estimating a weighted average of stratum specific parameters this article investigates estimators of a weighted average of stratum specific univariate parameters and compares them in terms of a design based estimate of mean squared error mse the research is motivated by a stratified survey sample of florida medicaid beneficiaries in which the parameters are population stratum means and the weights are known and determined by the population sampling frame assuming heterogeneous parameters it is common to estimate the weighted average with the weighted sum of sample stratum means under homogeneity one ignores the known weights in favor of precision weighting adaptive estimators arise from random effects models for the parameters we propose adaptive estimators motivated from these random effects models but we compare their design based performance we further propose selecting the tuning parameter to minimize a design based estimate of mean squared error this differs from the model based approach of selecting the tuning parameter to accurately represent the heterogeneity of stratum means our design based approach effectively downweights strata with small weights in the assessment of homogeneity which can lead to a smaller mse we compare the standard random effects model with identically distributed parameters to a novel alternative which models the variances of the parameters as inversely proportional to the known weights we also present theoretical and computational details for estimators based on a general class of random effects models the methods are applied to estimate average satisfaction with health plan and care among florida beneficiaries just prior to medicaid reform

analysis of the objective space in multiple objective linear programming abstract a multiple objective linear program is defined by a matrix c consisting of the coefficients of the linear objectives and a convex polytope x defined by the linear constraints an analysis of the objective space y c x for this problem is presented a characterization between a face of y and the corresponding faces of x is obtained this result gives a necessary and sufficient condition for a face to be efficient the theory and examples demonstrate the collapsing simplification that occurs in mapping x to y these results form a basis for a new approach to analyzing multiple objective linear programs

augmented weighted estimators dealing with practical positivity violation to causal inferences in a random coefficient model the inverse probability of treatment weighted iptw estimator can be used to make causal inferences under two assumptions 1 no unobserved confounders ignorability and 2 positive probability of treatment and of control at every level of the confounders positivity but is vulnerable to bias if by chance the proportion of the sample assigned to treatment or proportion of control is zero at certain levels of the confounders we propose to deal with this sampling zero problem also known as practical violation of the positivity assumption in a setting where the observed confounder is cluster identity i e treatment assignment is ignorable within clusters specifically based on a random coefficient model assumed for the potential outcome we augment the iptw estimating function with the estimated potential outcomes of treatment or of control for clusters that have no observation of treatment or control if the cluster specific potential outcomes are estimated correctly the augmented estimating function can be shown to converge in expectation to zero and therefore yield consistent causal estimates the proposed method can be implemented in the existing software and it performs well in simulated data as well as with real world data from a teacher preparation evaluation study

relative efficiencies of two stage sampling schemes for mean estimation in multilevel populations when cluster size is informative in multilevel populations there are two types of population means of an outcome variable ie the average of all individual outcomes ignoring cluster membership and the average of cluster specific means to estimate the first mean individuals can be sampled directly with simple random sampling or with two stage sampling tss that is sampling clusters first and then individuals within the sampled clusters when cluster size varies in the population three tss schemes can be considered ie sampling clusters with probability proportional to cluster size and then sampling the same number of individuals per cluster sampling clusters with equal probability and then sampling the same percentage of individuals per cluster and sampling clusters with equal probability and then sampling the same number of individuals per cluster unbiased estimation of the average of all individual outcomes is discussed under each sampling scheme assuming cluster size to be informative furthermore the three tss schemes are compared in terms of efficiency with each other and with simple random sampling under the constraint of a fixed total sample size the relative efficiency of the sampling schemes is shown to vary across different cluster size distributions however sampling clusters with probability proportional to size is the most efficient tss scheme for many cluster size distributions model based and design based inference are compared and are shown to give similar results the results are applied to the distribution of high school size in italy and the distribution of patient list size for general practices in england

a procedure to find discrete representations of the efficient set with specified coverage errors an important issue in multiple objective mathematical programming is finding discrete representations of the efficient set because discrete points can be directly studied by a decision maker a discrete representation can serve as the solution to the multiple objective problem at hand however the discrete representation must be of acceptable quality to ensure that a most preferred solution identified by a decision maker is of acceptable quality recently attributes for measuring the quality of discrete representations have been proposed although discrete representations can be obtained in many different ways and their quality evaluated afterwards the ultimate goal should be to find such representations so as to conform to specified quality standards we present a method that can find discrete representations of the efficient set according to a specified level of quality the procedure is based on mathematical programming tools and can be implemented relatively easily when the domain of interest is a polyhedron the nonconvexity of the efficient set is dealt with through a coordinated decomposition approach we conduct computational experiments and report results

measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming one way of solving multiple objective mathematical programming problems is finding discrete representations of the efficient set a modified goal of finding good discrete representations of the efficient set would contribute to the practicality of vector maximization algorithms we define coverage uniformity and cardinality as the three attributes of quality of discrete representations and introduce a framework that includes these attributes in which discrete representations can be evaluated compared to each other and judged satisfactory or unsatisfactory by a decision maker we provide simple mathematical programming formulations that can be used to compute the coverage error of a given discrete representation our formulations are practically implementable when the problem under study is a multiobjective linear programming problem we believe that the interactive algorithms along with the vector maximization methods can make use of our framework and its tools

survey design under the regression superpopulation model abstract the construction of sample designs and estimators under a linear regression superpopulation model is considered the anticipated variance the variance of the predictor computed with respect to the sampling design and the superpopulation model is used as a criterion for evaluating probability designs and model unbiased predictors regression predictors that are model unbiased and design consistent are constructed

multilevel mixed linear model analysis using iterative generalized least squares summary models for the analysis of hierarchically structured data are discussed an iterative generalized least squares estimation procedure is given and shown to be equivalent to maximum likelihood in the normal case there is a discussion of applications to complex surveys longitudinal data and estimation in multivariate models with missing responses an example is given using educational data

shake and bake algorithms for generating uniform points on the boundary of bounded polyhedra we present a class of shake and bake algorithms for generating asymptotically uniform points on the boundary of full dimensional bounded polyhedra we also report results of simulations for some elementary test problems

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

small area estimation based on natural exponential family quadratic variance function models and survey weights summary we propose pseudo empirical best linear unbiased estimators of small area means based on natural exponential family quadratic variance function models when the basic data consist of survey weighted estimators of these means area specific covariates and certain summary measures involving the weights we also provide explicit approximate mean squared errors of these estimators in the spirit of prasad rao 1990 and these estimators can be readily evaluated a simulation study is undertaken to evaluate the performance of the proposed inferential procedure we estimate also the proportion of poor children in the 5 17 years age group for the different counties in one of the states in the united states

model selection by testing for the presence of small area effects and application to area level data the models used in small area inference often involve unobservable random effects while this can significantly improve the adaptivity and flexibility of a model it also increases the variability of both point and interval estimators if we could test for the existence of the random effects and if the test were to show that they were unlikely to be present then we would arguably not need to incorporate them into the model and thus could significantly improve the precision of the methodology in this article we suggest an approach of this type we develop simple bootstrap methods for testing for the presence of random effects applicable well beyond the conventional context of the natural exponential family if the null hypothesis that the effects are not present is not rejected then our general methodology immediately gives us access to estimators of unknown model parameters and estimators of small area means such estimators can be substantially more effective for example because they enjoy much fa

latent class analysis of complex sample survey data application to dietary data high fruit and vegetable intake is associated with decreased cancer risk however dietary recall data from national surveys suggest that on any given day intake falls below the recommended minima of three daily servings of vegetables and two daily servings of fruit there is no single widely accepted measure of usual intake one approach is to regard the distribution of intake as a mixture of regular relatively frequent and nonregular relatively infrequent consumers using an indicator of whether an individual consumed the food of interest on the recall day we use a new approach to summarizing dietary data latent class analysis lca to estimate usual intake of vegetables the data consist of four 24 hour dietary recalls from the 1985 continuing survey of intakes by individuals collected from 1 028 women traditional lca based on simple random sampling was extended to complex survey data by introducing sample weights into the latent class estimation algorithm and by accounting for the co

efforts to adjust for confounding by neighborhood using complex survey data in social epidemiology one often considers neighborhood or contextual effects on health outcomes in addition to effects of individual exposures this paper is concerned with the estimation of an individual exposure effect in the presence of confounding by neighborhood effects motivated by an analysis of national health interview survey nhis data in the analysis we operationalize neighborhood as the secondary sampling unit of the survey which consists of small groups of neighboring census blocks thus the neighborhoods are sampled with unequal probabilities as are individuals within neighborhoods we develop and compare several approaches for the analysis of the effect of dichotomized individual level education on the receipt of adequate mammography screening in the analysis neighborhood effects are likely to confound the individual effects due to such factors as differential availability of health services and differential neighborhood culture the approaches can be grouped into three broad classes ordinary logistic regression for survey data with either no effect or a fixed effect for each cluster conditional logistic regression extended for survey data and generalized linear mixed model glmm regression for survey data standard use of glmms with small clusters fails to adjust for confounding by cluster e g neighborhood this motivated us to develop an adaptation we use theory simulation and analyses of the nhis data to compare and contrast all of these methods one conclusion is that all of the methods perform poorly when the sampling bias is strong more research and new methods are clearly needed

multi level modelling under informative sampling we consider a model dependent approach for multi level modelling that accounts for informative probability sampling of first and lower level population units the proposed approach consists of first extracting the hierarchical model holding for the sample data given the selected sample as a function of the corresponding population model and the first and lower level sample selection probabilities and then fitting the resulting sample model using bayesian methods an important implication of the use of the model holding for the sample is that the sample selection probabilities feature in the analysis as additional data that possibly strengthen the estimators a simulation experiment is carried out in order to study the performance of this approach and compare it to the use of design based methods the simulation study indicates that both approaches perform in general equally well in terms of point estimation but the model dependent approach yields confidence credibility intervals with better coverage properties another simulation study assesses the impact of misspecification of the models assumed for the sample selection probabilities the use of maximum likelihood estimation is also considered

a theory of statistical models for monte carlo integration summary the task of estimating an integral by monte carlo methods is formulated as a statistical model using simulated observations as data the difficulty in this exercise is that we ordinarily have at our disposal all of the information required to compute integrals exactly by calculus or numerical integration but we choose to ignore some of the information for simplicity or computational feasibility our proposal is to use a semiparametric statistical model that makes explicit what information is ignored and what information is retained the parameter space in this model is a set of measures on the sample space which is ordinarily an infinite dimensional object none the less from simulated data the base line measure can be estimated by maximum likelihood and the required integrals computed by a simple formula previously derived by vardi and by lindsay in a closely related model for biased sampling the same formula was also suggested by geyer and by meng and wong using entirely different arguments by contrast with geyer s retrospective likelihood a correct estimate of simulation error is available directly from the fisher information the principal advantage of the semiparametric model is that variance reduction techniques are associated with submodels in which the maximum likelihood estimator in the submodel may have substantially smaller variance than the traditional estimator the method is applicable to markov chain and more general monte carlo sampling schemes with multiple samplers

a note on multiple imputation under complex sampling summary multiple imputation is popular for handling item nonresponse in survey sampling current multiple imputation techniques with complex survey data assume that the sampling design is ignorable in this paper we propose a new multiple imputation procedure for parametric inference without this assumption instead of using the sample data likelihood we use the sampling distribution of the pseudo maximum likelihood estimator to derive the posterior distribution of the parameters the asymptotic properties of the proposed method are investigated a simulation study confirms that the new procedure provides unbiased point estimation and valid confidence intervals with correct coverage properties whether or not the sampling design is ignorable

estimating variance components by using survey data summary inflation type weighted estimators for variance components can be badly biased modified weighted estimators suggested in the literature are also badly biased for certain sampling designs we propose new estimators for variance components some of which are approximately unbiased regardless of the sampling design these estimators require knowledge of the joint inclusion probabilities of the observations the small sample properties of the estimators are studied via simulation for the simple one way random effects model an application is given by using data from the us hispanic health and nutrition examination survey

efficient monte carlo procedures for generating points uniformly distributed over bounded regions we consider the monte carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region the class of markovian methods considered generate points asymptotically uniformly distributed within the region computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions

small area estimates for cross classifications we develop a class of log linear structural models that is suited to estimation of small area cross classified counts based on survey data this allows us to account for various association structures within the data and includes as a special case the restricted log linear model underlying structure preserving estimation the effect of survey design can be incorporated into estimation through the specification of an unbiased direct estimator and its associated covariance structure we illustrate our approach by applying it to estimation of small area labour force characteristics in norway

weighting for unequal selection probabilities in multilevel models when multilevel models are estimated from survey data derived using multistage sampling unequal selection probabilities at any stage of sampling may induce bias in standard estimators unless the sources of the unequal probabilities are fully controlled for in the covariates this paper proposes alternative ways of weighting the estimation of a two level model by using the reciprocals of the selection probabilities at each stage of sampling consistent estimators are obtained when both the sample number of level 2 units and the sample number of level 1 units within sampled level 2 units increase scaling of the weights is proposed to improve the properties of the estimators and to simplify computation variance estimators are also proposed in a limited simulation study the scaled weighted estimators are found to perform well although non negligible bias starts to arise for informative designs when the sample number of level 1 units becomes small the variance estimators perform extremely well the procedures are illustrated using data from the survey of psychiatric morbidity

a representation of the set of feasible objectives in multiple objective linear programs most of the analysis and algorithms for multiple objective linear programming have focused on the feasible decision set rather than the set of feasible objective values further previous research in analyzing the set of feasible objective values has focused only on the optimality aspects in this work an explicit representation of the set of feasible objective values in the form of linear inequalities is developed furthermore we develop a representation for a polyhedron in the objective space which has the same maximal pareto efficient structure as that of the set of feasible objective values and moreover is such that all of the extreme points of this polyhedron are maximal pareto efficient points this latter polyhedron provides a new approach for the analysis of large multiple objective linear programs

the possible values of critical points between varieties of lattices abstract we denote by con c l the 0 semilattice of all finitely generated congruences of a lattice l for varieties i e equational classes v and w of lattices such that v is contained neither in w nor in its dual and such that every simple member of w contains a prime interval we prove that there exists a bounded lattice a v with at most 2 elements such that con c a is not isomorphic to con c b for any b w the bound 2 is optimal as a corollary of our results there are continuum many congruence classes of locally finite varieties of bounded modular lattices