an extended hazard model with longitudinal covariates summary in clinical trials and other medical studies it has become increasingly common to observe an event time of interest and longitudinal covariates simultaneously in the literature joint modelling approaches have been employed to analyze both survival and longitudinal processes and to investigate their association early attention has mostly been placed on developing adaptive and flexible longitudinal processes based on a prespecified survival model most commonly the cox proportional model in this paper we propose a general class of semi parametric hazard regres

information geometry on hierarchy of probability distributions an exponential family or mixture family of probability distributions has a natural hierarchical structure this paper gives an orthogonal decomposition of such a system based on information geometry a typical example is the decomposition of stochastic dependency among a number of random variables in general they have a complex structure of dependencies pairwise dependency is easily represented by correlation but it is more difficult to measure effects of pure triplewise or higher order interactions dependencies among these variables stochastic dependency is decomposed quantitatively into an orthogonal sum of pairwise triplewise and further higher order dependencies this gives a new invariant decomposition of joint entropy this problem is important for extracting intrinsic interactions in firing patterns of an ensemble of neurons and for estimating its functional connections the orthogonal decomposition is given in a wide class of hierarchical structures including both exponential and mixture families as an example we decompose the dependency in a higher order markov chain into a sum of those in various lower order markov chains

joint modelling of accelerated failure time and longitudinal data summary the accelerated failure time model is an attractive alternative to the cox model when the proportionality assumption fails to capture the relationship between the survival time and longitudinal covariates several complications arise when the covariates are measured intermittently at different time points for different subjects possibly with measurement errors or measurements are not available after the failure time joint modelling of the failure time and longitudinal data offers a solution to such complications we explore the joint modelling approach under the accelerated failure time assumption when covariates are assumed to follow a linear mixed effects model with measurement errors the procedure is based on maximising the joint likelihood function with random effects treated as missing data a monte carlo em algorithm is used to estimate all the unknown parameters including the unknown baseline hazard function the performance of the proposed procedure is checked in simulation studies a case study of reproductive egg laying data for female mediterranean fruit flies and their relationship to longevity demonstrate the effectiveness of the new procedure

modelling dependence within joint tail regions standard approaches for modelling dependence within joint tail regions are based on extreme value methods which assume max stability a particular form of joint tail dependence we develop joint tail models based on a broader class of dependence structure which provides a natural link between max stable models and weaker forms of dependence including independence and negative association this approach overcomes many of the problems that are encountered with standard methods and is the basis for a poisson process representation that generalizes existing bivariate results we apply the new techniques to simulated and environmental data and demonstrate the marked advantage that the new approach offers for joint tail extrapolation

survival curve estimation for informatively coarsened discrete event time data interval censored or more generally coarsened event time data arise when study participants are observed at irregular time periods and experience the event of interest in between study observations such data are often analysed assuming non informative censoring which can produce biased results if the assumption is wrong this paper extends the standard approach for estimating survivor functions to allow informatively interval censored data by incorporating various assumptions about the censoring mechanism into the model we include a bayesian extension in which final estimates are produced by mixing over a distribution of assumed censoring mechanisms we illustrate these methods with a natural history study of hiv infected individuals using assumptions elicited from an aids expert

global dynamics of a system governing an algorithm for regression with censored and non censored data under general errors we present an investigation into the dynamics of a system which underlies a new estimating algorithm for regression with grouped and nongrouped data the algorithm springs from a simplification of the well known em algorithm in which the expectation step of the em is substituted by a modal step this avoids awkward integrations when the error distribution is assumed to be general the sequences generated by the estimating procedure proposed here define our objective system which is piecewise linear the study tackles the system s asymptotic stability as well as its speed of convergence to the equilibrium point in this sense to reduce the speed of convergence we propose an alternative estimating procedure numerical examples illustrate the theoretical results compare the proposed procedures and analyze the precision of the estimate

information geometric approach to inferring causal directions while conventional approaches to causal inference are mainly based on conditional in dependences recent methods also account for the shape of conditional distributions the idea is that the causal hypothesis x causes y imposes that the marginal distribution p x and the conditional distribution p y x represent independent mechanisms of nature recently it has been postulated that the shortest description of the joint distribution p x y should therefore be given by separate descriptions of p x and p y x since description length in the sense of kolmogorov complexity is uncomputable practical implementations rely on other notions of independence here we define independence via orthogonality in information space this way we can explicitly describe the kind of dependence that occurs between p y and p x y making the causal hypothesis y causes x implausible remarkably this asymmetry between cause and effect becomes particularly simple if x and y are deterministically related we present an inference method that works in this case we also discuss some theoretical results for the non deterministic case although it is not clear how to employ them for a more general inference method

a markov chain monte carlo em algorithm for analyzing interval censored data under the cox proportional hazards model summary this paper proposes a monte carlo em mcem algorithm for fitting the proportional hazards model for interval censored failure time data the algorithm generates orderings of the failures from their probability distribution under the model we maximize the average of the log likelihoods from these completed data sets to obtain updated parameter estimates as with the standard cox model this algorithm does not require the estimation of the baseline hazard function the performance of the algorithm is evaluated using simulations and the method is applied to data from aids and cancer studies our results indicate that our method produced more precise and unbiased estimates than methods of right and midpoint imputation

checking the assumptions of rasch s model for speed tests two new tests for a model for the response times on pure speed tests by rasch 1960 are proposed the model is based on the assumption that the test response times are approximately gamma distributed with known index parameters and unknown rate parameters the rate parameters are decomposed in a subject ability parameter and a test difficulty parameter by treating the ability as a gamma distributed random variable maximum marginal likelihood mml estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived also the model tests proposed here pertain to the framework of mml two tests or modification indices are proposed the first one is focused on the assumption of local stochastic independence the second one on the assumption of the test characteristic functions the tests are based on lagrange multiplier statistics and can therefore be computed using the parameter estimates under the null model therefore model violations for all items and pairs of items can be assessed as a by product of one single estimation run power studies and applications to real data are included as numerical examples

an m estimator for tail dependence in arbitrary dimensions consider a random sample in the max domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model a new estimator for the unknown parameter is defined as the value that minimizes the distance between a vector of weighted integrals of the tail dependence function and their empirical counterparts the minimization problem has with probability tending to one a unique global solution the estimator is consistent and asymptotically normal the spectral measures of the tail dependence models to which the method applies can be discrete or continuous examples demonstrate the applicability and the performance of the method

regression models for identifying noise sources in magnetic resonance images stochastic noise susceptibility artifacts magnetic field and radiofrequency inhomogeneities and other noise components in magnetic resonance images mris can introduce serious bias into any measurements made with those images we formally introduce three regression models including a rician regression model and two associated normal models to characterize stochastic noise in various magnetic resonance imaging modalities including diffusion weighted imaging dwi and functional mri fmri estimation algorithms are introduced to maximize the likelihood function of the three regression models we also develop a diagnostic procedure for systematically exploring mr images to identify noise components other than simple stochastic noise and to detect discrepancies between the fitted regression models and mri data the diagnostic procedure includes goodness of fit statistics measures of influence and tools for graphical display the goodness of fit statistics can assess the key assumptions of the three r

likelihood methods for incomplete longitudinal binary responses with incomplete categorical covariates summary we consider longitudinal studies in which the outcome observed over time is binary and the covariates of interest are categorical with no missing responses or covariates one specifies a multinomial model for the responses given the covariates and uses maximum likelihood to estimate the parameters unfortunately incomplete data in the responses and covariates are a common occurrence in longitudinal studies here we assume the missing data are missing at random rubin 1976 biometrika63 581 592 since all of the missing data responses and covariates are categorical a useful technique for obtaining maximum likelihood parameter estimates is the em algorithm by the method of weights proposed in ibrahim 1990 journal of the american statistical association85 765 769 in using the em algorithm with missing responses and covariates one specifies the joint distribution of the responses and covariates here we consider the parameters of the covariate distribution as a nuisance in data sets where the percentage of missing data is high the estimates of the nuisance parameters can lead to highly unstable estimates of the parameters of interest we propose a conditional model for the covariate distribution that has several modeling advantages for the em algorithm and provides a reduction in the number of nuisance parameters thus providing more stable estimates in finite samples

regression analysis of interval censored survival data with covariates using log linear models we considered the regression analysis of the event time data with left right or interval censored observations we extended life table techniques for censored survival data using log linear models to incorporate interval censored failures the em algorithm was used to calculate maximum likelihood estimates for the parameters we assumed that the hazard function was a stepwise function over disjoint intervals of time thus the nonparametric model the parametric exponential model and the semiparametric cox proportional hazard model were easily implemented as special cases we adapted the restricted em algorithm to test hypotheses and to construct confidence intervals for the parameters these methods were applied in an analysis of the recurrence time for treated melanoma patients

estimation of allocation rates in a cluster analysis context abstract a sample of multivariate observations is assumed to be drawn from a mixture of a given number of underlying populations the mixture likelihood approach to clustering is used to allocate each individual in the sample to its population of origin on the basis of the estimated posterior probabilities of population membership estimation of the correct allocation rate is considered for individual populations as well as for the overall mixture by averaging functions of the maximum of these posterior probabilities the estimates of the correct allocation rates provide a means of assessing the performance of the mixture approach to clustering the bootstrap technique is investigated for its effectiveness in reducing the bias of the estimates so obtained results are reported for three real data sets and a simulation study it is demonstrated that the proposed estimates generally provide useful information on the unobservable allocation rates of the mixture approach encouraging results are obtained for

a new class of models for bivariate joint tails summary a fundamental issue in applied multivariate extreme value analysis is modelling dependence within joint tail regions the primary focus of this work is to extend the classical pseudopolar treatment of multivariate extremes to develop an asymptotically motivated representation of extremal dependence that also encompasses asymptotic independence starting with the usual mild bivariate regular variation assumptions that underpin the coefficient of tail dependence as a measure of extremal dependence our main result is a characterization of the limiting structure of the joint survivor function in terms of an essentially arbitrary non negative measure that must satisfy some mild constraints we then construct parametric models from this new class and study in detail one example that accommodates asymptotic dependence asymptotic independence and asymmetry within a straightforward parsimonious parameterization we provide a fast simulation algorithm for this example and detail likelihood based inference including tests for asymptotic dependence and symmetry which are useful for submodel selection we illustrate this model by application to both simulated and real data in contrast with the classical multivariate extreme value approach which concentrates on the limiting distribution of normalized componentwise maxima our framework focuses directly on the structure of the limiting joint survivor function and provides significant extensions of both the theoretical and the practical tools that are available for joint tail modelling

a monte carlo implementation of the em algorithm and the poor man s data augmentation algorithms abstract the first part of this article presents the monte carlo implementation of the e step of the em algorithm given the current guess to the maximizer of the posterior distribution latent data patterns are generated from the conditional predictive distribution the expected value of the augmented log posterior is then updated as a mixture of augmented log posteriors mixed over the generated latent data patterns multiple imputations in the m step of the algorithm this mixture is maximized to obtain the update to the maximizer of the observed posterior the gradient and hessian of the observed log posterior are also expressed as mixtures mixed over the multiple imputations the relation between the monte carlo em mcem algorithm and the data augmentation algorithm is noted two modifications to the mcem algorithm the poor man s data augmentation algorithms which allow for the calculation of the entire posterior are then presented these approximations serve as diagnostics for the validity o

the use of gaussian quadrature for estimation in frailty proportional hazards models in this paper we propose a novel gaussian quadrature estimation method in various frailty proportional hazards models we approximate the unspecified baseline hazard by a piecewise constant one resulting in a parametric model that can be fitted conveniently by gaussian quadrature tools in standard software such as sas proc nlmixed we first apply our method to simple frailty models for correlated survival data e g recurrent or clustered failure times then to joint frailty models for correlated failure times with informative dropout or a dependent terminal event such as death simulation studies show that our method compares favorably with the well received penalized partial likelihood method and the monte carlo em mcem method for both normal and gamma frailty models we apply our method to three real data examples 1 the time to blindness of both eyes in a diabetic retinopathy study 2 the joint analysis of recurrent opportunistic diseases in the presence of death for hiv infected patients and 3 the joint modeling of local distant tumor recurrences and patients survival in a soft tissue sarcoma study the proposed method greatly simplifies the implementation of the joint frailty models and makes them much more accessible to general statistical practitioners

a differential equation approach to the computation of the fourier transform of the images of translating objects the frequency domain analysis of constant velocity motion has proven useful in a number of different contexts ranging from television signal processing to computer vision this work considers the frequency domain analysis of a generalization of such simple dynamics which includes the effect of acceleration and its time derivatives of any order in the frequency domain the contribution due to the object s shape and the contribution due to translation terms are clearly separated motion information in the frequency domain is given by functions characterized by a family of differential equations such differential equations are introduced in the work and their solutions are exemplified in order to compute the frequency domain motion contributions for simplicity the results are presented for the case of translations but they apply equally well to rotations

maximum likelihood estimation and likelihood ratio test for square tables with missing data missing data complicate the analysis of paired categorical data this paper considers with the use of the em algorithm the maximum likelihood estimation and likelihood ratio test for incomplete square tables with missing data an example involving the susceptibility of micro organisms to antimicrobial drugs illustrates the procedure

hierarchical construction of orientation and velocity selective filters as a step towards the early measurement of visual primitives the authors outline design criteria for the extraction of orientation and velocity information and present a variety of tools useful in the construction of simple linear filters a hierarchical parallel processing scheme is used in which nodes compute a weighted sum of inputs from within a small spatio temporal neighborhood the resulting scheme is easily analyzed and provides mechanisms sensitive to narrow ranges of both image velocity and orientation the hierarchical approach in combination with separability in the first levels yields an efficient implementation

the calculation of posterior distributions by data augmentation abstract the idea of data augmentation arises naturally in missing value problems as exemplified by the standard ways of filling in missing cells in balanced two way tables thus data augmentation refers to a scheme of augmenting the observed data so as to make it more easy to analyze this device is used to great advantage by the em algorithm dempster laird and rubin 1977 in solving maximum likelihood problems in situations when the likelihood cannot be approximated closely by the normal likelihood maximum likelihood estimates and the associated standard errors cannot be relied upon to make valid inferential statements from the bayesian point of view one must now calculate the posterior distribution of parameters of interest if data augmentation can be used in the calculation of the maximum likelihood estimate then in the same cases one ought to be able to use it in the computation of the posterior distribution it is the purpose of this article to explain how this can be done the basic idea

missing covariates in generalized linear models when the missing data mechanism is non ignorable we propose a method for estimating parameters in generalized linear models with missing covariates and a non ignorable missing data mechanism we use a multinomial model for the missing data indicators and propose a joint distribution for them which can be written as a sequence of one dimensional conditional distributions with each one dimensional conditional distribution consisting of a logistic regression we allow the covariates to be either categorical or continuous the joint covariate distribution is also modelled via a sequence of one dimensional conditional distributions and the response variable is assumed to be completely observed we derive the e and m steps of the em algorithm with non ignorable missing covariate data for categorical covariates we derive a closed form expression for the e and m steps of the em algorithm for obtaining the maximum likelihood estimates mles for continuous covariates we use a monte carlo version of the em algorithm to obtain the mles via the gibbs sampler computational techniques for gibbs sampling are proposed and implemented the parametric form of the assumed missing data mechanism itself is not testable from the data and thus the non ignorable modelling considered here can be viewed as a sensitivity analysis concerning a more complicated model therefore although a model may have passed the tests for a certain missing data mechanism this does not mean that we have captured even approximately the correct missing data mechanism hence model checking for the missing data mechanism and sensitivity analyses play an important role in this problem and are discussed in detail several simulations are given to demonstrate the methodology in addition a real data set from a melanoma cancer clinical trial is presented to illustrate the methods proposed

statistics for near independence in multivariate extreme values we propose a multivariate extreme value threshold model for joint tail estimation which overcomes the problems encountered with existing techniques when the variables are near independence we examine inference under the model and develop tests for independence of extremes of the marginal variables both when the thresholds are fixed and when they increase with the sample size motivated by results obtained from this model we give a new and widely applicable characterisation of dependence in the joint tail which includes existing models as special cases a new parameter which governs the form of dependence is of fundamental importance to this characterisation by estimating this parameter we develop a diagnostic test which assesses the applicability of bivariate extreme value joint tail models the methods are demonstrated through simulation and by analysing two previously published data sets

a shared response model for clustered binary data in developmental toxicity studies summary existing distributions for modeling fetal response data in developmental toxicology such as the beta binomial distribution have a tendency of inflating the probability of no malformed fetuses and hence understating the risk of having at least one malformed fetus within a litter as opposed to a shared probability extra binomial model we advocate a shared response model that allows a random number of fetuses within the same litter to share a common response an explicit formula is given for the probability function and graphical plots suggest that it does not suffer from the problem of assigning too much probability to the event of no malformed fetuses the em algorithm can be used to estimate the model parameters results of a simulation study show that the em estimates are nearly unbiased and the associated confidence intervals based on the usual standard error estimates have coverage close to the nominal level simulation results also suggest that the shared response model estimates of the marginal malformation probabilities are robust to misspecification of the distributional form but not so for the estimates of intralitter correlation and the litter level probability of having at least one malformed fetus the proposed model is fitted to a set of data from the u s national toxicology program for the same dose response relationship the fit based on the shared response distribution is superior to that based on the beta binomial and comparable to that based on the recently proposed q power distribution kuk 2004 applied statistics53 369 386 an advantage of the shared response model over the q power distribution is that it is more interpretable and can be extended more easily to the multivariate case to illustrate this a bivariate shared response model is fitted to fetal response data involving visceral and skeletal malformation

regression for skewed biomarker outcomes subject to pooling epidemiological studies involving biomarkers are often hindered by prohibitively expensive laboratory tests strategically pooling specimens prior to performing these lab assays has been shown to effectively reduce cost with minimal information loss in a logistic regression setting when the goal is to perform regression with a continuous biomarker as the outcome regression analysis of pooled specimens may not be straightforward particularly if the outcome is right skewed in such cases we demonstrate that a slight modification of a standard multiple linear regression model for poolwise data can provide valid and precise coefficient estimates when pools are formed by combining biospecimens from subjects with identical covariate values when these x homogeneous pools cannot be formed we propose a monte carlo expectation maximization mcem algorithm to compute maximum likelihood estimates mles simulation studies demonstrate that these analytical methods provide essentially unbiased estimates of coefficient parameters as well as their standard errors when appropriate assumptions are met furthermore we show how one can utilize the fully observed covariate data to inform the pooling strategy yielding a high level of statistical efficiency at a fraction of the total lab cost

analyzing sequential categorical data individual variation in markov chains markov chains are probabilistic models for sequences of categorical events with applications throughout scientific psychology this paper provides a method for anlayzing data consisting of event sequences and covariate observations it is assumed that each sequence is a markov process characterized by a distinct transition probability matrix the objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data the elements of the transition probability matrices are written as functions of a vector of latent variables with variation in the latent variables explained through a multivariate regression on the covariates the regression is estimated using the em algorithm and requires the numerical calculation of a multivariate integral an example using simulated cognitive developmental data is presented which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance even when individual differences are not the focus of the investigator s concerns

a generalized speed accuracy response model for dichotomous items we propose a generalization of the speed accuracy response model sarm introduced by maris and van der maas psychometrika 77 615 633 2012 in these models the scores that result from a scoring rule that incorporates both the speed and accuracy of item responses are modeled our generalization is similar to that of the one parameter logistic or rasch model to the two parameter logistic or birnbaum model in item response theory an expectation maximization em algorithm for estimating model parameters and standard errors was developed furthermore methods to assess model fit are provided in the form of generalized residuals for item score functions and saddlepoint approximations to the density of the sum score the presented methods were evaluated in a small simulation study the results of which indicated good parameter recovery and reasonable type i error rates for the residuals finally the methods were applied to two real data sets it was found that the two parameter sarm showed improved fit compared to the one parameter sarm in both data sets

a model for evaluating sensitivity and specificity for correlated diagnostic tests in efficacy studies with an imperfect reference test abstract the purpose of a diagnostic efficacy study is to evaluate and compare the sensitivities and specificities of several diagnostic tests usually the diagnostic tests are correlated conditional on disease status and the reference test is subject to error in the chlamydia trachomatis study five screening tests for detecting chlamydia in endocervical specimens were compared the five tests are correlated and the reference test the cell culture test has less than 100 sensitivity the conventional method ignores both the correlations between the tests and the misclassification of the reference test and thus cannot provide a valid analysis we propose a model to evaluate and compare the sensitivities and specificities of correlated diagnostic tests when there is either an imperfect reference test or even no reference test the model also can estimate the effects of covariates it is a generalized linear mixed model with two unobserved variables one continuous and one dichotomous we use a hybrid

hierarchical likelihood approach for frailty models systematic likelihood inference for frailty models is possible using lee nelder s 1996 hierarchical likelihood we develop an inferential method for frailty models via hierarchical likelihood which gives a simple unified framework and a numerically efficient algorithm simulations and practical examples are presented to illustrate the new method

approximate posterior distributions for incomplete data problems summary we consider the problem of developing a simple approximation to a posterior distribution arising from incomplete data sampling we compare approximations based on the normal distribution and upon conjugate distributions theoretically where feasible and in some numerical examples two general conclusions can be made on the basis of our numerical work first when there is missing data approximations which fail to take loss of information into account give overly concentrated posterior distributions second the gaussian approximation matching mode and observed fisher information is quite good with large sample sizes and true posteriors which are not highly skewed further work delimiting these conditions more precisely will be useful finally the use of a conjugate posterior which matches both mode and information performs well in all of our examples and is decidedly superior to the gaussian approximation with small samples

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

item response theory observed score kernel equating item response theory irt observed score kernel equating is introduced for the non equivalent groups with anchor test equating design using either chain equating or post stratification equating t

causal inference using the algorithmic markov condition inferring the causal structure that links n observables is usually based upon detecting statistical dependences and choosing simple graphs that make the joint measure markovian here we argue why causal inference is also possible when the sample size is one we develop a theory how to generate causal graphs explaining similarities between single objects to this end we replace the notion of conditional stochastic independence in the causal markov condition with the vanishing of conditional algorithmic mutual information and describe the corresponding causal inference rules we explain why a consistent reformulation of causal inference in terms of algorithmic complexity implies a new inference principle that takes into account also the complexity of conditional probability densities making it possible to select among markov equivalent causal graphs this insight provides a theoretical foundation of a heuristic principle proposed in earlier work we also sketch some ideas on how to replace kolmogorov complexity with decidable complexity criteria this can be seen as an algorithmic analog of replacing the empirically undecidable question of statistical independence with practical independence tests that are based on implicit or explicit assumptions on the underlying distribution

maximum likelihood estimation of the multivariate normal mixture model the hessian of the multivariate normal mixture model is derived and estimators of the information matrix are obtained thus enabling consistent estimation of all parameters and their precisions the usefulness of the new theory is illustrated with two examples and some simulation experiments the newly proposed estimators appear to be superior to the existing ones

maximum likelihood estimation of nonlinear structural equation models the existing maximum likelihood theory and its computer software in structural equation modeling are established based on linear relationships among manifest variables and latent variables however models with nonlinear relationships are often encountered in social and behavioral sciences in this article an em type algorithm is developed for maximum likelihood estimation of a general nonlinear structural equation model to avoid computation of the complicated multiple integrals involved the e step is completed by a metropolis hastings algorithm it is shown that the m step can be completed efficiently by simple conditional maximization standard errors of the maximum likelihood estimates are obtained via louis s formula the methodology is illustrated with results from a simulation study and two real examples

a frailty model for informative censoring to account for the correlation between failure and censoring we propose a new frailty model for clustered data in this model the risk to be censored is affected by the risk of failure this model allows flexibility in the direction and degree of dependence between failure and censoring it includes the traditional frailty model as a special case it allows censoring by some causes to be analyzed as informative while treating censoring by other causes as noninformative it can also analyze data for competing risks to fit the model the em algorithm is used with markov chain monte carlo simulations in the e steps simulation studies and analysis of data for kidney disease patients are provided consequences of incorrectly assuming noninformative censoring are investigated

assessing influence in multiple linear regression with incomplete data the problem of assessing influence and detecting influential cases in multiple linear regression with incomplete data is considered a case is said to be influential if appreciable changes in fitted regression coefficients occur when it is removed from the data a one step influence measure is derived based on the em algorithm for detecting cases that are influential in the maximum likelihood estimation of the regression coefficients results are compared with the complete data cook s distance measure techniques are demonstrated by examples

frequency domain analysis of translations with piecewise cubic trajectories translations with piecewise cubic trajectories are studied in the frequency domain this class of motion has as an important subcase cubic spline trajectories translations with trajectories depending on time with general polynomial law are preliminarily considered and a general theorem concerning this type of motion is introduced the application of this theorem to the case of cubic time dependence and the consideration of finite duration effects lead to the solution of the piecewise cubic trajectory case the results which are remarkably different from those concerning constant velocity translations clearly indicate the importance of the role of velocity and time duration in this respect they confirm the validity of constant velocity motion as a first order model for frequency domain analysis of motion

estimation in a cox proportional hazards cure model summary some failure time data come from a population that consists of some subjects who are susceptible to and others who are nonsusceptible to the event of interest the data typically have heavy censoring at the end of the follow up period and a standard survival analysis would not always be appropriate in such situations where there is good scientific or empirical evidence of a nonsusceptible population the mixture or cure model can be used farewell 1982 biometrics38 1041 1046 it assumes a binary distribution to model the incidence probability and a parametric failure time distribution to model the latency kuk and chen 1992 biometrika79 531 541 extended the model by using cox s proportional hazards regression for the latency we develop maximum likelihood techniques for the joint estimation of the incidence and latency regression parameters in this model using the nonparametric form of the likelihood and an em algorithm a zero tail constraint is used to reduce the near nonidentifiability of the problem the inverse of the observed information matrix is used to compute the standard errors a simulation study shows that the methods are competitive to the parametric methods under ideal conditions and are generally better when censoring from loss to follow up is heavy the methods are applied to a data set of tonsil cancer patients treated with radiation therapy

maximizing generalized linear mixed model likelihoods with an automated monte carlo em algorithm summary two new implementations of the em algorithm are proposed for maximum likelihood fitting of generalized linear mixed models both methods use random independent and identically distributed sampling to construct monte carlo approximations at the e step one approach involves generating random samples from the exact conditional distribution of the random effects given the data by rejection sampling using the marginal distribution as a candidate the second method uses a multivariate t importance sampling approximation in many applications the two methods are complementary rejection sampling is more efficient when sample sizes are small whereas importance sampling is better with larger sample sizes monte carlo approximation using random samples allows the monte carlo error at each iteration to be assessed by using standard central limit theory combined with taylor series methods specifically we construct a sandwich variance estimate for the maximizer at each approximate e step this suggests a rule for automatically increasing the monte carlo sample size after iterations in which the true em step is swamped by monte carlo error in contrast techniques for assessing monte carlo error have not been developed for use with alternative implementations of monte carlo em algorithms utilizing markov chain monte carlo e step approximations three different data sets including the infamous salamander data of mccullagh and nelder are used to illustrate the techniques and to compare them with the alternatives the results show that the methods proposed can be considerably more efficient than those based on markov chain monte carlo algorithms however the methods proposed may break down when the intractable integrals in the likelihood function are of high dimension

using em to obtain asymptotic variance covariance matrices the sem algorithm abstract the expectation maximization em algorithm is a popular and often remarkably simple method for maximum likelihood estimation in incomplete data problems one criticism of em in practice is that asymptotic variance covariance matrices for parameters e g standard errors are not automatic byproducts as they are when using some other methods such as newton raphson in this article we define and illustrate a procedure that obtains numerically stable asymptotic variance covariance matrices using only the code for computing the complete data variance covariance matrix the code for em itself and code for standard matrix operations the basic idea is to use the fact that the rate of convergence of em is governed by the fractions of missing information to find the increased variability due to missing information to add to the complete data variance covariance matrix we call this supplemented em algorithm the sem algorithm theory and particular examples reinforce the conclusion that the sem alg

an expectation maximization algorithm for fitting the generalized odds rate model to interval censored data the generalized odds rate model is a class of semiparametric regression models which includes the proportional hazards and proportional odds models as special cases there are few works on estimation of the generalized odds rate model with interval censored data because of the challenges in maximizing the complex likelihood function in this paper we propose a gamma poisson data augmentation approach to develop an expectation maximization algorithm which can be used to fit the generalized odds rate model to interval censored data the proposed expectation maximization algorithm is easy to implement and is computationally efficient the performance of the proposed method is evaluated by comprehensive simulation studies and illustrated through applications to datasets from breast cancer and hemophilia studies in order to make the proposed method easy to use in practice an r package icgor was developed copyright 2016 john wiley sons ltd

on the convergence properties of the em algorithm two convergence aspects of the em algorithm are studied i does the em algorithm find a local maximum or a stationary value of the incomplete data likelihood function ii does the sequence of parameter estimates generated by em converge several convergence results are obtained under conditions that are applicable to many practical situations two useful special cases are a if the unobserved complete data specification can be described by a curved exponential family with compact parameter space all the limit points of any em sequence are stationary points of the likelihood function b if the likelihood function is unimodal and a certain differentiability condition is satisfied then any em sequence converges to the unique maximum likelihood estimate a list of key properties of the algorithm is included

design in nonlinear mixed effects models optimization using the fedorov wynn algorithm and power of the wald test for binary covariates we extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi exponential model we first show the relevance of the predicted standard errors ses given by the computation of the population fisher information matrix using the r function pfim in comparison to those computed with the stochastic approximation expectation maximization algorithm implemented in the monolix software we then highlight the usefulness of the fedorov wynn fw algorithm for designs optimization compared to the simplex algorithm from the predicted se of pfim we compute the predicted power of the wald test to detect a treatment effect as well as the number of subjects needed to achieve a given power using the fw algorithm we investigate the influence of the design on the power and show that for optimized designs with the same total number of samples the power increases when the number of subjects increases and the number of samples per subject decreases a simulation study is also performed with the nlme function of r to confirm this result and show the relevance of the predicted powers compared to those observed by simulation

generalized residuals for general models for contingency tables with application to item response theory generalized residuals are a tool employed in the analysis of contingency tables to examine possible sources of model error they have typically been applied to log linear models and to latent class models a general approach to generalized residuals is developed for a very general class of models for contingency tables to illustrate their use generalized residuals are applied to models based on item response theory irt models such models are commonly applied to analysis of standardized achievement or aptitude tests to obtain a realistic perspective on application of generalized residuals actual testing data are employed

general formulas for obtaining the mles and the asymptotic variance covariance matrix in mapping quantitative trait loci when using the em algorithm we present in this paper general formulas for deriving the maximum likelihood estimates and the asymptotic variance covariance matrix of the positions and effects of quantitative trait loci qtls in a finite normal mixture model when the em algorithm is used for mapping qtls the general formulas are based on two matrices d and q where d is the genetic design matrix characterizing the genetic effects of the qtls and q is the conditional probability matrix of qtl genotypes given flanking marker genotypes containing the information on qtl positions with the general formulas it is relatively easy to extend qtl mapping analysis to using multiple marker intervals simultaneously for mapping multiple qtls for analyzing qtl epistasis and for estimating the heritability of quantitative traits simulations were performed to evaluate the performance of the estimates of the asymptotic variances of qtl positions and effects

em based joint data detection and channel estimation of ds cdma signals we present two efficient iterative receiver structures of tractable complexity for joint multiuser detection and multichannel estimation jde of direct sequence code division multiple access signals the schemes result from an application of the expectation maximization em and the space alternating generalized expectation maximization sage algorithms respectively the em jde receiver updates the data bit sequences in parallel while the sage jde receiver reestimates them successively the channel parameters are updated in parallel in both schemes the em algorithm provides a set of free parameters called weight coefficients which can be selected to optimize its performance two optimality criteria are defined and analytical expressions for the corresponding optimized weight coefficients are given monte carlo simulations of a synchronous scenario show that the proposed jde receivers have excellent multiuser efficiency and are robust against errors in the estimation of the channel parameters moreover very short training sequences are required for the jde schemes to converge simulation results further demonstrate that the sage jde receiver exhibits a better performance when the users bit sequences are updated in the order of increasing signal strength i e the bit sequence of the user with the weakest signal strength is updated first at each stage

a conditional approach for multivariate extreme values with discussion summary multivariate extreme value theory and methods concern the characterization estimation and extrapolation of the joint tail of the distribution of a d dimensional random variable existing approaches are based on limiting arguments in which all components of the variable become large at the same rate this limit approach is inappropriate when the extreme values of all the variables are unlikely to occur together or when interest is in regions of the support of the joint distribution where only a subset of components is extreme in practice this restricts existing methods to applications where d is typically 2 or 3 under an assumption about the asymptotic form of the joint distribution of a d dimensional random variable conditional on its having an extreme component we develop an entirely new semiparametric approach which overcomes these existing restrictions and can be applied to problems of any dimension we demonstrate the performance of our approach and its advantages over existing methods by using theoretical examples and simulation studies the approach is used to analyse air pollution data and reveals complex extremal dependence behaviour that is consistent with scientific understanding of the process we find that the dependence structure exhibits marked seasonality with ex tremal dependence between some pollutants being significantly greater than the dependence at non extreme levels

majorization minimization algorithms in signal processing communications and machine learning this paper gives an overview of the majorization minimization mm algorithmic framework which can provide guidance in deriving problem driven algorithms with low computational cost a general introduction of mm is presented including a description of the basic principle and its convergence results the extensions acceleration schemes and connection to other algorithmic frameworks are also covered to bridge the gap between theory and practice upperbounds for a large number of basic functions derived based on the taylor expansion convexity and special inequalities are provided as ingredients for constructing surrogate functions with the pre requisites established the way of applying mm to solving specific problems is elaborated by a wide range of applications in signal processing communications and machine learning

recognition and velocity computation of large moving objects in images two one dimensional time sequences are generated from the projections of the two dimensional sequence on the x and y axes then the two dimensional fast fourier transform for the generated time sequences is computed a peak in the spectrum for the selected spatial frequency is detected the temporal frequency at which the peak is detected gives an estimate of the velocity of the moving object analytical formulations for large moving objects in a time sequence with zero background are presented an algorithm is given for velocity formulation

a sum characterization of hidden regular variation with likelihood inference via expectation maximization a fundamental deficiency of classical multivariate extreme value theory is the inability to distinguish between asymptotic independence and exact independence in this work we examine multivariate threshold modelling in the framework of regular variation on cones tail dependence is described by a limiting measure which in some cases is degenerate on joint tail regions despite strong subasymptotic dependence in such regions hidden regular variation a higher order tail decay on these regions offers a refinement of the classical theory we develop a representation of random vectors possessing hidden regular variation as the sum of independent regular varying components the representation is shown to be asymptotically valid via a multivariate tail equivalence result we develop a likelihood based estimation procedure from this representation via a monte carlo expectation maximization algorithm which has been modified for tail estimation the method is demonstrated on simulated data and applied to air pollution measurements

semi supervised interpolation in an anticausal learning scenario according to a recently stated independence postulate the distribution pcause contains no information about the conditional peffect cause while peffect may contain information about pcause effect since semi supervised learning ssl attempts to exploit information from px to assist in predicting y from x it should only work in anticausal direction i e when y is the cause and x is the effect in causal direction when x is the cause and y the effect unlabelled x values should be useless to shed light on this asymmetry we study a deterministic causal relation y f x as recently assayed in information geometric causal inference igci within this model we discuss two options to formalize the independence of px and f as an orthogonality of vectors in appropriate inner product spaces we prove that unlabelled data help for the problem of interpolating a monotonically increasing function if and only if the orthogonality conditions are violated which we only expect for the anticausal direction here performance of ssl and its supervised baseline analogue is measured in terms of two different loss functions first the mean squared error and second the surprise in a bayesian prediction scenario

high dimensional multivariate probit analysis a computationally practical form of probit analysis for multiple response variables based on an assumed common factor model for the latent tolerances is proposed numerical integration over the factor space provides maximum likelihood estimation of the probit regression parameters and of the probabilities of response combinations under the model the procedure is applied to five variables from the pneumoconiosis field trial two variables of which were previously analyzed by ashford and sowden 1970 biometrics 26 535 546

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

estimation and inference on correlations between biomarkers with repeated measures and left censoring due to minimum detection levels statistical approaches for estimating and drawing inference on the correlation between two biomarkers that are repeatedly assessed over time and subject to left censoring because minimum detection levels are lacking we propose a linear mixed effects model and estimate the parameters with the monte carlo expectation maximization mcem method inferences regarding the model parameters and the correlation between the biomarkers are performed by applying louis s method and the delta method simulation studies were conducted to compare the proposed mcem method with existing methods including the maximum likelihood estimation method the multiple imputation method and two widely used ad hoc approaches replacing the censored values with the detection limit or with half of the detection limit the results show that the performance of the mcem with respect to relative bias and coverage probability for the 95 confidence interval is superior to the detection limit and half of the detection limit approaches and exceeds that of the multiple imputation method at medium to high levels of censoring and the standard error estimates from the mcem method are close to ideal the maximum likelihood estimation method can estimate the parameters accurately however a nonpositive definite information matrix can occur so that the variances are not estimable these five methods are illustrated with data from a longitudinal human immunodeficiency virus study to estimate and draw inference on the correlation between human immunodeficiency virus rna levels measured in plasma and in cervical secretions at multiple time points copyright 2012 john wiley sons ltd

empirical bayes analysis for systems of mixed models with linked autocorrelated random effects abstract empirical bayes concepts are implemented in a simultaneous analysis of a system of mixed linear models having linked and serially correlated random effects emphasis is placed on the estimation of the random effects and exploration of the relationships between them application is made to the investigation of several series of laboratory assay data that were observed during overlapping time intervals and were therefore subjected to common systematic errors or daily effects the motivation for this work was the need to investigate methods of adjustment for such daily effects and to estimate the degree to which concurrently run series are impacted in common attention is given to the construction of confidence intervals for daily effects tractable methods are proposed that yield approximately correct coverage for large samples although derived within a bayes empirical bayes framework these intervals are somewhat similar to intervals constructed by the method of kackar and harville implement

gamma frailty transformation models for multivariate survival times we propose a class of transformation models for multivariate failure times the class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time nonparametric maximum likelihood estimation is used for inference the maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal and their asymptotic variances attain the semiparametric efficiency bound simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes the method is illustrated using data from a cardiovascular study

variable selection with incomplete covariate data summary application of classical model selection methods such as akaike s information criterion aic becomes problematic when observations are missing in this article we propose some variations on the aic which are applicable to missing covariate problems the method is directly based on the expectation maximization em algorithm and is readily available for em based estimation methods without much additional computational efforts the missing data aic criteria are formally derived and shown to work in a simulation study and by application to data on diabetic retinopathy

use of historical controls in time adjusted trend tests for carcinogenicity we develop a method for incorporating historical control information into time adjusted tests for dose effects in carcinogenicity studies after discretizing the time scale we use a multinomial distribution to model the number of animals dying with tumor in each interval data from past studies are used to estimate the parameters characterizing the prior a score test derived from the resulting dirichlet multinomial generalizes the test of tarone 1982 biometrics 38 215 220 and reduces in the limit to the log rank test in the case of a diffuse prior the methodology is illustrated with data from a study of the fire retardant 2 2 bis bromomethyl 1 3 propanediol