stable isomorphism of dual operator spaces we prove that two dual operator spaces x and y are stably isomorphic if and only if there exist completely isometric normal representations and of x and y respectively and ternary rings of operators m1 m2 such that x m2 y m1 w and y m2 x m1 w we prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic we apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic consequently we obtain that certain complex domains are biholomorphically equivalent if and only if their algebras of bounded analytic functions are morita equivalent in our sense finally we provide examples motivated by the theory of csl algebras

a morita theorem for dual operator algebras abstract we prove that two dual operator algebras are weak morita equivalent in the sense of d p blecher u kashyap morita equivalence of dual operator algebras j pure appl algebra 212 2008 2401 2412 if and only if they have equivalent categories of dual operator modules via completely contractive functors which are also weak continuous on appropriate morphism spaces moreover in a fashion similar to the operator algebra case we characterize such functors as the module normal haagerup tensor product with an appropriate weak morita equivalence bimodule we also develop the theory of the w dilation which connects the non selfadjoint dual operator algebra with the w algebraic framework in the case of weak morita equivalence this w dilation is a w module over a von neumann algebra generated by the non selfadjoint dual operator algebra the theory of the w dilation is a key part of the proof of our main theorem

brief paper pseudo state feedback stabilization of commensurate fractional order systems this paper addresses the problem of pseudo state feedback stabilization of commensurate fractional order systems fos in the proposed approach linear matrix inequalities lmi formalism is used to check if the pseudo state matrix eigenvalues belong to the fos stability region of the complex plane a review of lmi stability conditions is first proposed for fractional order 0 n 1 and 1 n 2 the paper then focuses particularly on the case 0 n 1 as the stability region is non convex and associated lmi condition is not as straightforward to obtain as in the case 1 n 2 a new lmi stability condition is thus proposed based on this condition a necessary and sufficient lmi method for the design of stabilizing controllers is given this method paves the way for extension to fos of various lmi based results among these possible extensions a first result on robust control of polytopic fractional order systems is given in this paper

variance component models with binary response interviewer variability summary interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non normal family the maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire this raises some interesting questions about the use of unbalanced ano va methods with these data two interviewers asking the same question of the same respondent can obtain different responses such interviewer effects create problems in the design and analysis of survey questionnaires collins 1980 gives a review of these problems together with a variety of partial remedies these include pilot studies and careful design to eliminate difficulties with wording of questions and instructions on the questionnaires in spite of these precautions interviewer effects remain questionnaire items are usually categorical and occasionally binary but usually for analysis the questionnaire item is reduced to a binary response it is the variability of the population of interviewers that is of interest and not just the individual interviewers thus this variability is best modelled as a random effect rather than a fixed effect the number of interviews completed by each interviewer varies so that the design is unbalanced thus we have an unbalanced variance component model with a categorical or binary response the intraclass correlation the ratio of the interviewer variance to the sum of all variances in the model is of great interest as a measure of interviewer variability in estimating the variance components the categorical or binary nature of the response is usually ignored and the analysis carried out using analysis of variance this is not maximum likelihood but analysis of variance does have some desirable properties when the error variables are non normal the rule of thumb generally applied is that the analysis of variance is reasonably accurate as long as the proportions in each of the categories of the response are between 0 1 and 0 9 scheffe 1959 p 343 discusses the effects of non normality in a one way balanced model very little theoretical work has been

comparison of statistical methods for analysis of clustered binary observations when correlated observations are obtained in a randomized controlled trial the assumption of independence among observations within cluster likely will not hold because the observations share the same cluster e g clinic physician or subject further the outcome measurements of interest are often binary the objective of this paper is to compare the performance of four statistical methods for analysis of clustered binary observations namely 1 full likelihood method 2 penalized quasi likelihood method 3 generalized estimating equation method 4 fixed effects logistic regression method the first three methods take correlations into account in inferential processes whereas the last method does not type i error rate power bias and standard error are compared across the four statistical methods through computer simulations under varying effect sizes intraclass correlation coefficients number of clusters and number of observations per cluster including large numbers 20 and 100 of observations per cluster the results show that the performance of the full likelihood and the penalized quasi likelihood methods is superior for analysis of clustered binary observations and is not necessarily inferior to that of the fixed effects logistic regression fit even when within cluster correlations are zero

a caveat concerning independence estimating equations with multivariate binary data clustered binary data occur commonly in both the biomedical and health sciences in this paper we consider logistic regression models for multivariate binary responses where the association between the responses is largely regarded as a nuisance characteristic of the data in particular we consider the estimator based on independence estimating equations iee which assumes that the responses are independent this estimator has been shown to be nearly efficient when compared with maximum likelihood ml and generalized estimating equations gee in a variety of settings the purpose of this paper is to highlight a circumstance where assuming independence can lead to quite substantial losses of efficiency in particular when the covariate design includes within cluster covariates assuming independence can lead to a considerable loss of efficiency in estimating the regression parameters associated with those covariates

the monotonic property and stability of solutions of fractional differential equations abstract in this paper we improve on the monotone property of lemma 1 7 3 in lakshmikantham et al 2009 5 for the case g t u u with a nonnegative real number we also investigate the mittag leffler stability of solutions of fractional differential equations by using the fractional comparison principle

association models for periodontal disease progression a comparison of methods for clustered binary data we investigate population averaged pa and cluster specific cs associations for clustered binary logistic regression in the context of a longitudinal clinical trial that investigated the association between tooth specific visual elastase kit results and periodontal disease progression within 26 weeks of follow up we address estimation of population averaged logistic regression models with generalized estimating equations gee and conditional likelihood cl and mixed effects me estimation of cs logistic regression models of particular interest is the impact of clusters that do not provide information for conditional likelihood methods non informative clusters on inferences based upon the various methodologies the empirical and analytical results indicate that cl methods yield smaller test statistics than me methods when non informative clusters exist and that cl estimates are less efficient than me estimates under certain conditions moreover previously reported relationships between population averaged and cluster specific parameters appear to hold for the corresponding estimates in the presence of these clusters

non existence of finite time stable equilibria in fractional order nonlinear systems we note that in the literature it is often taken for granted that for fractional order system without delays whenever the system trajectory reaches the equilibrium it will stay there in fact this is the well known phenomenon of finite time stability however in this paper we will prove that for fractional order nonlinear system described by caputo s or riemann liouville s definition any equilibrium cannot be finite time stable as long as the continuous solution corresponding to the initial value problem globally exists in addition some examples of stability analysis are revisited and linear lyapunov function is used to prove the asymptotic stability of positive fractional order nonlinear systems

random effects models for serial observations with binary response this paper presents a general mixed model for the analysis of serial dichotomous responses provided by a panel of study participants each subject s serial responses are assumed to arise from a logistic model but with regression coefficients that vary between subjects the logistic regression parameters are assumed to be normally distributed in the population inference is based upon maximum likelihood estimation of fixed effects and variance components and empirical bayes estimation of random effects exact solutions are analytically and computationally infeasible but an approximation based on the mode of the posterior distribution of the random parameters is proposed and is implemented by means of the em algorithm this approximate method is compared with a simpler two step method proposed by korn and whittemore using data from a panel study of asthmatics originally described in that paper one advantage of the estimation strategy described here is the ability to use all of the data including that from subjects with insufficient data to permit fitting of a separate logistic regression model as required by the korn and whittemore method however the new method is computationally intensive

strong morita equivalence of operator spaces abstract we introduce and examine the notions of strong equivalence and strong tro equivalence for operator spaces we show that they behave in an analogous way to how strong morita equivalence does for the category of c algebras in particular we prove that strong equivalence coincides with stable isomorphism under the expected countability hypothesis and that strongly tro equivalent operator spaces admit a correspondence between particular representations furthermore we show that strongly equivalent operator spaces have stably isomorphic second duals and strongly equivalent tro envelopes in the case of unital operator spaces strong equivalence implies stable isomorphism of the c envelopes

a comparison of generalized linear mixed model procedures with estimating equations for variance and covariance parameter estimation in longitudinal studies and group randomized trials response data in longitudinal studies and group randomized trials are gathered on units that belong to clusters within which data are usually positively correlated therefore estimates and confidence intervals for intraclass correlation or variance components are helpful when designing a longitudinal study or group randomized trial data simulated from both study designs are used to investigate the estimation of variance and covariance parameters from the following procedures for continuous outcomes restricted maximum likelihood reml and estimating equations ee for binary outcomes restricted pseudo likelihood repl and estimating equations ee we evaluate these procedures to see which provide valid and precise estimates as well as correct standard errors for the intraclass correlation coefficient or variance components reml seems the better choice for estimating terms related to correlation for models with normal outcomes especially in group randomized trial situations results for reml and ee are mixed when outcomes are continuous and non normal with binary outcomes neither repl nor ee provides satisfactory estimation or inference in longitudinal study situations while repl is preferable for group randomized trials

mixed effects logistic regression models for longitudinal binary response data with informative drop out a shared parameter model with logistic link is presented for longitudinal binary response data to accommodate informative drop out the model consists of observed longitudinal and missing response components that share random effects parameters to our knowledge this is the first presentation of such a model for longitudinal binary response data comparisons are made to an approximate conditional logit model in terms of a clinical trial dataset and simulations the naive mixed effects logit model that does not account for informative drop out is also compared the simulation based differences among the models with respect to coverage of confidence intervals bias and mean squared error mse depend on at least two factors whether an effect is a between or within subject effect and the amount of between subject variation as exhibited by variance components of the random effects distributions when the shared parameter model holds the approximate conditional model provides confidence intervals with good coverage for within cluster factors but not for between cluster factors the converse is true for the naive model under a different drop out mechanism when the probability of drop out is dependent only on the current unobserved observation all three models behave similarly by providing between subject confidence intervals with good coverage and comparable mse and bias but poor within subject confidence intervals mse and bias the naive model does more poorly with respect to the within subject effects than do the shared parameter and approximate conditional models the data analysis which entails a comparison of two pain relievers and a placebo with respect to pain relief conforms to the simulation results based on the shared parameter model but not on the simulation based on the outcome driven drop out process this comparison between the data analysis and simulation results may provide evidence that the shared parameter model holds for the pain data

testing logistic regression coefficients with clustered data and few positive outcomes applications frequently involve logistic regression analysis with clustered data where there are few positive outcomes in some of the independent variable categories for example an application is given here that analyzes the association of asthma with various demographic variables and risk factors using data from the third national health and nutrition examination survey a weighted multi stage cluster sample although there are 742 asthma cases in all out of 18 395 individuals for one of the categories of one of the independent variables there are only 25 asthma cases out of 695 individuals generalized wald and score hypothesis tests which use appropriate cluster level variance estimators and a bootstrap hypothesis test have been proposed for testing logistic regression coefficients with cluster samples when there are few positive outcomes simulations presented in this paper show that these tests can sometimes have either inflated or very conservative levels a simulation based method is proposed for testing logistic regression coefficients with cluster samples when there are few positive outcomes this testing methodology is shown to compare favorably with the generalized wald and score tests and the bootstrap hypothesis test in terms of maintaining nominal levels the proposed method is also useful when testing goodness of fit of logistic regression models using deciles of risk tables published in 2007 by john wiley sons ltd

analysis of clustered data a combined estimating equations approach summary examples of clustered data include data from longitudinal studies and data sampled within groups this paper proposes a regression analysis method for clustered data that optimally weights and combines contrasts of the data through a combination of estimating equations examples of combining between cluster within cluster and longitudinal data contrasts are presented the method results in increased estimation efficiency relative to generalised estimating equations with standard working correlation structures the proposed method also simplifies modelling decisions regarding the true correlation structure of the data and avoids correlation parameter estimation

inference for covariates that accounts for ascertainment and random genetic effects in family studies summary family studies to identify disease related genes often collect families with multiple cases if environmental exposures or other measured covariates are also important they should be incorporated into these genetic analyses to control for confounding and increase statistical power we propose a two level mixed effects model that allows us to estimate environmental effects while accounting for varying genetic correlations among family members and adjusting for ascertainment by conditioning on the number of cases in the family we describe a conditional maximum likelihood analysis based on this model when genetic effects are negligible this conditional likelihood reduces to standard conditional logistic regression we show that the simpler conditional logistic regression typically yields biased estimators of exposure effects and we describe conditions under which the conditional logistic approach has little or no bias

stably isomorphic dual operator algebras we prove that two unital dual operator algebras a b are stably isomorphic if and only if they are equivalent eleftherakis in j pure appl algebra arxiv math oa 0607489v4 2007 if and only if they have completely isometric normal representations on hilbert spaces h k respectively and there exists a ternary ring of operators mathcal m subset b h k such that alpha a mathcal m beta b mathcal m w and beta b mathcal m alpha a mathcal m w

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

lmi stability conditions for fractional order systems after an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives also denoted fractional order systems this paper deals with linear matrix inequality lmi stability conditions for fractional order systems under commensurate order hypothesis it is shown that a direct extension of the second lyapunov s method is a tedious task if the fractional order n is such that 0 n 1 the stability domain is not a convex region of the complex plane however through a direct stability domain characterization three lmi stability analysis conditions are proposed the first one is based on the stability domain deformation and the second one on a characterization of the instability domain which is convex the third one is based on generalized lmi framework these conditions are applied to the gain margin computation of a crone suspension

efficiency of regression estimates for clustered data statistical methods for clustered data such as generalized estimating equations gee and generalized least squares gls require selecting a correlation or convariance structure to specify the dependence between observations within a cluster valid regression estimates can be obtained that do not depend on correct specification of the true correlation but inappropriate specifications can result in a loss of efficiency we derive general expressions for the asymptotic relative efficiency of gee and gls estimators under nested correlation structures efficiency is shown to depend on the covariate distribution the cluster sizes the response variable correlation and the regression parameters the results demonstrate that efficiency is quite sensitive to the between and within cluster variation of the covariates and provide useful characterizations of models for which upper and lower efficiency bounds are attained efficiency losses for simple working correlation matrices such as independence can be large even for small to moderate correlations and cluster sizes

estimation efficiency and tests of covariate effects with clustered binary data several approaches have been proposed to analyze clustered binary data which arise in fields such as teratology and ophthalmology these methods include mixed effects and quasi likelihood approaches as well as models that use cluster responses as covariates the three approaches measure different effects of covariates on binary responses but simple approximations relate the magnitudes of their parameters in this article we present approximations to relate the standard errors of model parameters and wald tests for covariate effects obtained from the different approaches these approximations show that wald tests involving cluster level covariates will be approximately equivalent using the different approaches however approaches that model intracluster correlation such as the mixed effects model provide more powerful tests of within cluster covariates than those that do not model the correlation simulations and example data illustrate these findings

an operator space characterization of dual operator algebras this paper is devoted to dual algebras that is w closed algebras of bounded operators on hilbert space we give abstract characterizations of unital dual algebras resp dual algebras up to w homeomorphic unital complete isometry resp complete isomorphism the results we obtain are natural w versions of analogous characterizations due to blecher ruan sinclair and blecher respectively in the category of operator algebras

some comments on rosner s multiple logistic model for clustered data rosner 1984 biometrics 41 1025 1035 proposed a binary regression model for analyzing binary response data gathered in clusters or groups this model is useful for understanding the degree of intracluster correlation among responses adjusted for the potential confounding effects of other covariates however estimates of the effects of covariates on the binary outcome obtained using rosner s model can be misleading for example we show that the covariate effects given by rosner s model do not correspond to those measured by either of the two standard approaches for correlated binary data we present an example that compares the regression coefficients arising from fits of rosner s model to other logistic models for clustered observations using data from a study of breast disease

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

fractional order systems and pi sup spl lambda d sup spl mu controllers dynamic systems of an arbitrary real order fractional order systems are considered the concept of a fractional order pi sup spl lambda d sup spl mu controller involving fractional order integrator and fractional order differentiator is proposed the laplace transform formula for a new function of the mittag leffler type made it possible to obtain explicit analytical expressions for the unit step and unit impulse response of a linear fractional order system with fractional order controller for both open and closed loops an example demonstrating the use of the obtained formulas and the advantages of the proposed pi sup spl lambda d sup spl mu controllers is given

optimal combination of estimating equations in the analysis of multilevel nested correlated data multilevel nested correlated data often arise in biomedical research examples include teeth nested within quadrants in a mouth or students nested within classrooms in schools in some settings cluster sizes may be large relative to the number of independent clusters and the degree of correlation may vary across clusters when cluster sizes are large fitting marginal regression models using generalized estimating equations with flexible correlation structures that reflect the nested structure may fail to converge and result in unstable covariance estimates also the use of patterned nested working correlation structures may not be efficient when correlation varies across clusters this paper describes a flexible marginal regression modeling approach based on an optimal combination of estimating equations particular within cluster and between cluster data contrasts are used without specification of the working covariance structure and without estimation of covariance parameters the method involves estimation of the covariance matrix only for the vector of component estimating equations which is typically of small dimension rather than the covariance matrix of the observations within a cluster which may be of large dimension in settings where the number of clusters is large relative to the cluster size the method is stable and is highly efficient while maintaining appropriate coverage levels performance of the method is investigated with simulation studies and an application to a periodontal study

two stage methods for the analysis of pooled data epidemiologic studies of disease often produce inconclusive or contradictory results due to small sample sizes or regional variations in the disease incidence or the exposures to clarify these issues researchers occasionally pool and reanalyse original data from several large studies in this paper we explore the use of a two stage random effects model for analysing pooled case control studies and undertake a thorough examination of bias in the pooled estimator under various conditions the two stage model analyses each study using the model appropriate to the design with study specific confounders and combines the individual study specific adjusted log odds ratios using a linear mixed effects model it is computationally simple and can incorporate study level covariates and random effects simulations indicate that when the individual studies are large two stage methods produce nearly unbiased exposure estimates and standard errors of the exposure estimates from a generalized linear mixed model by contrast joint fixed effects logistic regression produces attenuated exposure estimates and underestimates the standard error when heterogeneity is present while bias in the pooled regression coefficient increases with interstudy heterogeneity for both models it is much smaller using the two stage model in pooled analyses where covariates may not be uniformly defined and coded across studies and occasionally not measured in all studies a joint model is often not feasible the two stage method is shown to be a simple valid and practical method for the analysis of pooled binary data the results are applied to a study of reproductive history and cutaneous melanoma risk in women using data from ten large case control studies

effects and non effects of paired identical observations in comparing proportions with binary matched pairs data binary matched pairs data occur commonly in longitudinal studies such as in cross over experiments many analyses for comparing the matched probabilities of a particular outcome do not utilize pairs having the same outcome for each observation an example is mcnemar s test some methodologists find this to be counterintuitive we review this issue in the context of subject specific and population averaged models for binary data with various link functions for standard models and inferential methods pairs with identical outcomes may affect the estimated size of the effect and its standard error but they have negligible if any effect on significance we also discuss extension of this result to matched sets

a characterization and a generalization of w modules we give a new banach module characterization of w modules also known as self dual hilbert c modules over a von neumann algebra this leads to a generalization of the notion and the theory of w modules to the setting where the operator algebras are weakly closed algebras of operators on a hilbert space that is we find the appropriate weak topology variant of our earlier notion of rigged modules and their theory which in turn generalizes the notions of a c module and a hilbert space successively our w rigged modules have canonical envelopes which are w modules indeed a w rigged module may be defined to be a subspace of a w module possessing certain properties

finite time stabilization of fractional order uncertain chain of integrator an integral sliding mode approach in this technical note a novel methodology for robust finite time stabilization of a chain of uncertain fractional order integrator is proposed this is achieved by first designing a nominal controller which stabilizes the system in finite time an integral sliding mode like surface and a switching controller is proposed such that when the system is on the surface the equivalent value of the integral sliding mode control is the negative of the disturbance and hence the disturbance is cancelled an improved strategy with more general kind of uncertainty is also proposed numerical examples are presented to illustrate the proposed methods

cluster sampling techniques in quantal response teratology and developmental toxicity studies summary this paper presents a model free approach for evaluating teratology and developmental toxicity data involving clustered binary responses in teratology studies a major statistical problem arises from the effect of intralitter correlation or the potential for littermates to respond similarly some statistical methods impose strict distributional assumptions to account for extra binomial variation while others rely on nonparametric resampling and empirical variance estimation techniques quasi likelihood methods and generalized estimating equations gee which model the marginal mean variance relationship also avoid strict distributional assumptions the proposed approach often used to analyze complex sample survey data is based on a first order taylor series approximation and a between cluster variance estimation procedure yielding consistent variance estimates for binomial based proportions and regression coefficients from dose response models the cluster sample technique presented here in the context of a logistic dose response model incorporates many of the advantages of quasi likelihood methods are valid for any underlying nested correlation structure and are adaptable to a variety of analytical settings the results of a simulation study show the cluster sample technique to be a viable competitor to gee methods currently receiving attention

conditional logistic regression with sandwich estimators application to a meta analysis motivated by a meta analysis of animal experiments on the effect of dietary fat and total caloric intake on mammary tumorigenesis we explore the use of sandwich estimators of variance with conditional logistic regression classical conditional logistic regression assumes that the parameters are fixed effects across all clusters while the sandwich estimator gives appropriate inferences for either fixed effects or random effects however inference using the standard wald test with the sandwich estimator requires that each parameter is estimated using information from a large number of clusters since our example violates this condition we introduce two modifications to the standard wald test first we reduce the bias of the empirical variance estimator the middle of the sandwich by using standardized residuals second we approximately account for the variance of these estimators by using the t distribution instead of the normal distribution where the degrees of freedom are estimated using satterthwaite s approximation through simulations we show that these sandwich estimators perform almost as well as classical estimators when the true effects are fixed and much better than the classical estimators when the true effects are random we achieve simulated nominal coverage for these sandwich estimators even when some parameters are estimated from a small number of clusters

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