion considering textile industry of china applied mathematics and computation 1 2004 263 273 g r jahanshahloo m khodabakhshi determining assurance interval for non archimedean ele improving outputs model in dea applied mathematics and computation 151 2 2004 501 506 m khodabakhshi a super efficiency model based on improved outputs in data envelopment analysis applied mathematics and computation 184 2 2007 695 703 m khodabakhshi m asgharian an input relaxation measure of efficiency in stochastic data analysis applied mathematical modelling 33 2009 2010 2023 this approach reduces solving three problems with the two model approach introduced in the first of the above mentioned reference to two problems which is certainly important from computational point of view the model is applied to a set of data extracted from isi database to estimate input congestion of 12 canadian business schools

mantel haenszel type inference for cumulative odds ratios with a stratified ordinal response this article proposes a mantel haenszel type estimator of an assumed common cumulative odds ratio in a proportional odds model for an ordinal response with several 2 x c contingency tables it is useful for instance for comparing two treatments on an ordinal response for data from several centers when the data are highly sparse the estimator has behavior similar to the mantel haenszel estimator of a common odds ratio for several 2 x 2 tables it is consistent under the ordinary asymptotic framework in which the number of tables is fixed and unlike the maximum likelihood ml estimator also under sparse asymptotics in which the number of tables grows with the sample size simulations reveal a considerable difference between it and the ml estimator when each table has few observations efficiency comparisons suggest that little efficiency loss occurs compared to the ml estimator when the data are not sparse tests and estimators are presented for detecting and handling heterogeneity in the odds ratios and generalizations are available for stratified r x c contingency tables

determining assurance interval for non archimedean element in the improving outputs model in dea recently jahanshahloo and khodabakhshi appl math comput in press in an article suitable combination of inputs for improving outputs in dea with determining inputs congestion presented a model in which some inputs can be increased on the contrary of existing models in dea it is important to determine the value or interval of non archimedean e such that envelopment form is bounded in other words multiplier form is feasible in this article in addition to determining assurance interval of e for boundedness of the envelopment model the feasibility of the multiplier model we also provide an alternative proof for unboundedness an illustrative example is exhibited too

an assurance interval for the non archimedean epsilon in dea models this paper clarifies the role of non archimedean infinitesimal e in dea models so that the associated linear programs may be infeasible for the multiplier side and unbounded for the envelopment side for certain values of e it is shown that the bound of e proposed by ali and seiford 1993 is invalid for feasibility and boundedness of the linear programs a procedure is presented for determining an assurance interval of e it is also shown that an assurance value for e can be found using a single linear program

small sample bias of point estimators of the odds ratio from matched sets the bias of several point estimators of the odds ratio arising from matched pair data is investigated for small samples simple alternatives to the traditional maximum likelihood estimator are suggested on both the original scale and the logarithm scale in each case the suggested estimators possess a superior performance in terms of mean square error generalizations are given for 1 r matched data sets

a note on the covariance of the mantel haenszel log odds ratio estimator and the sample marginal rates a simple technique developed in phillips unpublished ph d dissertation university of windsor windsor ontario 1987 is used to approximate cov theta mh pi i 1 2 where theta mh is the mantel haenszel log odds ratio estimator for a 2 x 2 x k table and the pi are the sample marginal proportions these results are then applied to obtain an approximate variance estimate of an adjusted risk difference based on the mantel haenszel odds ratio estimator

estimators of the mantel haenszel variance consistent in both sparse data and large strata limiting models summary this paper proposes a new estimator of the variance of the mantel haenszel estimator of common odds ratio that is easily computed and consistent in both sparse data and large strata limiting models monte carlo experiments compare its performance to that of previously proposed variance estimators

a random effects ordinal regression model for multilevel analysis a random effects ordinal regression model is proposed for analysis of clustered or longitudinal ordinal response data this model is developed for both the probit and logistic response functions the threshold concept is used in which it is assumed that the observed ordered category is determined by the value of a latent unobservable continuous response that follows a linear regression model incorporating random effects a maximum marginal likelihood mml solution is described using gauss hermite quadrature to numerically integrate over the distribution of random effects an analysis of a dataset where students are clustered or nested within classrooms is used to illustrate features of random effects analysis of clustered ordinal data while an analysis of a longitudinal dataset where psychiatric patients are repeatedly rated as to their severity is used to illustrate features of the random effects approach for longitudinal ordinal data

a complete ranking of dmus using restrictions in dea models abstract data envelopment analyses dea is a linear programming based method which evaluates relative efficiency of decision making units dmus it can include multiple outputs and inputs without a priori weights and without requiring explicit specification of functional forms between inputs and outputs it computes a scalar measure of efficiency and determines efficient levels of inputs and outputs for each dmu under evaluation which has a range of zero to 1 hence it has the ability to rank dmus unless when some dmus are the same in efficiency score such as efficient dmus or inefficient dmus with the same efficiency score in many cases it is necessary to give a full ranking of the dmus hence this paper introduces a new method for complete ranking of decision making units which it does not need any changes in the models also for presentation of the ability of this method it is employed to rank the bank branch of a commercial bank branches in an empirical example

fitting stratified proportional odds models by amalgamating conditional likelihoods classical methods for fitting a varying intercept logistic regression model to stratified data are based on the conditional likelihood principle to eliminate the stratum specific nuisance parameters when the outcome variable has multiple ordered categories a natural choice for the outcome model is a stratified proportional odds or cumulative logit model however classical conditioning techniques do not apply to the general k category cumulative logit model k 2 with varying stratum specific intercepts as there is no reduction due to sufficiency the nuisance parameters remain in the conditional likelihood we propose a methodology to fit stratified proportional odds model by amalgamating conditional likelihoods obtained from all possible binary collapsings of the ordinal scale the method allows for categorical and continuous covariates in a general regression framework we provide a robust sandwich estimate of the variance of the proposed estimator for binary exposures we show equivalence of our approach to the estimators already proposed in the literature the proposed recipe can be implemented very easily in standard software we illustrate the methods via three real data examples related to biomedical research simulation results comparing the proposed method with a random effects model on the stratification parameters are also furnished

extended mantel haenszel estimating procedure for multivariate logistic regression models a class of estimating functions is proposed for the estimation of multivariate relative risk in stratified case control studies it reduces to the well known mantel haenszel estimator when there is a single binary risk factor large sample properties of the solutions to the proposed estimating equations are established for two distinct situations efficiency calculations suggest that the proposed estimators are nearly fully efficient relative to the conditional maximum likelihood estimator for the parameters considered application of the proposed method to family data and longitudinal data where the conditional likelihood approach fails is discussed two examples from case control studies and one example from a study on familial aggregation are presented

heterogeneity in mantel haenszel type models summary the mantel haenszel problem involves inferences about a common odds ratio in a set of 2 x 2 tables although it is a fairly standard practice to test whether the odds ratios are indeed constant there is remarkably little methodology available for proceeding when there is evidence of some heterogeneity our interest is in models where the log odds ratios ok for tables k 1 2 k are thought of as a sample from a population with mean 0 and standard deviation a and inferences are desired regarding the parameters 0 a by mantel haenszel type models we mean to include the generalization involving pairs of poisson observations rather than 2 x 2 tables where the ok are logarithms of ratios of the poisson means within pairs direct computation of the likelihood function for 0 a in these settings involves numerical integration and the main point here is a simple approximation to this likelihood the approximation is based on laplace s method and is very accurate for practical applications inference regarding the parameter 0 of primary interest may be made from the profile likelihood function an alternative approach to likelihood methods based on approximations to the marginal means and variances is also considered the methods explored here can be readily generalized to settings where the parameters ok depend on covariables as well

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