the lagrangian relaxation method for solving integer programming problems this article originally appeared in management science january 1981 volume 27 number 1 pp 1 18 published by the institute of management sciences one of the most computationally useful ideas of the 1970s is the observation that many hard integer programming problems can be viewed as easy problems complicated by a relatively small set of side constraints dualizing the side constraints produces a lagrangian problem that is easy to solve and whose optimal value is a lower bound for minimization problems on the optimal value of the original problem the lagrangian problem can thus be used in place of a linear programming relaxation to provide bounds in a branch and bound algorithm this approach has led to dramatically improved algorithms for a number of important problems in the areas of routing location scheduling assignment and set covering this paper is a review of lagrangian relaxation based on what has been learned in the last decade

blind spectral unmixing based on sparse nonnegative matrix factorization nonnegative matrix factorization nmf is a widely used method for blind spectral unmixing su which aims at obtaining the endmembers and corresponding fractional abundances knowing only the collected mixing spectral data it is noted that the abundance may be sparse i e the endmembers may be with sparse distributions and sparse nmf tends to lead to a unique result so it is intuitive and meaningful to constrain nmf with sparseness for solving su however due to the abundance sum to one constraint in su the traditional sparseness measured by l0 l1 norm is not an effective constraint any more a novel measure termed as s measure of sparseness using higher order norms of the signal vector is proposed in this paper it features the physical significance by using the s measure constraint smc a gradient based sparse nmf algorithm termed as nmf smc is proposed for solving the su problem where the learning rate is adaptively selected and the endmembers and abundances are simultaneously estimated in the proposed nmf smc there is no pure index assumption and no need to know the exact sparseness degree of the abundance in prior yet it does not require the preprocessing of dimension reduction in which some useful information may be lost experiments based on synthetic mixtures and real world images collected by aviris and hydice sensors are performed to evaluate the validity of the proposed method

nonsmooth nonnegative matrix factorization nsnmf we propose a novel nonnegative matrix factorization model that aims at finding localized part based representations of nonnegative multivariate data items unlike the classical nonnegative matrix factorization nmf technique this new model denoted nonsmooth nonnegative matrix factorization nsnmf corresponds to the optimization of an unambiguous cost function designed to explicitly represent sparseness in the form of nonsmoothness which is controlled by a single parameter in general this method produces a set of basis and encoding vectors that are not only capable of representing the original data but they also extract highly focalized patterns which generally lend themselves to improved interpretability the properties of this new method are illustrated with several data sets comparisons to previously published methods show that the new nsnmf method has some advantages in keeping faithfulness to the data in the achieving a high degree of sparseness for both the estimated basis and the encoding vectors and in better interpretability of the factors

sample size determination for hierarchical longitudinal designs with differential attrition rates we consider the problem of sample size determination for three level mixed effects linear regression models for the analysis of clustered longitudinal data three level designs are used in many areas but in particular multicenter randomized longitudinal clinical trials in medical or health related research in this case level 1 represents measurement occasion level 2 represents subject and level 3 represents center the model we consider involves random effects of the time trends at both the subject level and the center level in the most common case we have two random effects constant and a single trend at both subject and center levels the approach presented here is general with respect to sampling proportions number of groups and attrition rates over time in addition we also develop a cost model as an aid in selecting the most parsimonious of several possible competing models i e different combinations of centers subjects within centers and measurement occasions we derive sample size requirements i e power characteristics for a test of treatment by time interaction s for designs based on either subject level or cluster level randomization the general methodology is illustrated using two characteristic examples

low rank matrix approximation with manifold regularization this paper proposes a new model of low rank matrix factorization that incorporates manifold regularization to the matrix factorization superior to the graph regularized nonnegative matrix factorization this new regularization model has globally optimal and closed form solutions a direct algorithm for data with small number of points and an alternate iterative algorithm with inexact inner iteration for large scale data are proposed to solve the new model a convergence analysis establishes the global convergence of the iterative algorithm the efficiency and precision of the algorithm are demonstrated numerically through applications to six real world datasets on clustering and classification performance comparison with existing algorithms shows the effectiveness of the proposed method for low rank factorization in general

mean squared error of estimation or prediction under a general linear model abstract the problem considered is that of predicting a linear combination of the fixed and random effects of a mixed effects linear model more generally the problem considered is that of predicting an unobservable random variable from a set of observable random variables the best linear unbiased predictor depends on parameters which generally are unknown various exact or approximate expressions are given for the mean squared error mse of the predictor obtained by replacing the unknown parameters with estimates several estimators of the mse are investigated

small sample adjustments in using the sandwich variance estimator in generalized estimating equations the generalized estimating equation gee approach is widely used in regression analyses with correlated response data under mild conditions the resulting regression coefficient estimator is consistent and asymptotically normal with its variance being consistently estimated by the so called sandwich estimator statistical inference is thus accomplished by using the asymptotic wald chi squared test however it has been noted in the literature that for small samples the sandwich estimator may not perform well and may lead to much inflated type i errors for the wald chi squared test here we propose using an approximate t or f test that takes account of the variability of the sandwich estimator the level of type i error of the proposed t or f test is guaranteed to be no larger than that of the wald chi squared test the satisfactory performance of the proposed new tests is confirmed in a simulation study our proposal also has some advantages when compared with other new approaches based on direct modifications of the sandwich estimator including the one that corrects the downward bias of the sandwich estimator in addition to hypothesis testing our result has a clear implication on constructing wald type confidence intervals or regions

conjoint optimization an exact branch and bound algorithm for the share of choice problem conjoint analysis is a statistical technique used to elicit partworth utilities for product attributes from consumers to aid in the evaluation of market potential for new products the objective of the share of choice problem a common approach to new product design is to find the design that maximizes the number of respondents for whom the new products utility exceeds a specific hurdle reservation utility we present an exact branch and bound algorithm to solve the share of choice problem our empirical results based on several large commercial data sets and simulated data from a controlled experiment suggest that the approach is useful for finding provably optimal solutions to realistically sized problems including cases where partworths contain estimation error

nenmf an optimal gradient method for nonnegative matrix factorization nonnegative matrix factorization nmf is a powerful matrix decomposition technique that approximates a nonnegative matrix by the product of two low rank nonnegative matrix factors it has been widely applied to signal processing computer vision and data mining traditional nmf solvers include the multiplicative update rule mur the projected gradient method pg the projected nonnegative least squares pnls and the active set method as however they suffer from one or some of the following three problems slow convergence rate numerical instability and nonconvergence in this paper we present a new efficient nenmf solver to simultaneously overcome the aforementioned problems it applies nesterov s optimal gradient method to alternatively optimize one factor with another fixed in particular at each iteration round the matrix factor is updated by using the pg method performed on a smartly chosen search point where the step size is determined by the lipschitz constant since nenmf does not use the time consuming line search and converges optimally at rate in optimizing each matrix factor it is superior to mur and pg in terms of efficiency as well as approximation accuracy compared to pnls and as that suffer from numerical instability problem in the worst case nenmf overcomes this deficiency in addition nenmf can be used to solve norm norm and manifold regularized nmf with the optimal convergence rate numerical experiments on both synthetic and real world datasets show the efficiency of nenmf for nmf and its variants comparing to representative nmf solvers extensive experiments on document clustering suggest the effectiveness of nenmf

some alternatives to asymptotic tests for the analysis of pharmacogenetic data using nonlinear mixed effects models nonlinear mixed effects models allow investigating individual differences in drug concentration profiles pharmacokinetics and responses pharmacogenetics focuses on the genetic component of this variability two tests often used to detect a gene effect on a pharmacokinetic parameter are 1 the wald test assessing whether estimates for the gene effect are significantly different from 0 and 2 the likelihood ratio test comparing models with and without the genetic effect because those asymptotic tests show inflated type i error on small sample size and or with unevenly distributed genotypes we develop two alternatives and evaluate them by means of a simulation study first we assess the performance of the permutation test using the wald and the likelihood ratio statistics second for the wald test we propose the use of the f distribution with four different values for the denominator degrees of freedom we also explore the influence of the estimation algorithm using both the first order conditional estimation with interaction linearization based algorithm and the stochastic approximation expectation maximization algorithm we apply these methods to the analysis of the pharmacogenetics of indinavir in hiv patients recruited in the cophar2 anrs 111 trial results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden one of the four f distribution based approaches provides a correct type i error estimate for the wald test and should be further investigated

cross sectional versus longitudinal designs for function estimation with an application to cerebral cortex development motivated by studies of the development of the human cerebral cortex we consider the estimation of a mean growth trajectory and the relative merits of cross sectional and longitudinal data for that task we define a class of relative efficiencies that compare function estimates in terms of aggregate variance of a parametric function estimate these generalize the classical design effect for estimating a scalar with cross sectional versus longitudinal data and are shown to be bounded above by it in certain cases turning to nonparametric function estimation we find that longitudinal fits may tend to have higher aggregate variance than cross sectional ones but that this may occur because the former have higher effective degrees of freedom reflecting greater sensitivity to subtle features of the estimand these ideas are illustrated with cortical thickness data from a longitudinal neuroimaging study

improved power in crossover designs through linear combinations of baselines in a crossover design in the absence of any carryover effect including period specific baselines as covariates in an analysis of covariance is known to increase the precision of the estimated treatment effect the extent of the efficiency gain is a function of the joint covariance structure of the baselines and post treatment responses as well as the metric used to incorporate the baselines into the analysis here we show how the underlying covariance structure can be leveraged to find an optimal linear combination of baselines so as to minimize the theoretical variance of the analysis of covariance based estimated treatment effect our work is relevant to complete designs with up to four periods specifically the 2 2 3 3 and 4 4 given that the optimal linear combination of baselines is a function of the covariance structure which in practice is unknown we propose an adaptive method here the covariance structure is chosen using information criterion to guide the choice of the linear combination of baselines evaluation of the proposed approach suggests that the type i error rate is maintained moreover relative to previously published methods sizeable gains in power are possible with this method results from a 2 2 trial exploring renal function and a 3 3 trial with heart rate as the outcome are used to illustrate the methods copyright 2016 john wiley sons ltd

some bayesian and non bayesian procedures for the analysis of comparative experiments and for small area estimation computational aspects frequentist properties and relationships abstract the estimation of a treatment contrast from experimental data and the estimation of a small area mean are special cases of the prediction of the realization of a linear combination of fixed and random effects in a possibly unbalanced two part mixed linear model in this article a bayesian approach to point and interval prediction is presented and its computational requirements are examined differences between the bayesian approach and the traditional classical approach are discussed in general terms and in addition in terms of two examples taken from the literature 1 the comparison of drug formulations in a bioavailability trial westlake and 2 the estimation of corn crop areas using satellite data battese harter and fuller some deficiencies in the classical approach are pointed out and the bayesian approach is considered from a frequentist perspective it is shown via a monte carlo study that for certain noninformative choices of the prior distribution the frequentist prop

a heuristic approach to product design a dynamic programming heuristic is described to find approximate solutions to the problem of identifying a new multi attribute product profile associated with the highest share of choices in a competitive market the input data consist of idiosyncratic multi attribute preference functions estimated using conjoint or hybrid conjoint analysis an individual is assumed to choose a new product profile if he she associates a higher utility with it than with a status quo alternative importance weights are assigned to individuals to account for differences in their purchase and or usage rates and the performance of a new product profile is evaluated after taking into account its cannibalization of a seller s existing brands in a simulation with real sized problems the proposed heuristic strictly dominates an alternative lagrangian relaxation heuristic in terms of both computational time and approximation of the optimal solution across 192 simulated problems the dynamic programming heuristic identifies product profiles whose share of choices on average are 98 2 of the share of choices of the optimal product profile suggesting that it closely approximates the optimal solution

on the analysis of very small samples of gaussian repeated measurements an alternative approach the analysis of very small samples of gaussian repeated measurements can be challenging first due to a very small number of independent subjects contributing outcomes over time statistical power can be quite small second nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size however available statistical strategies that ensure valid statistical inference may lack power whereas more powerful methods may have the potential for inflated test sizes therefore we explore an alternative approach to the analysis of very small samples of gaussian repeated measurements with the goal of maintaining valid inference while also improving statistical power relative to other valid methods this approach uses generalized estimating equations with a bias corrected empirical covariance matrix that accounts for all small sample aspects of nuisance correlation parameter estimation in order to maintain valid inference furthermore the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power in our study we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation this method can improve power relative to existing methods that yield valid inference copyright 2017 john wiley sons ltd

online blind source separation using incremental nonnegative matrix factorization with volume constraint online blind source separation bss is proposed to overcome the high computational cost problem which limits the practical applications of traditional batch bss algorithms however the existing online bss methods are mainly used to separate independent or uncorrelated sources recently nonnegative matrix factorization nmf shows great potential to separate the correlative sources where some constraints are often imposed to overcome the non uniqueness of the factorization in this paper an incremental nmf with volume constraint is derived and utilized for solving online bss the volume constraint to the mixing matrix enhances the identifiability of the sources while the incremental learning mode reduces the computational cost the proposed method takes advantage of the natural gradient based multiplication updating rule and it performs especially well in the recovery of dependent sources simulations in bss for dual energy x ray images online encrypted speech signals and high correlative face images show the validity of the proposed method

exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification in this paper two supervised methods for enhancing the classification accuracy of the nonnegative matrix factorization nmf algorithm are presented the idea is to extend the nmf algorithm in order to extract features that enforce not only the spatial locality but also the separability between classes in a discriminant manner the first method employs discriminant analysis in the features derived from nmf in this way a two phase discriminant feature extraction procedure is implemented namely nmf plus linear discriminant analysis lda the second method incorporates the discriminant constraints inside the nmf decomposition thus a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived the introduced methods have been applied to the problem of frontal face verification using the well known xm2vts database both methods greatly enhance the performance of nmf for frontal face verification

convex and semi nonnegative matrix factorizations we present several new variations on the theme of nonnegative matrix factorization nmf considering factorizations of the form x fgt we focus on algorithms in which g is restricted to containing nonnegative entries but allowing the data matrix x to have mixed signs thus extending the applicable range of nmf methods we also consider algorithms in which the basis vectors of f are constrained to be convex combinations of the data points this is used for a kernel extension of nmf we provide algorithms for computing these new factorizations and we provide supporting theoretical analysis we also analyze the relationships between our algorithms and clustering algorithms and consider the implications for sparseness of solutions finally we present experimental results that explore the properties of these new methods

tests for the analysis of variance of crossover designs with correlated errors the usual analysis of variance based on ordinary least squares ols may be inappropriate to analyze the crossover designs because of correlations within subjects arising from the repeated measurements the tests used with ols are compared with three alternative tests that take into account the structure of the covariance matrix for testing the treatment and carryover effects under the assumption of multivariate normality a modified f test approximation and a test derived from a pearson curve fit are shown to give adequate control over type i error compared to the ols tests and to tests following an empirical generalized least squares analysis

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

d optimal design of split split plot experiments in industrial experimentation there is growing interest in studies that span more than one processing step convenience often dictates restrictions in randomization in passing from one processing step to another when the study encompasses three processing steps this leads to split split plot designs we provide an algorithm for computing d optimal split split plot designs and several illustrative examples

a general strategy for analyzing data from split plot and multistratum experimental designs increasingly industrial experiments use multistratum designs such as split plot and strip plot designs often these experiments span more than one processing stage the challenge is to identify an appropriate multistratum design along with an appropriate statistical model in this article we introduce hasse diagrams in the response surface context as a tool to visualize the unit structure of the experimental design the randomization and sampling approaches used the stratum in which each experimental factor is applied and the degrees of freedom available in each stratum to estimate main effects interactions and variance components we illustrate their use on several responses measured in a large study of the adhesion properties of coatings to polypropylene we discuss quantitative binary and ordered categorical responses for designs ranging from a simple split plot to a strip plot that involves repeated measurements of the response the datasets discussed in this article are available online a

optimizing product line designs efficient methods and comparisons we take advantage of recent advances in optimization methods and computer hardware to identify globally optimal solutions of product line design problems that are too large for complete enumeration we then use this guarantee of global optimality to benchmark the performance of more practical heuristic methods we use two sources of data 1 a conjoint study previously conducted for a real product line design problem and 2 simulated problems of various sizes for both data sources several of the heuristic methods consistently find optimal or near optimal solutions including simulated annealing divide and conquer product swapping and genetic algorithms

optimal product design using conjoint analysis computational complexity and algorithms abstract the problem of maximizing the share of a new product introduced in a competitive market is shown to be np hard a directed graph representation of the problem is used to construct shortest path and dynamic programming heuristics both heuristics are shown to have arbitrarily bad worst case bounds computational experience with real sized problems is reported both heuristics identify near optimal solutions for the simulated problems the dynamic programming heuristic performing better than the shortest path heuristic

non negative matrix factorization revisited uniqueness and algorithm for symmetric decomposition non negative matrix factorization nmf has found numerous applications due to its ability to provide interpretable decompositions perhaps surprisingly existing results regarding its uniqueness properties are rather limited and there is much room for improvement in terms of algorithms as well uniqueness aspects of nmf are revisited here from a geometrical point of view both symmetric and asymmetric nmf are considered the former being tantamount to element wise non negative square root factorization of positive semidefinite matrices new uniqueness results are derived e g it is shown that a sufficient condition for uniqueness is that the conic hull of the latent factors is a superset of a particular second order cone checking this condition is shown to be np complete yet this and other results offer insights on the role of latent sparsity in this context on the computational side a new algorithm for symmetric nmf is proposed which is very different from existing ones it alternates between procrustes rotation and projection onto the non negative orthant to find a non negative matrix close to the span of the dominant subspace simulation results show promising performance with respect to the state of art finally the new algorithm is applied to a clustering problem for co authorship data yielding meaningful and interpretable results

symmetric nonnegative matrix factorization algorithms and applications to probabilistic clustering nonnegative matrix factorization nmf is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents this paper focuses on symmetric nmf snmf which is a special case of nmf decomposition three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem first by minimizing the euclidean distance a multiplicative update algorithm is proposed and its convergence under mild conditions is proved based on it we further propose another two fast parallel methods snmf and snmf algorithms all of them are easy to implement these algorithms are applied to probabilistic clustering we demonstrate their effectiveness for facial image clustering document categorization and pattern clustering in gene expression

the analysis of very small samples of repeated measurements ii a modified box correction there is a need for appropriate methods for the analysis of very small samples of continuous repeated measurements a key feature of such analyses is the role played by the covariance matrix of the repeated observations when subjects are few it can be difficult to assess the fit of parsimonious structures for this matrix while the use of an unstructured form may lead to a serious lack of power the kenward roger adjustment is now widely adopted as a means of providing an appropriate inferences in small samples but does not perform adequately in very small samples adjusted tests based on the empirical sandwich estimator can be constructed that have good nominal properties but are seriously underpowered further when such data are incomplete or unbalanced or non saturated mean models are used exact distributional results do not exist that justify analyses with any sample size in this paper a modification of box s correction applied to a linear model based f statistic is developed for such small sample settings and is shown to have both the required nominal properties and acceptable power across a range of settings for repeated measurements

random effects models for longitudinal data models for the analysis of longitudinal data must recognize the relationship between serial observations on the same unit multivariate models with general covariance structure are often difficult to apply to highly unbalanced data whereas two stage random effects models can be used easily in two stage models the probability distributions for the response vectors of different individuals belong to a single family but some random effects parameters vary across individuals with a distribution specified at the second stage a general family of models is discussed which includes both growth models and repeated measures models as special cases a unified approach to fitting these models based on a combination of empirical bayes and maximum likelihood estimation of model parameters and using the em algorithm is discussed two examples are taken from a current epidemiological study of the health effects of air pollution

fixed effects random effects and gee what are the differences for analyses of longitudinal repeated measures data statistical methods include the random effects model fixed effects model and the method of generalized estimating equations we examine the assumptions that underlie these approaches to assessing covariate effects on the mean of a continuous dichotomous or count outcome access to statistical software to implement these models has led to widespread application in numerous disciplines however careful consideration should be paid to their critical assumptions to ascertain which model might be appropriate in a given setting to illustrate similarities and differences that might exist in empirical results we use a study that assessed depressive symptoms in low income pregnant women using a structured instrument with up to five assessments that spanned the pre natal and post natal periods understanding the conceptual differences between the methods is important in their proper application even though empirically they might not differ substantively the choice of model in specific applications would depend on the relevant questions being addressed which in turn informs the type of design and data collection that would be relevant

a branch and price approach to the share of choice product line design problem we develop a branch and price algorithm for constructing an optimal product line using partworth estimates from choice based conjoint analysis the algorithm determines the specific attribute levels for each multiattribute product in a set of products to maximize the resulting product line s share of choice i e the number of respondents for whom at least one new product s utility exceeds the respondent s reservation utility computational results using large commercial and simulated data sets demonstrate that the algorithm can identify provably optimal robust solutions to realistically sized problems

a note on non parametric ancova for covariate adjustment in randomized clinical trials by emmanuel lesaffre and stephen senn statistics in medicine 2003 22 3583 3596

improved small sample inference in the mixed linear model bartlett correction and adjusted likelihood summary the mixed linear model is a popular method for analysing unbalanced repeated measurement data the classical statistical tests for parameters in this model are based on asymptotic theory that is unreliable in the small samples that are often encountered in practice for testing a given fixed effect parameter with a small sample we develop and investigate refined likelihood ratio lr tests the refinements considered are the bartlett correction and use of the cox reid adjusted likelihood these are examined separately and in combination we illustrate the various lr tests on an actual data set and compare them in two simulation studies the conventional lr test yields type i error rates that are higher than nominal the adjusted lr test yields rates that are lower than nominal with absolute accuracy similar to that of the conventional lr test in the first simulation study and better in the second the bartlett correction substantially improves the accuracy of the type i error rates with either the conventional or the adjusted lr test in many cases error rates that are very close to nominal are achieved with the refined methods

mixed response surface models with heterogeneous within block error variances the experimental error variance in a response surface model with a block effect has traditionally been assumed to be constant in some experimental situations however this variance may be different for the different blocks that compose the associated design this article discusses the analysis of a response surface model with a random block effect and heterogeneous error variances among the blocks the model includes interactions between the fixed polynomial effects and the block effect procedures for estimating and testing the fixed effects and the random effects in the model are described in particular anova based procedures for testing equality of the error variances and testing the random effects are introduced

sample size calculation for stepped wedge and other longitudinal cluster randomised trials the sample size required for a cluster randomised trial is inflated compared with an individually randomised trial because outcomes of participants from the same cluster are correlated sample size calculations for longitudinal cluster randomised trials including stepped wedge trials need to take account of at least two levels of clustering the clusters themselves and times within clusters we derive formulae for sample size for repeated cross section and closed cohort cluster randomised trials with normally distributed outcome measures under a multilevel model allowing for variation between clusters and between times within clusters our formulae agree with those previously described for special cases such as crossover and analysis of covariance designs although simulation suggests that the formulae could underestimate required sample size when the number of clusters is small whether using a formula or simulation a sample size calculation requires estimates of nuisance parameters which in our model include the intracluster correlation cluster autocorrelation and individual autocorrelation a cluster autocorrelation less than 1 reflects a situation where individuals sampled from the same cluster at different times have less correlated outcomes than individuals sampled from the same cluster at the same time nuisance parameters could be estimated from time series obtained in similarly clustered settings with the same outcome measure using analysis of variance to estimate variance components copyright 2016 john wiley sons ltd

robust structured nonnegative matrix factorization for image representation dimensionality reduction has attracted increasing attention because high dimensional data have arisen naturally in numerous domains in recent years as one popular dimensionality reduction method nonnegative matrix factorization nmf whose goal is to learn parts based representations has been widely studied and applied to various applications in contrast to the previous approaches this paper proposes a novel semisupervised nmf learning framework called robust structured nmf that learns a robust discriminative representation by leveraging the block diagonal structure and the ell 2 p norm especially when 0 loss function specifically the problems of noise and outliers are well addressed by the ell 2 p norm 0 loss function while the discriminative representations of both the labeled and unlabeled data are simultaneously learned by explicitly exploring the block diagonal structure the proposed problem is formulated as an optimization problem with a well defined objective function solved by the proposed iterative algorithm the convergence of the proposed optimization algorithm is analyzed both theoretically and empirically in addition we also discuss the relationships between the proposed method and some previous methods extensive experiments on both the synthetic and real world data sets are conducted and the experimental results demonstrate the effectiveness of the proposed method in comparison to the state of the art methods

constrained nonnegative matrix factorization for image representation nonnegative matrix factorization nmf is a popular technique for finding parts based linear representations of nonnegative data it has been successfully applied in a wide range of applications such as pattern recognition information retrieval and computer vision however nmf is essentially an unsupervised method and cannot make use of label information in this paper we propose a novel semi supervised matrix decomposition method called constrained nonnegative matrix factorization cnmf which incorporates the label information as additional constraints specifically we show how explicitly combining label information improves the discriminating power of the resulting matrix decomposition we explore the proposed cnmf method with two cost function formulations and provide the corresponding update solutions for the optimization problems empirical experiments demonstrate the effectiveness of our novel algorithm in comparison to the state of the art approaches through a set of evaluations based on real world applications

multilevel model prediction multilevel models are proven tools in social research for modeling complex hierarchical systems in multilevel modeling statistical inference is based largely on quantification of random variables this paper distinguishes among three types of random variables in multilevel modeling model disturbances random coefficients and future response outcomes and provides a unified procedure for predicting them these predictors are best linear unbiased and are commonly known via the acronym blup they are optimal in the sense of minimizing mean square error and are bayesian under a diffuse prior

small sample gee estimation of regression parameters for longitudinal data longitudinal clustered response data arise in many bio statistical applications which in general cannot be assumed to be independent generalized estimating equation gee is a widely used method to estimate marginal regression parameters for correlated responses the advantage of the gee is that the estimates of the regression parameters are asymptotically unbiased even if the correlation structure is misspecified although their small sample properties are not known in this paper two bias adjusted gee estimators of the regression parameters in longitudinal data are obtained when the number of subjects is small one is based on a bias correction and the other is based on a bias reduction simulations show that the performances of both the bias corrected methods are similar in terms of bias efficiency coverage probability average coverage length impact of misspecification of correlation structure and impact of cluster size on bias correction both these methods show superior properties over the gee estimates for small samples further analysis of data involving a small number of subjects also shows improvement in bias mse standard error and length of the confidence interval of the estimates by the two bias adjusted methods over the gee estimates for small to moderate sample sizes n 50 either of the bias corrected methods geebc and geebr can be used however the method geebc should be preferred over geebr as the former is computationally easier for large sample sizes the gee method can be used copyright 2014 john wiley sons ltd

recovery of inter block information in cross over trials for cross over designs we show that one can recover information on direct and or residual treatment effects from an inter block patients as blocks analysis as is done in an incomplete block design 1 by combining the intra and inter block estimates we obtain the generalized least squares estimate in analysing cross over trials we recommended this approach provided the between patient variance component can be estimated efficiently

online nonnegative matrix factorization with robust stochastic approximation nonnegative matrix factorization nmf has become a popular dimension reduction method and has been widely applied to image processing and pattern recognition problems however conventional nmf learning methods require the entire dataset to reside in the memory and thus cannot be applied to large scale or streaming datasets in this paper we propose an efficient online rsa nmf algorithm or nmf that learns nmf in an incremental fashion and thus solves this problem in particular or nmf receives one sample or a chunk of samples per step and updates the bases via robust stochastic approximation benefitting from the smartly chosen learning rate and averaging technique or nmf converges at the rate of in each update of the bases furthermore we prove that or nmf almost surely converges to a local optimal solution by using the quasi martingale by using a buffering strategy we keep both the time and space complexities of one step of the or nmf constant and make or nmf suitable for large scale or streaming datasets preliminary experimental results on real world datasets show that or nmf outperforms the existing online nmf onmf algorithms in terms of efficiency experimental results of face recognition and image annotation on public datasets confirm the effectiveness of or nmf compared with the existing onmf algorithms

small sample inference for fixed effects from restricted maximum likelihood restricted maximum likelihood reml is now well established as a method for estimating the parameters of the general gaussian linear model with a structured covariance matrix in particular for mixed linear models conventionally estimates of precision and inference for fixed effects are based on their asymptotic distribution which is known to be inadequate for some small sample problems in this paper we present a scaled wald statistic together with an f approximation to its sampling distribution that is shown to perform well in a range of small sample settings the statistic uses an adjusted estimator of the covariance matrix that has reduced small sample bias this approach has the advantage that it reproduces both the statistics and f distributions in those settings where the latter is exact namely for hotelling t2 type statistics and for analysis of variance f ratios the performance of the modified statistics is assessed through simulation studies of four different reml analyses and the methods are illustrated using three examples

a noniterative sample size procedure for tests based on t distributions a noniterative sample size procedure is proposed for a general hypothesis test based on the t distribution by modifying and extending guenther s approach for the one sample and two sample t tests the generalized procedure is employed to determine the sample size for treatment comparisons using the analysis of covariance ancova and the mixed effects model for repeated measures in randomized clinical trials the sample size is calculated by adding a few simple correction terms to the sample size from the normal approximation to account for the nonnormality of the t statistic and lower order variance terms which are functions of the covariates in the model but it does not require specifying the covariate distribution the noniterative procedure is suitable for superiority tests noninferiority tests and a special case of the tests for equivalence or bioequivalence and generally yields the exact or nearly exact sample size estimate after rounding to an integer the method for calculating the exact power of the two sample t test with unequal variance in superiority trials is extended to equivalence trials we also derive accurate power formulae for ancova and mixed effects model for repeated measures and the formula for ancova is exact for normally distributed covariates numerical examples demonstrate the accuracy of the proposed methods particularly in small samples

variational regularized 2 d nonnegative matrix factorization a novel approach for adaptive regularization of 2 d nonnegative matrix factorization is presented the proposed matrix factorization is developed under the framework of maximum a posteriori probability and is adaptively fine tuned using the variational approach the method enables 1 a generalized criterion for variable sparseness to be imposed onto the solution and 2 prior information to be explicitly incorporated into the basis features the method is computationally efficient and has been demonstrated on two applications that is extracting features from image and separating single channel source mixture in addition it is shown that the basis features of an information bearing matrix can be extracted more efficiently using the proposed regularized priors experimental tests have been rigorously conducted to verify the efficacy of the proposed method

adaptive method for nonsmooth nonnegative matrix factorization nonnegative matrix factorization nmf is an emerging tool for meaningful low rank matrix representation in nmf explicit constraints are usually required such that nmf generates desired products or factorizations especially when the products have significant sparseness features it is known that the ability of nmf in learning sparse representation can be improved by embedding a smoothness factor between the products motivated by this result we propose an adaptive nonsmooth nmf ans nmf method in this paper in our method the embedded factor is obtained by using a data related approach so it matches well with the underlying products implying a superior faithfulness of the representations besides due to the usage of an adaptive selection scheme to this factor the sparseness of the products can be separately constrained leading to wider applicability and interpretability furthermore since the adaptive selection scheme is processed through solving a series of typical linear programming problems it can be easily implemented simulations using computer generated data and real world data show the advantages of the proposed ans nmf method over the state of the art methods

optimal new product positioning a genetic algorithm approach abstract identifying an optimal positioning strategy for new products is a critical and difficult strategic decision in this research we develop a genetic algorithm based procedure called ga search that identifies optimal new product positions in two simulation comparisons and an empirical study we compare the results from ga search to those obtained from the best currently available algorithm prodsrch we find that ga search performs better regardless of the number of ideal points existing products number of attributes or choice set size furthermore ga search can account for choice set size heterogeneity results show that ga search outperformed the best current algorithm when choice set size varied at the individual level an important source of consumer heterogeneity that has been ignored in current algorithms formulated to solve this optimization problem

row column α designs in row column designs the experimental units are grouped in two directions i e two blocking factors are used with one factor representing the rows of the design and the other factor representing columns for instance in an agricultural experiment the rows and columns of a design might represent different times and method of application of fertilizers in a preference testing experiment the columns might represent different subjects and the rows the order in which different products are presented to the subjects in an insulin response experiment the rows columns and treatments may represent respectively individual animals date of injection and levels of insulin in all these experiments it is hoped that there will be a gain in the accuracy of estimating treatment comparisons resulting from eliminating the effects of the row and column factors

a fast algorithm for nonnegative matrix factorization and its convergence nonnegative matrix factorization nmf has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the nmf however for the common nmf approach of minimizing the euclidean distance between approximate and true values the convergence of multiplicative update algorithms has not been well resolved this paper first discusses the convergence of existing multiplicative update algorithms we then propose a new multiplicative update algorithm for minimizing the euclidean distance between approximate and true values based on the optimization principle and the auxiliary function method we prove that our new algorithm not only converges to a stationary point but also does faster than existing ones to verify our theoretical results the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods

the influence of design on validity and efficiency of neighbour methods summary neighbour methods have often been shown to be apparently more efficient than analysis of variance for the analysis of field experiments this means that the precision of the analysis estimated by the statistical method itself is smaller for the neighbour method than for the classical one this comparison is meaningful only if the analysis is valid in the sense that it estimates its own precision without bias although precise validity properties are known for the analysis of variance of randomized designs no analogous properties are known for neighbour analyses in this paper we investigate the validity and efficiency of some neighbour methods and their relations with the design first we give precise definitions of the desirable properties of the combination of design including randomization and method of analysis then we report on a simulation study we show that neighbour methods are often valid or conservative with higher efficiency than classical ones to better ensure these properties we advocate the use of randomized neighbour designs and corrections to degrees of freedom finally we discuss how these results can be used to assess neighbour methods for routine trials

a powerful and robust test statistic for randomization inference in group randomized trials with matched pairs of groups summary for group randomized trials randomization inference based on rank statistics provides robust exact inference against nonnormal distributions however in a matched pair design the currently available rank based statistics lose significant power compared to normal linear mixed model lmm test statistics when the lmm is true in this article we investigate and develop an optimal test statistic over all statistics in the form of the weighted sum of signed mann whitney wilcoxon statistics under certain assumptions this test is almost as powerful as the lmm even when the lmm is true but it is much more powerful for heavy tailed distributions a simulation study is conducted to examine the power

on efficiency of constrained longitudinal data analysis versus longitudinal analysis of covariance in randomized clinical trials measurements are often collected on each subject at a baseline visit and several post randomization time points the longitudinal analysis of covariance in which the postbaseline values form the response vector and the baseline value is treated as a covariate can be used to evaluate the treatment differences at the postbaseline time points liang and zeger 2000 sankhy the indian journal of statistics series b 62 134 148 propose a constrained longitudinal data analysis in which the baseline value is included in the response vector together with the postbaseline values and a constraint of a common baseline mean across treatment groups is imposed on the model as a result of randomization if the baseline value is subject to missingness the constrained longitudinal data analysis is shown to be more efficient for estimating the treatment differences at postbaseline time points than the longitudinal analysis of covariance the efficiency gain increases with the number of subjects missing baseline and the number of subjects missing all postbaseline values and for the pre post design decreases with the absolute correlation between baseline and postbaseline values

individual participant data meta analysis of continuous outcomes a comparison of approaches for specifying and estimating one stage models one stage individual participant data meta analysis models should account for within trial clustering but it is currently debated how to do this for continuous outcomes modeled using a linear regression framework two competing approaches are a stratified intercept or a random intercept the stratified approach involves estimating a separate intercept term for each trial whereas the random intercept approach assumes that trial intercepts are drawn from a normal distribution here through an extensive simulation study for continuous outcomes we evaluate the impact of using the stratified and random intercept approaches on statistical properties of the summary treatment effect estimate further aims are to compare i competing estimation options for the one stage models including maximum likelihood and restricted maximum likelihood and ii competing options for deriving confidence intervals ci for the summary treatment effect including the standard normal based 95 ci and more conservative approaches of kenward roger and satterthwaite which inflate cis to account for uncertainty in variance estimates the findings reveal that for an individual participant data meta analysis of randomized trials with a 1 1 treatment control allocation ratio and heterogeneity in the treatment effect i bias and coverage of the summary treatment effect estimate are very similar when using stratified or random intercept models with restricted maximum likelihood and thus either approach could be taken in practice ii cis are generally best derived using either a kenward roger or satterthwaite correction although occasionally overly conservative and iii if maximum likelihood is required a random intercept performs better than a stratified intercept model an illustrative example is provided

a covariance estimator for gee with improved small sample properties summary in this paper we propose an alternative covariance estimator to the robust covariance estimator of generalized estimating equations gee hypothesis tests using the robust covariance estimator can have inflated size when the number of independent clusters is small resampling methods such as the jackknife and bootstrap have been suggested for covariance estimation when the number of clusters is small a drawback of the resampling methods when the response is binary is that the methods can break down when the number of subjects is small due to zero or near zero cell counts caused by resampling we propose a bias corrected covariance estimator that avoids this problem in a small simulation study we compare the bias corrected covariance estimator to the robust and jackknife covariance estimators for binary responses for situations involving 10 40 subjects with equal and unequal cluster sizes of 16 64 observations the bias corrected covariance estimator gave tests with sizes close to the nominal level even when the number of subjects was 10 and cluster sizes were unequal whereas the robust and jackknife covariance estimators gave tests with sizes that could be 2 3 times the nominal level the methods are illustrated using data from a randomized clinical trial on treatment for bone loss in subjects with periodontal disease

parameter estimation and inference in the linear mixed model the paper reviews the linear mixed model with a focus on parameter estimation and inference parameter estimation for the different components of the model are reviewed with an emphasis on variance parameter estimation inferential procedures for the fixed effects random effects or a combination of both fixed and random effects are also discussed

fast nonnegative matrix tensor factorization based on low rank approximation nonnegative matrix factorization nmf algorithms often suffer from slow convergence speed due to the nonnegativity constraints especially for large scale problems low rank approximation methods such as principle component analysis pca are widely used in matrix factorizations to suppress noise reduce computational complexity and memory requirements however they cannot be applied to nmf directly so far as they result in factors with mixed signs in this paper low rank approximation is introduced to nmf named lranmf which is not only able to reduce the computational complexity of nmf algorithms significantly but also suppress bipolar noise in fact the new update rules are typically about times faster than traditional ones of nmf here is the number of observations and is the low rank of latent factors therefore lranmf is particularly efficient in the case where which is the general case in nmf the proposed update rules can also be incorporated into most existing nmf algorithms straightforwardly as long as they are based on euclidean distance then the concept of lranmf is generalized to the tensor field to perform a fast sequential nonnegative tucker decomposition ntd by applying the proposed methods the practicability of nmf ntd is significantly improved simulations on synthetic and real data show the validity and efficiency of the proposed approaches

the analysis of very small samples of repeated measurements i an adjusted sandwich estimator the statistical analysis of repeated measures or longitudinal data always requires the accommodation of the covariance structure of the repeated measurements at some stage in the analysis the general linear mixed model is often used for such analyses and allows for the specification of both a mean model and a covariance structure often the covariance structure itself is not of direct interest but only a means to producing valid inferences about the response existing methods of analysis are often inadequate where the sample size is small more precisely statistical measures of goodness of fit are not necessarily the right measure of the appropriateness of a covariance structure and inferences based on conventional wald type procedures do not approximate sufficiently well their nominal properties when data are unbalanced or incomplete this is shown to be the case when adopting the kenward roger adjustment where the sample size is very small a generalization of an approach to wald tests using a bias adjusted empirical sandwich estimator for the covariance matrix of the fixed effects parameters from generalized estimating equations is developed for gaussian repeated measurements this is shown to attain the correct test size but has very low power copyright 2010 john wiley sons ltd

nonnegative blind source separation by sparse component analysis based on determinant measure the problem of nonnegative blind source separation nbss is addressed in this paper where both the sources and the mixing matrix are nonnegative because many real world signals are sparse we deal with nbss by sparse component analysis first a determinant based sparseness measure named d measure is introduced to gauge the temporal and spatial sparseness of signals based on this measure a new nbss model is derived and an iterative sparseness maximization ism approach is proposed to solve this model in the ism approach the nbss problem can be cast into row to row optimizations with respect to the unmixing matrix and then the quadratic programming qp technique is used to optimize each row furthermore we analyze the source identifiability and the computational complexity of the proposed ism qp method the new method requires relatively weak conditions on the sources and the mixing matrix has high computational efficiency and is easy to implement simulation results demonstrate the effectiveness of our method

detecting the number of clusters in n way probabilistic clustering recently there has been a growing interest in multiway probabilistic clustering some efficient algorithms have been developed for this problem however not much attention has been paid on how to detect the number of clusters for the general n way clustering n 2 to fill this gap this problem is investigated based on n way algebraic theory in this paper a simple yet efficient detection method is proposed by eigenvalue decomposition evd which is easy to implement we justify this method in addition its effectiveness is demonstrated by the experiments on both simulated and real world data sets

nested partitions method for global optimization we propose a new randomized method for solving global optimization problems this method the nested partitions np method systematically partitions the feasible region and concentrates the search in regions that are the most promising the most promising region is selected in each iteration based on information obtained from random sampling of the entire feasible region and local search the method hence combines global and local search we first develop the method for discrete problems and then show that the method can be extended to continuous global optimization the method is shown to converge with probability one to a global optimum in finite time in addition we provide bounds on the expected number of iterations required for convergence and we suggest two stopping criteria numerical examples are also presented to demonstrate the effectiveness of the method

multiplicative update rules for concurrent nonnegative matrix factorization and maximum margin classification the state of the art classification methods which employ nonnegative matrix factorization nmf employ two consecutive independent steps the first one performs data transformation dimensionality reduction and the second one classifies the transformed data using classification methods such as nearest neighbor centroid or support vector machines svms in the following we focus on using nmf factorization followed by svm classification typically the parameters of these two steps e g the nmf bases coefficients and the support vectors are optimized independently thus leading to suboptimal classification performance in this paper we merge these two steps into one by incorporating maximum margin classification constraints into the standard nmf optimization the notion behind the proposed framework is to perform nmf while ensuring that the margin between the projected data of the two classes is maximal the concurrent nmf factorization and support vector optimization are performed through a set of multiplicative update rules in the same context the maximum margin classification constraints are imposed on the nmf problem with additional discriminant constraints and respective multiplicative update rules are extracted the impact of the maximum margin classification constraints on the nmf factorization problem is addressed in section vi experimental results in several databases indicate that the incorporation of the maximum margin classification constraints into the nmf and discriminant nmf objective functions improves the accuracy of the classification

dynamic bundle methods lagrangian relaxation is a popular technique to solve difficult optimization problems however the applicability of this technique depends on having a relatively low number of hard constraints to dualize when there are many hard constraints it may be preferable to relax them dynamically according to some rule depending on which multipliers are active from the dual point of view this approach yields multipliers with varying dimensions and a dual objective function that changes along iterations we discuss how to apply a bundle methodology to solve this kind of dual problems our framework covers many separation procedures to generate inequalities that can be found in the literature including but not limited to the most violated inequality we analyze the resulting dynamic bundle method giving a positive answer for its primal dual convergence properties and under suitable conditions show finite termination for polyhedral problems

average information reml an efficient algorithm for variance parameter estimation in linear mixed models a strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by restricted maximum likelihood reml in the mixed linear model three applications are described the motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1 071 experiments representing 10 years and 60 locations in new south wales we also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments

multiple imputation approaches for the analysis of dichotomized responses in longitudinal studies with missing data often a binary variable is generated by dichotomizing an underlying continuous variable measured at a specific time point according to a prespecified threshold value in the event that the underlying continuous measurements are from a longitudinal study one can use the repeated measures model to impute missing data on responder status as a result of subject dropout and apply the logistic regression model on the observed or otherwise imputed responder status standard bayesian multiple imputation techniques rubin 1987 in multiple imputation for nonresponse in surveys that draw the parameters for the imputation model from the posterior distribution and construct the variance of parameter estimates for the analysis model as a combination of within and between imputation variances are found to be conservative the frequentist multiple imputation approach that fixes the parameters for the imputation model at the maximum likelihood estimates and construct the variance of parameter estimates for the analysis model using the results of robins and wang 2000 biometrika 87 113 124 is shown to be more efficient we propose to apply kenward and roger 1997 biometrics 53 983 997 degrees of freedom to account for the uncertainty associated with variance covariance parameter estimates for the repeated measures model

internal pilots for a class of linear mixed models with gaussian and compound symmetric data an internal pilot design uses interim sample size analysis without interim data analysis to adjust the final number of observations the approach helps to choose a sample size sufficiently large to achieve the statistical power desired but not too large which would waste money and time we report on recent research in cerebral vascular tortuosity curvature in three dimensions which would benefit greatly from internal pilots due to uncertainty in the parameters of the covariance matrix used for study planning unfortunately observations correlated across the four regions of the brain and small sample sizes preclude using existing methods however as in a wide range of medical imaging studies tortuosity data have no missing or mistimed data a factorial within subject design the same between subject design for all responses and a gaussian distribution with compound symmetry for such restricted models we extend exact small sample univariate methods for internal pilots to linear mixed models with any between subject design not just two groups planning a new tortuosity study illustrates how the new methods help to avoid sample sizes that are too small or too large while still controlling the type i error rate

stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints such as the famous nonnegative matrix factorization nmf and its many variants however despite several years of research on the topic the understanding of their convergence properties is still to be improved in this paper we show that lyapunov s stability theory provides a very enlightening viewpoint on the problem we prove the exponential or asymptotic stability of the solutions to general optimization problems with nonnegative constraints including the particular case of supervised nmf and finally study the more difficult case of unsupervised nmf the theoretical results presented in this paper are confirmed by numerical simulations involving both supervised and unsupervised nmf and the convergence speed of nmf multiplicative updates is investigated

choosing appropriate analysis methods for cluster randomised cross over trials with a binary outcome in cluster randomised cross over crxo trials clusters receive multiple treatments in a randomised sequence over time in such trials there is usual correlation between patients in the same cluster in addition within a cluster patients in the same period may be more similar to each other than to patients in other periods we demonstrate that it is necessary to account for these correlations in the analysis to obtain correct type i error rates we then use simulation to compare different methods of analysing a binary outcome from a two period crxo design our simulations demonstrated that hierarchical models without random effects for period within cluster which do not account for any extra within period correlation performed poorly with greatly inflated type i errors in many scenarios in scenarios where extra within period correlation was present a hierarchical model with random effects for cluster and period within cluster only had correct type i errors when there were large numbers of clusters with small numbers of clusters the error rate was inflated we also found that generalised estimating equations did not give correct error rates in any scenarios considered an unweighted cluster level summary regression performed best overall maintaining an error rate close to 5 for all scenarios although it lost power when extra within period correlation was present especially for small numbers of clusters results from our simulation study show that it is important to model both levels of clustering in crxo trials and that any extra within period correlation should be accounted for copyright 2016 john wiley sons ltd

random effects meta analysis coverage performance of 95 confidence and prediction intervals following reml estimation a random effects meta analysis combines the results of several independent studies to summarise the evidence about a particular measure of interest such as a treatment effect the approach allows for unexplained between study heterogeneity in the true treatment effect by incorporating random study effects about the overall mean the variance of the mean effect estimate is conventionally calculated by assuming that the between study variance is known however it has been demonstrated that this approach may be inappropriate especially when there are few studies alternative methods that aim to account for this uncertainty such as hartung knapp sidik jonkman and kenward roger have been proposed and shown to improve upon the conventional approach in some situations in this paper we use a simulation study to examine the performance of several of these methods in terms of the coverage of the 95 confidence and prediction intervals derived from a random effects meta analysis estimated using restricted maximum likelihood we show that in terms of the confidence intervals the hartung knapp correction performs well across a wide range of scenarios and outperforms other methods when heterogeneity was large and or study sizes were similar however the coverage of the hartung knapp method is slightly too low when the heterogeneity is low i2 30 and study sizes are similar in other situations especially when heterogeneity is small and the study sizes are quite varied the coverage is far too low and could not be consistently improved by either increasing the number of studies altering the degrees of freedom or using variance inflation methods therefore researchers should be cautious in deriving 95 prediction intervals following a frequentist random effects meta analysis until a more reliable solution is identified 2016 the authors statistics in medicine published by john wiley sons ltd

non negative matrix factorization with sparseness constraints non negative matrix factorization nmf is a recently developed technique for finding parts based linear representations of non negative data although it has successfully been applied in several applications it does not always result in parts based representations in this paper we show how explicitly incorporating the notion of sparseness improves the found decompositions additionally we provide complete matlab code both for standard nmf and for our extension our hope is that this will further the application of these methods to solving novel data analysis problems

multistratum response surface designs response surface designs are usually described as if the treatments have been completely randomized to the experimental units however in practice there is often a structure to the units implying the need for blocking if in addition some factors are more difficult to vary between units than others a multistratum structure arises naturally we present a general strategy for constructing response surface designs in multistratum unit structures designs are constructed stratum by stratum starting in the highest stratum in each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata allowing for all the effects that have to be estimated three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set finally some practical considerations in randomization are discussed

classical and bayesian prediction as applied to an unbalanced mixed linear model unbalanced mixed linear models that contain a single set of random effects are frequently employed in animal breeding applications in small area estimation and in the analysis of comparative experiments the problem considered is that of the point or interval prediction of the value of a linear combination of the fixed and random effects or the value of a future data point a common approach is empirical blup best linear unbiased prediction in which an estimate of the variance ratio is regarded as the true value empirical blup is satisfactory or can be made satisfactory by introducing appropriate modifications unless the estimate of the variance ratio is imprecise and is close to zero in which case more sensible point and interval predictions can be obtained by adopting a bayesian approach two animal breeding examples are used to illustrate the similarities and differences between the bayesian and empirical blup approaches

the application of reml in clinical trials residual maximum likelihood reml is a technique for estimating variance components in multi classified data in contrast to analysis of variance it can be routinely applied to unbalanced data and avoids some of the problems of biased variance estimates found with standard maximum likelihood estimation the full reml method is of particular value for the analysis of unbalanced clinical trials as it allows recovery of all the available information on treatment effects which can lead to significant improvements in their precision the use of reml has until recently been limited by heavy computational requirements and lack of readily available software this is no longer such a restriction however as reml procedures are now available in several widely used statistical packages including bmdp genstat and sas this paper describes the reml technique and discusses its application to three common types of clinical trial crossover repeated measures and multicentre

decomposition of prediction error abstract the problem considered is that of predicting the value of an unobservable random variable w from the value of an observable random vector y this problem is considered under each of four states of knowledge about the joint distribution of w and y ranging from complete knowledge to no knowledge a point predictor or predictors are presented for each case prediction error is decomposed so that each component reflects an absence of information under certain conditions these components are uncorrelated and have zero means an exact or approximate expression is given for the variance of each component

specification of covariance structure in longitudinal data analysis for randomized clinical trials misspecification of the covariance structure for repeated measurements in longitudinal analysis may lead to biased estimates of the regression parameters and under or overestimation of the corresponding standard errors in the presence of missing data the so called sandwich estimator can correct the variance but it does not reduce the bias in point estimates removing all assumptions from the covariance structure i e using an unstructured un covariance will remove such biases however an excessive amount of missing data may cause convergence problems for iterative algorithms such as the default newton raphson algorithm in the popular sas proc mixed this article examines both through theory and simulations the existence and the magnitude of these biases we recommend the use of un covariance as the default strategy for analyzing longitudinal data from randomized clinical trials with moderate to large number of subjects and small to moderate number of time points we also present an algorithm to assist in the convergence when the un covariance is used

linear mixed model selection for false discovery rate control in microarray data analysis in a microarray experiment one experimental design is used to obtain expression measures for all genes one popular analysis method involves fitting the same linear mixed model for each gene obtaining gene specific p values for tests of interest involving fixed effects and then choosing a threshold for significance that is intended to control false discovery rate fdr at a desired level when one or more random factors have zero variance components for some genes the standard practice of fitting the same full linear mixed model for all genes can result in failure to control fdr we propose a new method that combines results from the fit of full and selected linear mixed models to identify differentially expressed genes and provide fdr control at target levels when the true underlying random effects structure varies across genes

an optimization framework for product design an important problem in the product design and development process is to use the part worths preferences of potential customers to design a new product such that market share is maximized the authors present a new optimization framework for this problem the nested partitions np method this method is globally convergent and may utilize existing heuristic methods to speed its convergence we incorporate several known heuristics into this framework and demonstrate through numerical experiments that using the np method results in superior product designs our numerical results suggest that the new framework is particularly useful for designing complex products with many attributes

projection pursuit based method for blind separation of nonnegative sources this paper presents a projection pursuit pp based method for blind separation of nonnegative sources first the available observation matrix is mapped to construct a new mixing model in which the inaccessible source matrix is normalized to be column sum to 1 then the pp method is proposed to solve this new model where the mixing matrix is estimated column by column through tracing the projections to the mapped observations in specified directions which leads to the recovery of the sources the proposed method is much faster than chan s method which has similar assumptions to ours due to the usage of optimal projection it is also more advantageous in separating cross correlated sources than the independence and uncorrelation based methods as it does not employ any statistical information of the sources furthermore the new method does not require the mixing matrix to be nonnegative simulation results demonstrate the superior performance of our method

nonnegative least correlated component analysis for separation of dependent sources by volume maximization although significant efforts have been made in developing nonnegative blind source separation techniques accurate separation of positive yet dependent sources remains a challenging task in this paper a joint correlation function of multiple signals is proposed to reveal and confirm that the observations after nonnegative mixing would have higher joint correlation than the original unknown sources accordingly a new nonnegative least correlated component analysis nlca method is proposed to design the unmixing matrix by minimizing the joint correlation function among the estimated nonnegative sources in addition to a closed form solution for unmixing two mixtures of two sources the general algorithm of nlca for the multisource case is developed based on an iterative volume maximization ivm principle and linear programming the source identifiability and required conditions are discussed and proven the proposed nlca algorithm denoted by nlca ivm is evaluated with both simulation data and real biomedical data to demonstrate its superior performance over several existing benchmark methods

approximations for standard errors of estimators of fixed and random effects in mixed linear models abstract best linear unbiased estimators of the fixed and random effects of mixed linear models are available when the true values of the variance ratios are known if the true values are replaced by estimated values the mean squared errors of the estimators of the fixed and random effects increase in size the magnitude of this increase is investigated and a general approximation is proposed the performance of this approximation is investigated in the context of a the estimation of the effects of the balanced one way random model and b the estimation of treatment contrasts for balanced incomplete block designs

handling of baseline measurements in the analysis of crossover trials different analytic approaches for modeling baseline data in crossover trials were compared based on the efficiency in estimating treatment effects jointly modeling baseline and post baseline data is recommended to best utilize baseline data it results in the most significant gain in efficiency when data are strongly correlated within the same period but weakly correlated between different periods its performance remains comparable to the best of various other modeling methods under small within period correlation or large between period correlation we also examined the use of baseline data in modeling carryover effect we noted that to model carryover effect in crossover trial generally would lead to a much less efficient estimator and much more sensitive inference copyright 2012 john wiley sons ltd

measurement error in a random walk model with applications to population dynamics population abundances are rarely if ever known instead they are estimated with some amount of uncertainty the resulting measurement error has its consequences on subsequent analyses that model population dynamics and estimate probabilities about abundances at future points in time this article addresses some outstanding questions on the consequences of measurement error in one such dynamic model the random walk with drift model and proposes some new ways to correct for measurement error we present a broad and realistic class of measurement error models that allows both heteroskedasticity and possible correlation in the measurement errors and we provide analytical results about the biases of estimators that ignore the measurement error our new estimators include both method of moments estimators and pseudo estimators that proceed from both observed estimates of population abundance and estimates of parameters in the measurement error model we derive the asymptotic properties of our methods and existing methods and we compare their finite sample performance with a simulation experiment we also examine the practical implications of the methods by using them to analyze two existing population dynamics data sets