finite sample adjustments in estimating equations and covariance estimators for intracluster correlations bias corrected covariance estimators are introduced in the context of an estimating equations approach for intracluster correlations among binary outcomes simulation study results show that the bias corrected covariance estimators perform better than uncorrected sandwich estimators in terms of bias and coverage probabilities additionally introduction of a matrix based bias correction into the estimating equations considerably improves point and interval estimation for the intracluster correlations the methods are illustrated using data from a nested cross sectional cluster trial on reducing underage drinking

brief paper stabilization of some fractional delay systems of neutral type in this note we give new stability tests which enable one to fully characterize the h stability of systems with transfer function g s r s p s q s e s h where h 0 and p q r are real polynomials in the variable s m for 0 p s q s 1

lmi based robust control of fractional order uncertain linear systems this paper concerns with the method of observer based control and static output feedback control for fractional order uncertain systems with the fractional commensurate order a 0 a 1 and a email protected email protected 2 via linear matrix inequality lmi approach respectively first the sufficient conditions for robust asymptotical stability of the closed loop control systems are presented next by using matrix s singular value decomposition svd and lmi technics the existence condition and method of designing a robust stabilizing controller for such fractional order control systems are derived unlike previous methods the results are obtained in terms of lmi which can be easily obtained by matlab s lmi toolbox finally two numerical examples demonstrate the validity of this approach

application of gee procedures for sample size calculations in repeated measures experiments derivation of the minimum sample size is an important consideration in an applied research effort when the outcome is measured at a single time point sample size procedures are well known and widely applied the corresponding situation for longitudinal designs however is less well developed in this paper we adapt the generalized estimating equation gee approach of liang and zeger to sample size calculations for discrete and continuous outcome variables the non central version of the wald 2 test is considered we use the damped exponential family of correlation structures described in munoz et al for the working correlation matrix among the repeated measures we present a table of minimum sample sizes for binary outcomes and discuss extensions that account for unequal allocation staggered entry and loss to follow up 1998 john wiley sons ltd

pid controller design for fractional order systems with time delays abstract classical proper pid controllers are designed for linear time invariant plants whose transfer functions are rational functions of s where 0 1 and s is the laplace transform variable effect of input output time delay on the range of allowable controller parameters is investigated the allowable pid controller parameters are determined from a small gain type of argument used earlier for finite dimensional plants

some methods of construction of a common lyapunov solution to a finite set of complex systems abstract in this work two methods of determining a common lyapunov solution for a finite number of complex matrices are proposed the first one is an extension to the complex case of buyukkoroglu s result dedicated to real matrices of order three whereas the second one extending and completing a very recent paper of gumus and xu can be applied to a finite set of complex matrices of arbitrary order as special cases some known results as well as new ones concerning the common lyapunov solution problem for complex triangular systems are derived numerical examples are presented to illustrate and to compare the results

robust stabilization for rectangular descriptor fractional order interval systems with order 0 α 1 abstract this paper considers the normalization and stabilization of rectangular descriptor fractional order interval systems with fractional order 0

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

brief paper on robust stability of lti fractional order delay systems of retarded and neutral type this paper deals with the analysis of robust bibo stability of lti fractional order delay systems in the presence of real parametric uncertainties two large classes of these systems namely retarded and neutral types are considered two theorems are given to check the robust bibo stability of these two families of fractional order systems one of these theorems provides necessary and sufficient conditions for the case of retarded type and another one presents only sufficient conditions for the case of neutral type furthermore upper and lower bounds cutoff frequencies are provided for drawing the value sets to illustrate the results two numerical examples are presented

calculation of all stabilizing fractional order pd controllers for integrating time delay systems in this paper a simple and effective stabilization method for integrating time delay systems using fractional order pd controllers c s k p k ds m is proposed the presented method is based on finding the stability regions according to the fractional orders of the derivative element in the range of 0 2 these regions are computed by using three stability boundaries real root boundary rrb complex root boundary crb and infinite root boundary irb the method gives the explicit formulae corresponding to these boundaries in terms of fractional order pd controller pd m controller parameters thus the complete set of stabilizing controllers for an arbitrary integrating time delay system can be obtained in order to demonstrate the effectiveness in solution accuracy and the simplicity of this method two simulation studies are given the simulation results indicate that the pd m controllers can provide larger stability regions than the integer order pd controllers

brief state space representation for fractional order controllers this article proposes an infinite dimensional state space realization for linear filters with transfer function c d s c 0 1 s w b 1 s w h d where 0 w b w h and 0

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

robust stability and stabilization of fractional order interval systems an lmi approach this technical note presents necessary and sufficient conditions for the stability and stabilization of fractional order interval systems the results are obtained in terms of linear matrix inequalities two illustrative examples are given to show that our results are effective and less conservative for checking the robust stability and designing the stabilizing controller for fractional order interval systems

robust stability and stabilization of fractional order interval systems with the fractional order alpha the 0 alpha 1 case this technical note firstly presents a sufficient and necessary condition for the robust asymptotical stability of fractional order interval systems with the fractional order satisfying 0 1 and then a sufficient condition for the robust asymptotical stabilization of such fractional order interval systems is derived all the results are obtained in terms of linear matrix inequalities finally two illustrative examples are given to show that our results are effective for checking the robust stability and designing the robust stabilizing controller for fractional order interval systems

stability of fractional order linear time invariant systems with multiple noncommensurate orders bounded input bounded output stability conditions for fractional order linear time invariant lti systems with multiple noncommensurate orders have been established in this paper the orders become noncommensurate orders when they do not have a common divisor sufficient and necessary conditions of stability for a fractional order lti system with multiple noncommensurate orders are presented in two cases based on the numerical inverse laplace transform technique time domain responses for a fractional order system with double noncommensurate orders are presented to illustrate the obtained stability results

bibo stability of some classes of delay systems and fractional systems a new test is presented for the bibo stability of delay systems of neutral type with a single delay specified in terms of their transfer functions enabling us to decide on some cases that were previously open next a class of fractional systems is considered and a method is given for determining the stability intervals for such systems

fractional order control of the two dimensional wave equation control of systems governed by the two dimensional linear wave equation in finite spatial domain is considered and presented through vibrating rectangular membranes the membranes are modeled by modal decomposition in one spatial axis and infinite dimensional transfer functions in the other the transfer functions are built of fractional order exponents regarded as non pure delays which are shown to represent traveling waves whose shape changes during motion the membranes are controlled in closed loop to achieve position profile tracking and attenuation of disturbances the actuation is along two opposite boundaries which controls the entire wave motion between them the control algorithm stops the wave propagation in the control axis by creating active non reflecting boundaries in addition it compensates the remaining non pure delay by extending the classical dead time compensation principle as a result despite the infinite dimension of the system and its fractional order transfer functions the closed loop transfer function is given by a rational first order lag with a pure time delay the resulting controllers are also of fractional order and their implementation is obtained by dedicated approximations the system stability with the approximated controllers is investigated formally using robustness tools the control algorithm is demonstrated by means of several examples

regression analysis of failure time data with informative interval censoring interval censoring arises when a subject misses prescheduled visits at which the failure is to be assessed most existing approaches for analysing interval censored failure time data assume that the censoring mechanism is independent of the true failure time however there are situations where this assumption may not hold in this paper we consider such a situation in which the dependence structure between the censoring variables and the failure time can be modelled through some latent variables and a method for regression analysis of failure time data is proposed the method makes use of the proportional hazards frailty model and an em algorithm is presented for estimation finite sample properties of the proposed estimators of regression parameters are examined through simulation studies and we illustrate the method with data from an aids study

bayesian models for multivariate current status data with informative censoring des donnees multivariees d etat consistent en un ensemble d indicatrices associees a la realisation de plusieurs evenements au moment d un examen nous nous interessons aux inferences sur les distributions jointes des temps d evenements les methodes conventionnelles d analyse des donnees de durees multiples ne peuvent etre utilisees parce que tous les temps d evenements sont censures et la censure peut etre informative nous prenons en compte la correlation des temps d evenements chez un sujet au moyen d une variable latente propre au sujet conditionnellement a laquelle les divers temps d evenements sont supposes independants nous supposons egalement que chaque evenement contribue independamment au risque de censure des fonctions en escalier non parametriques sont utilisees pour caracteriser les distributions de base des differents temps d evenements et des temps d examen les covariables et les effets specifiques du sujet sont incorpores grace au modele lineaire generalise un algorithme de monte carlo par chaines de markov est decrit pour l estimation des distributions a posteriori des inconnues les methodes sont illustrees par une application sur des donnees de sites multiples de tumeurs dans une etude de carcinogenicite animale

robust stability test of a class of linear time invariant interval fractional order system using lyapunov inequality this paper provides a new analytical robust stability checking method of fractional order linear time invariant interval uncertain system this paper continues the authors previous work yangquan chen hyo sung ahn i podlubny robust stability check of fractional order linear time invariant systems with interval uncertainties in proceedings of the ieee conference on mechatronics and automation niagara falls canada july 2005 pp 210 215 where matrix perturbation theory was used for the new robust stability checking lyapunov inequality is utilized for finding the maximum eigenvalue of a hermitian matrix through numerical examples the usefulness and the effectiveness of the newly proposed method are verified

l2 and bibo stability of systems with variable delays this paper considers l 2 and bibo stability and stabilization issues for systems with time varying delays which can be of retarded or neutral type an important role is played by a nominal system with fixed delays which are close to the time varying ones under stability or stabilizability conditions of this nominal system sufficient conditions are given in order to ensure similar properties for the system with time varying delays

generalized estimating equations for correlated binary data using the odds ratio as a measure of association summary moment methods for analyzing repeated binary responses have been proposed by liang zeger 1986 and extended by prentice 1988 in their generalized estimating equations both liang zeger 1986 and prentice 1988 estimate the parameters associated with the expected value of an individual s vector of binary responses as well as the correlations between pairs of binary responses because the odds ratio has many desirable properties and some investigators may find the odds ratio is easier to interpret we discuss modelling the association between binary responses at pairs of times with the odds ratio we then modify the estimating equations of prentice to estimate the odds ratios in simulations the parameter estimates for the logistic regression model for the marginal probabilities appear slightly more efficient when using the odds ratio parameterization

robust asymptotical stability of fractional order linear systems with structured perturbations this paper considers the robust asymptotical stability problem of fractional order linear systems with structured perturbations which are more general than the investigated fractional order interval systems based on the kronecker product and m analysis necessary and sufficient conditions for the robust asymptotical stability are established by transforming such a problem into checking the nonsingularity of a class of uncertain matrices furthermore the robustness bounds with respect to parametric perturbations to preserve the asymptotical stability are given in terms of the structured singular values finally illustrative examples are given to show the effectiveness of the proposed approach

analysis of repeated bouts of measurements in the framework of generalized estimating equations we consider a longitudinal study of interstitial cystitis ic in women in which the time between bouts of repeated measurements is large relative to the within bout separation in time our outcome of interest is the number of nocturnal voids that we model via quasi least squares qls in the framework of generalized estimating equations gee to account for potential intra subject correlation we directly apply a banded toeplitz correlation structure that previously was only implemented in an ad hoc approach using gee we describe this structure its appropriateness for data from the ic study and the results of our analysis we then demonstrate that correct specification of the underlying correlation structure versus incorrectly applying a simpler structure can prevent substantial losses in efficiency in estimation of the regression parameter these comparisons involve the limiting values of the estimates of the correlation parameters which are not consistent for the misspecification scenarios considered here we therefore obtain the limiting values of the qls estimates when the structure is incorrectly specified

brief analysis of fractional delay systems of retarded and neutral type this paper analyses several properties linked to the robust control of fractional differential systems with delays the bibo stability of both retarded and neutral fractional delay systems is related to the location of their poles in the particular case of retarded systems we give some properties of the poles of the system and the singular values of its hankel operator

new sufficient conditions for observer based control of fractional order uncertain systems new simple linear matrix inequalities are proposed to ensure the stability of a class of uncertain fractional order linear systems by means of a fractional order deterministic observer it is shown that the conditions of existence of an observer based feedback can be split into a set of linear matrix inequalities that are numerically tractable the presented results show that it is possible to decouple the conditions containing the bilinear variables into separate conditions without imposing equality constraints or considering an iterative search of the controller and the observer gains simulations results are given to approve the efficiency and the straightforwardness of the proposed design

latent variable models for longitudinal data with multiple continuous outcomes summary multiple outcomes are often used to properly characterize an effect of interest this paper proposes a latent variable model for the situation where repeated measures over time are obtained on each outcome these outcomes are assumed to measure an underlying quantity of main interest from different perspectives we relate the observed outcomes using regression models to a latent variable which is then modeled as a function of covariates by a separate regression model random effects are used to model the correlation due to repeated measures of the observed outcomes and the latent variable an em algorithm is developed to obtain maximum likelihood estimates of model parameters unit specific predictions of the latent variables are also calculated this method is illustrated using data from a national panel study on changes in methadone treatment practices

root locus and boundary feedback design for a class of distributed parameter systems in this paper a fairly complete parallel of the finite dimensional root locus theory is presented for quite general nonconstant coefficient even order ordinary differential operators on a finite interval with control and output boundary conditions representative of a choice of colocated point actuators and sensors root locus design methods for linear distributed parameter systems have also been studied for some time and the primary difficulties in rigorously interpreting root locus conclusions for distributed parameter systems are well known first the transfer function of a distributed parameter system may not be meromorphic at infinity so that many of the standard rouche arguments required even in the lumped case to determine the asymptotic behavior of the root loci are not generally valid another difficulty is that the infinitesimal generator in the state space model for a closed loop system may not be selfadjoint accretive or even satisfy the spectrum determined growth condition thus regardless of whether the root loci interpreted as closed loop eigenvalues lie in the open left half plane additional analysis would be required to conclude that the closed loop system would be asymptotically stable formulating the systems in the classical format of a boundary control problem the asymptotic analysis of the root loci can be based on the pioneering work by birkhoff on eigenfunction expansions for boundary value problems work that predated and indeed motivated the development of spectral theory in hilbert space birkhoff s work also contains an asymptotic expansion of eigenfunctions in the spatial variable generalizing the earlier sturm liouville theory for second order operators by further extending this general asymptotic analysis to also include expansions in the gain parameter a rigorous treatment of the open and closed loop transfer functions and of the corresponding return difference equation can be presented the asymptotic analysis of the return difference equation forms the basis for both our rigorous formulation of the basic problem and its solution

coprime factorizations and stability of fractional differential systems we give a frequency domain approach to stabilization for a large class of systems with transfer functions involving fractional powers of s a necessary and sufficient criterion for bibo stability is given and it is shown how to construct coprime factorizations and associated bezout factors in order to parametrize all stabilizing controllers of these systems

a note on the use of the lambert w function in the stability analysis of time delay systems the lambert w function is defined to be the multivalued inverse of the function w we w z this function has been used in an extremely wide variety of applications including the stability analysis of fractional order as well as integer order time delay systems the latter application is based on taking the mth power and or nth root of the transcendental characteristic equation tce and representing the roots of the derived tce s in terms of w functions in this note we re examine such an application of using the lambert w function through actually computing the root distributions of the derived tces of some chosen orders it is found that the rightmost root of the original tce is not necessarily a principal branch lambert w function solution and that a derived tce obtained by taking the mth power of the original tce introduces superfluous roots to the system with these observations some deficiencies displayed in the literature chen y q moore k l 2002a analytical stability bound for delayed second order systems with repeating poles using lambert w function automatica 38 5 891 895 chen y q moore k l 2002b analytical stability bound for a class of delayed fractional order dynamic systems nonlinear dynamics 29 1 4 191 200 are pointed out moreover we clarify the correct use of lambert w function to stability analysis of a class of time delay systems this will actually enlarge the application scope of the lambert w function which is becoming a standard library function for various commercial symbolic software packages to time delay systems

a numerical algorithm for stability testing of fractional delay systems this paper presents an effective numerical algorithm for testing the bibo stability of fractional delay systems described by fractional order delay differential equations it is based on using cauchy s integral theorem and solving an initial value problem the algorithm has a reliable result which is illustrated by several examples and hence is practically useful in the analysis and design of feedback control for both integer and fractional order systems having time delays

stabilizing and robust fractional order pi controller synthesis for first order plus time delay systems for all the stable first order plus time delay foptd systems a fractional order proportional integral fopi or a traditional integer order proportional integral derivative iopid controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously gain crossover frequency and phase margin in this paper a guideline for choosing two feasible or achievable specifications and a new fopi iopid controller synthesis are proposed for all the stable foptd systems using this synthesis scheme the complete feasible region of two specifications can be obtained and visualized in the plane with this region as the prior knowledge all combinations of two specifications can be verified before the controller design especially it is interesting to compare the areas of these two feasible regions for the iopid and fopi controllers this area comparison reveals for the first time the potential advantages of one controller over the other in terms of achievable performances a simulation illustration is presented to show the effectiveness and the performance of the designed fopi controller compared with the optimized integer order pi controller and the iopid controller designed following the same synthesis for the fopi in this paper

analysis of data with multiple sources of correlation in the framework of generalized estimating equations this paper is motivated by a study of physical activity participation habits in african american women with three potential sources of correlation among study outcomes according to method of assessment timing of measurement and intensity of physical activity to adjust for the multiple sources of correlation in this study we implement an approach based on generalized estimating equations that models association via a patterned correlation matrix we present a general algorithm that is relatively straightforward to program an analysis of our physical activity study and some asymptotic relative efficiency comparisons between correctly specifying the correlation structure vs ignoring two sources of correlation in the analysis of data from this study the efficiency comparisons demonstrate that correctly modeling the correlation structure can prevent substantial losses in efficiency in estimation of the regression parameter

interval censoring identifiability and the constant sum property the constant sum property given in oller et al 2004 for censoring models justifies the use of a simplified likelihood to obtain the nonparametric maximum likelihood estimator of the lifetime distribution in this paper we study the relevance of the constant sum property in the identifiability of the lifetime distribution we show that the lifetime distribution is not identifiable outside the class of constant sum models we also show that the lifetime probabilities assigned to the observable intervals are identifiable inside the class of constant sum models we illustrate all these notions with several examples

stability of linear time invariant fractional delay systems of retarded type in the space of delay parameters this paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type in the proposed method first by mapping the principal sheet of the riemann surface and a pseudo delay transformation an auxiliary polynomial is generated then this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis the properties of the root path close to these roots are used to identify intervals of delay values in which the system is stable the obtained results are illustrated via some numerical examples

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

an effective analytical criterion for stability testing of fractional delay systems this paper investigates the bibo stability of a class of fractional delay systems with rational orders a stability that holds true if all the characteristic roots have negative real parts only based on the argument principle for complex functions as well as hassard s technique for ordinary time delay systems an explicit formula is established for calculating the number of characteristic roots lying in the closed right half complex plane of the first sheet of the riemann surface and in turn a sufficient and necessary condition is obtained for testing the bibo stability of fractional delay systems as shown in the illustrative examples this stability criterion involves easy computation and works effectively

on the mixed sensitivity minimization for systems with infinitely many unstable modes in this note we consider a class of linear time invariant systems with infinitely many unstable modes by using the parameterization of all stabilizing controllers and a data transformation we show that h controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes

asymptotic properties of fractional delay differential equations abstract in this paper we study the asymptotic properties of d dimensional linear fractional differential equations with time delay we present necessary and sufficient conditions for asymptotic stability of equations of this type using the inverse laplace transform method and prove polynomial decay of stable solutions two examples illustrate the obtained analytical results

robust stabilization criterion of fractional order controllers for interval fractional order plants the robust stabilization criterion of fractional order controllers for interval fractional order plants is proposed in this study for the interval uncertainties existing in the numerator and denominator of a transfer function with respect to a fractional order plant the vertices of the value set corresponding to the characteristic function are offered by the minkowski sum this algorithm for getting the vertices avoids to calculate the redundant vertices reducing the computational complexity an auxiliary function reflecting the position relationship between the origin and the value set is defined to investigate the robust stability conditions the lower and upper limits of the test frequency interval are offered to check the auxiliary function within a finite frequency supposing that the fractional order controller can stabilize the nominal fractional order plant the stabilization criterion of the closed loop system with interval uncertainties is provided based on the auxiliary function and other two conditions finally three illustrative examples with fractional order controllers are given to validate the effectiveness of this robust stabilization criterion

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

direct stability boundary method for distributed systems with discrete delay the distributed systems considered are those with a characteristic equation expressed in terms of u s where s is the usual laplace transform variable the discrete delay h enters the characteristic equation as a term or terms with a factor exp sh the stability boundary method requires four steps a the stability or instability at h 0 is determined b values of u taking the form u exp i 4 v v real at which a change of stability may take place are determined by solving a polynomial equation in v c the sign of the gradient d res dh is deduced simply at each of these values d finally the h values corresponding to the critical values of v are found or possibly just arranged in order if qualitative results suffice stability changes require a consistent sequence of the signs of d res dh as h increases

a computing method on stability intervals of time delay for fractional order retarded systems with commensurate time delays abstract this paper investigates the stability intervals of time delays for fractional order retarded time delay systems by the orlando formula the existence of the crossing frequencies is brought to verify the stability related to the commensurate time delay for each crossing frequency the corresponding critical time delays are determined by the generalized eigenvalues of two matrices constructed by the crossing frequency the commensurate fractional order and the coefficients of the characteristic function the root tendency rt is defined to provide a method to analyze the number of the unstable roots for a given crossing frequency and critical time delay based on the rt values and the number of the unstable roots for fractional order systems with no time delay a computing method on the stability intervals of time delay is proposed in this paper finally a numerical example is offered to validate the effectiveness of this method

a comparison of mixed effects logistic regression models for binary response data with two nested levels of clustering we compare mixed effects logistic regression models for binary response data with two nested levels of clustering the comparison of these models occurs in the context of developmental toxicity data sets for which multiple types of outcomes first level are measured on each rat pup second level nested within a litter third level because the nested nature of such data is occasionally accommodated by ignoring one level of clustering we consider three models i a three level model adjusting for clustering due to both pup and litter m1 ii a two level model adjusting for just pup m2 and iii another two level model adjusting for just litter m3 the three types of effects of interest are i differences among malformation types first level effects ii differences among groups of pups for example sex of pup second level effects and iii differences among groups of litters for example dose third level effects simulations and data analyses suggest that the m3 model leads to more bias than the m1 or m2 models for all three types of effects in terms of coverage of confidence intervals for fixed effects log odds ratio parameters the m1 model achieves nominal coverage whereas the m2 model reduces coverage for the third level effects and the m3 model obtains poor coverage for both first and second level effects these reductions in coverage for certain model parameter combinations worsen as baseline risk increases the data analyses support these simulation based conclusions to some extent copyright 1999 john wiley sons ltd

stability of viscoelastic control systems classical root locus plot analysis is adapted to some one dimensional controlled distributed viscoelastic structures the constitutive law that is used for the viscoelastic material may be modeled with fractional order derivatives provided the control law s involve similar derivatives two sample one dimensional structures and control systems are used to introduce the approach a partial differential equation representation of each structure is used as well as ritz approximation the effect of error due to approximation on stability conclusions is discussed in the context of this comparison

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

miscellanea on nonidentifiability and noninformative censoring for current status data the event times and examination times that produce current status data are typically assumed to be independent here an increasing sequence of nested models is considered for current status data namely independence models constant sum models and models for which the conditional probability of the occurrence of the event prior to the examination time given the examination time is nondecreasing in the examination time in the class of constant sum models the distribution of the event time is identifiable and the examination times are noninformative in the class of models with nondecreasing conditional probability the distribution of the event time is nonidentifiable outside this class the examination times cannot be ignored

technical communique necessary and sufficient stability condition of fractional order interval linear systems this paper establishes a necessary and sufficient stability condition of fractional order interval linear systems it is supposed that the system matrix a is an interval uncertain matrix and fractional commensurate order belongs to email protected email protected 2 using the existence condition of hermitian p p for a complex lyapunov inequality we prove that the fractional order interval linear system is robust stable if and only if there exists hermitian matrix p p such that a certain type of complex lyapunov inequality is satisfied for all vertex matrices the results are directly extended to the robust stability condition of fractional order interval polynomial systems

a numerical method for stability windows and unstable root locus calculation for linear fractional time delay systems this paper aims to provide a numerical algorithm able to locate all unstable poles and therefore the characterization of the stability as a function of the delay for a class of linear fractional order neutral systems with multiple commensurate delays we start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay when these conditions are met the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis providing therefore the complete characterization of the stability windows the same method can be extended to provide the position of all unstable poles as a function of the delay

analysis of serially correlated data using quasi least squares summary quasi least squares qls a marginal statistical approach via generalized estimating equations that is described in the balanced data setting by chaganty 1997 journal of statistical planning and inference 63 39 54 allows for application of a wide range of working correlation structures when analyzing serially correlated data we extend the application of qls to serially correlated unequally spaced and unbalanced data using three useful working correlation models the firstorder autoregressive ar 1 the markov and the generalized markov structure described by nuniez anton and woodworth 1994 biometrics 50 445 456 we compare qls and the original formulation of the generalized estimating equation approach gee for these structures demonstrating that i infeasibility of the gee correlation parameter estimates can be a problem ii it is difficult to obtain consistent moment estimates of the correlation parameters for the generalized markov structure and iii the use of qls can lead to reduced mean square error of the estimate of the regression parameter for small samples of moderately correlated data to choose between alternative correlation models we propose a criterion that is based on the principle of generalized least squares finally data for which the generalized markov structure is appropriate are analyzed to demonstrate the use of qls in selecting a suitable working correlation structure and identifying in this paper we apply a statistical method based on the generalized estimating equation approach of liang and zeger 1986 to the analysis of longitudinal data that may be difficult to analyze using other established methods we consider repeated measures data collected by taking measurements of an outcome variable and associated covariates on each of a group of independent subjects our primary data analysis goal is to identify important covariates and to explain their effect on the marginal mean of the outcome variable while also accounting for the correlation among observations on each subject accomplishing this research objective may be difficult due to certain conditions that are typical in longitudinal studies the timing and total number of measurements taken may vary from subject to subject so that the data may be unbalanced and unequally spaced the outcome variable may not be normally distributed the intrasubject correlation may be described using a time dependent pattern for example the correlation between two measurements may decrease as they become more

use of quasi least squares to adjust for two levels of correlation this article considers data with two levels of association our motivating example is an international intervention trial with repeated observations on subjects who reside within geographically defined clusters to account for the potential correlation within clusters and within the repeated measurements that pertain to each subject we apply a method based on generalized estimating equations for a correlation structure proposed by lefkopoulou moore and ryan 1989 journal of the american statistical association 84 810 815

stabilization of miso fractional systems with delays abstract we consider multi input single output miso fractional systems of commensurate fractional orders with different input or output delays we derive explicit expressions of left and right coprime factorizations over h and of the associated bezout factors of the transfer matrix of the systems these factors allow the construction of the youla kucera parametrization of the set of stabilizing controllers which guarantee the internal stability of the closed loop systems

a graphical test for the interval stability of fractional delay systems this paper investigates the bibo bounded input and bounded output interval stability testing of fractional delay systems a problem of justifying the bibo stability of a polytopic family of functions involving fractional order powers as well as exponential powers it proves that the bibo stability of the polytope is governed by the bibo stability of the edges of the polytope and the latter can be tested graphically via frequency response plots the main results generalize some results in the literature

nonidentifiability in the presence of factorization for truncated data a time to event formula see text is left truncated by formula see text if formula see text can be observed only if formula see text this often results in oversampling of large values of formula see text and necessitates adjustment of estimation procedures to avoid bias simple risk set adjustments can be made to standard risk set based estimators to accommodate left truncation when formula see text and formula see text are quasi independent we derive a weaker factorization condition for the conditional distribution of formula see text given formula see text in the observable region that permits risk set adjustment for estimation of the distribution of formula see text but not of the distribution of formula see text quasi independence results when the analogous factorization condition for formula see text given formula see text holds also in which case the distributions of formula see text and formula see text are easily estimated while we can test for factorization if the test does not reject we cannot identify which factorization condition holds or whether quasi independence holds hence we require an unverifiable assumption in order to estimate the distribution of formula see text or formula see text based on truncated data this contrasts with the common understanding that truncation is different from censoring in requiring no unverifiable assumptions for estimation we illustrate these concepts through a simulation of left truncated and right censored data

sample size estimation for gee method for comparing slopes in repeated measurements data sample size calculation is an important component at the design stage of clinical trials controlled clinical trials often use a repeated measurement design in which individuals are randomly assigned to treatment groups and followed up for measurements at intervals across a treatment period of fixed duration in studies with repeated measurements one of the popular primary interests is the comparison of the rates of change in a response variable between groups statistical models for calculating sample sizes for repeated measurement designs often fail to take into account the impact of missing data correctly in this paper we propose to use the generalized estimating equation gee method in comparing the rates of change in repeated measurements and introduce closed form formulae for sample size and power that can be calculated using a scientific calculator since the sample size formula is based on asymptotic theory we investigate the performance of the estimated sample size in practical settings through simulations

multivariate linear mixed models for multiple outcomes we propose a multivariate linear mixed mlmm for the analysis of multiple outcomes which generalizes the latent variable model of sammel and ryan the proposed model assumes a flexible correlation structure among the multiple outcomes and allows a global test of the impact of exposure across outcomes in contrast to the sammel ryan model the mlmm separates the mean and correlation parameters so that the mean estimation will remain reasonably robust even if the correlation is misspecified the model is applied to birth defects data where continuous data on the size of infants who were exposed to anticonvulsant medications in utero are compared to controls

exact stability test and stabilization for fractional systems in this paper we point out a connection between regular chains and the stability of fractional order systems this observation leads to an elementary test for the stability of commensurate fractional systems

an algorithm for stabilization of fractional order time delay systems using fractional order pid controllers this technical note presents a solution to the problem of stabilizing a given fractional order system with time delay using fractional order pllambdadmu controllers it is based on determining a set of global stability regions in the kp ki kd space corresponding to the fractional orders lambda and mu in the range of 0 2 and then choosing the biggest global stability region in this set this method can be also used to find the set of stabilizing controllers that guarantees prespecified gain and phase margin requirements the algorithm is simple and has reliable result which is illustrated by an example and hence is practically useful in the analysis and design of fractional order control systems

robust stability of fractional order system with general interval uncertainties abstract this paper focuses on the analysis of robust stability of fractional order system with general interval uncertainties the concept of general interval uncertainties means that the interval uncertainties exist both in the coefficients and orders of the fractional order system necessary and sufficient conditions are proposed to check the robust stability of general interval fractional order system according to the proposed stability criterion it is interesting to find that the edge theorem which was initially proposed for integer order system cannot be directly extended to test the stability of fractional order system with general interval uncertainties examples are followed to verify the validity of the proposed method

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

analytical and numerical methods for the stability analysis of linear fractional delay differential equations in this paper several analytical and numerical approaches are presented for the stability analysis of linear fractional order delay differential equations the main focus of interest is asymptotic stability but bounded input bounded output bibo stability is also discussed the applicability of the laplace transform method for stability analysis is first investigated jointly with the corresponding characteristic equation which is broadly used in bibo stability analysis moreover it is shown that a different characteristic equation involving the one parameter mittag leffler function may be obtained using the well known method of steps which provides a necessary condition for asymptotic stability stability criteria based on the argument principle are also obtained the stability regions obtained using the two methods are evaluated numerically and comparison results are presented several key problems are highlighted

a stability test for non commensurate fractional order systems this paper presents a necessary and sufficient condition to evaluate non commensurate fractional order systems bounded input bounded output stability this condition is based on an algorithm that relies on a recursively defined closed loop realization of the system and involves cauchy s theorem its efficiency is attested by several numerical examples

stability analysis for a single degree of freedom fractional oscillator abstract this paper investigates the analytical solution asymptotical stability and bibo stability of a single degree of freedom sdof fractional oscillator by applying the laplace transform an analytical solution is provided in terms of prabhakar s function with the decomposition of state space an equivalent incommensurate fractional differential system is obtained new criteria on the asymptotical stability and bibo stability are derived based on the distribution of the characteristic roots and the poles respectively an example under three diverse cases is presented to illustrate the validity and flexibility of our main results and the memory and hereditary effects of the fractional orders

robust stability for fractional order systems with structured and unstructured uncertainties the issues of robust stability for uncertain fractional order systems of two types of order a 0 1 are dealt with in this paper for the polytope type uncertainty case a less conservative sufficient condition for robust stability is given for the norm bounded uncertainty case a sufficient and necessary condition for robust stability is presented both of these conditions can be checked by solving sets of linear matrix inequalities two numerical examples are presented to confirm the proposed conditions

models for interval censoring and simulation based inference for lifetime distributions summary interval censored lifetime data arise when individuals in a study are inspected inter mittently so that a lifetime is observed to lie between two successive times in settings where only these two times are available methods exist for nonparametric or parametric estimation of lifetime distributions however there has been virtually no discussion of how inspection processes may be estimated or identified such estimates are needed if one is to generate interval censored data by simulation this paper identifies which aspects of an independent inspection process are estimable from interval censored data and shows how to obtain nonparametric estimates the results allow interval censored data from any specified distribution to be generated and give new simulation procedures for estimation or testing a new omnibus goodness of fit test is introduced

necessary and sufficient conditions for bibo stability of some fractional delay systems of neutral type in this note bounded input bounded output bibo stability of a large class of neutral type fractional delay systems is investigated necessary and sufficient conditions of bibo stability are presented for the intended class of systems the sufficient conditions have been provided for a more general case in the previous studies two lemmas are provided for checking a prerequisite imposed on the considered class of systems finally two numerical examples are given to illustrate the obtained results

multivariate regression analyses for categorical data summary it is common to observe a vector of discrete and or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes the response vector can comprise repeated observations on one variable as in longitudinal studies or genetic studies of families or can include observations for different variables this paper discusses a class of models for the marginal expectations of each response and for pairwise associations the marginal models are contrasted with log linear models two generalized estimating equation approaches are compared for parameter estimation the first focuses on the regression parameters the second simultaneously estimates the regression and association parameters the robustness and efficiency of each is discussed the methods are illustrated with analyses of two data sets from public health research

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