NEAR OPTIMUM MULTIVARIATE STRATIFIED SAMPLING DESIGN WITH RANDOM MEASUREMENT COSTS

Usually in sample surveys information on more than one characteristic are collected and the data obtained are analyzed to get the required estimates for the multivariate population under study. If stratified sampling design is to be applied on such a population the individual optimum allocations don’t help much unless the characteristics are highly correlated. Therefore, in multivariate stratified sampling we need to work out an allocation that is optimum for all characteristics in some sense, that is, near optimum for all characteristics. Such an allocation is called a compromise allocation. Furthermore, in surveys usually the per unit measurement costs are taken as deterministic, that is, they remain constant throughout the survey. In practice the costs of measurement of different characteristics in various strata may change during the course of survey for reasons beyond the control of the sampler. Thus in some practical situations the measurement costs may become a random variable and the  problem of obtaining a compromise allocation becomes a Stochastic Integer Nonlinear Programming Problem (SINLPP). The present paper addresses the problem of obtaining an integer compromise allocation for multivariate stratified sampling with random cost of measurements. A solution procedure has been developed for the formulated problem. A practical application of the procedure is also given through a numerical example to illustrate the computational details

Estimation of Finite Population Mean in Multivariate Stratified Sampling under Cost Function Using Goal Programming

In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real life situations, a linear cost function of a sample size nh is not a good approximation to actual cost of sample survey when traveling cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling with proposed cost function is formulated in integer nonlinear multiobjective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of proposed compromise allocation

On The Efficiency of Some Techniques For Optimum Allocation In Multivariate Stratified Survey.

In multivariate stratified sampling, the major concern is on the problem of estimation of more than one population characteristics which often make conflicting demands on sampling technique. In this type of survey, an allocation which is optimum for one characteristic may not be optimum for other characteristics. In such situations a compromise criterion is needed to work out a usable allocation which is optimum for all characteristics in some sense. This study is focuses on the efficiency of some techniques for optimum sample allocation which are Yates/Chatterjee, Booth and Sedransk and Vector maximum criterion (VMC) on the set of real life data stratified into six strata and two variates with desired variances using: (i) method of minimum variance with fixed sample size and (ii) an arbitrary fixing of variances. The stratum sample sizes  among the classes were obtained to examine the criterion that will produce the smallest n. In this paper, it was discovered that VMC and Booth and Sedransk are superior to Yates/Chatterjee. Even though, no universal conclusion can be drawn, the work clearly brings out the fact that the best allocation is not always obvious and that sufficient care is necessary in the choice of allocation of the sample sizes to different strata with several items. Keywords:- Stratified Survey; Optimum Allocation; Vector Maximum Criterion (VMC); Yates/Chatterjee;Booth and Sedrans

Standard survey methods for estimating colony losses and explanatory risk factors in Apis mellifera

This chapter addresses survey methodology and questionnaire design for the collection of data pertaining to estimation of honey bee colony loss rates and identification of risk factors for colony loss. Sources of error in surveys are described. Advantages and disadvantages of different random and non-random sampling strategies and different modes of data collection are presented to enable the researcher to make an informed choice. We discuss survey and questionnaire methodology in some detail, for the purpose of raising awareness of issues to be considered during the survey design stage in order to minimise error and bias in the results. Aspects of survey design are illustrated using surveys in Scotland. Part of a standardized questionnaire is given as a further example, developed by the COLOSS working group for Monitoring and Diagnosis. Approaches to data analysis are described, focussing on estimation of loss rates. Dutch monitoring data from 2012 were used for an example of a statistical analysis with the public domain R software. We demonstrate the estimation of the overall proportion of losses and corresponding confidence interval using a quasi-binomial model to account for extra-binomial variation. We also illustrate generalized linear model fitting when incorporating a single risk factor, and derivation of relevant confidence intervals

Multiple imputation in an international database of social science surveys

'In diesem Beitrag wird das Verfahren der multiplen Imputation anhand von Datensätzen aus dem International Social Survey Programme diskutiert. Da es in den meisten Variablen fehlende Werte gibt, die in vielen unterschiedlichen Kombinationen vorkommen, werden die Imputations in mehreren Schritten durchgeführt. Als erstes werden die Angaben bei den sozio-demografischen Merkmalen ersetzt, da es hier in der Regel nur relativ wenige fehlende Werte gibt. Bei Blöcken von Items werden nur deren Summenwerte geschätzt, was die Aufgabe der Imputation vereinfacht, ohne daß dabei auf wichtige Informationen verzichtet wird. Ein weiterer Vorteil dieser Vorgehensweise ist, daß die Anzahl der einzusetzenden Werte reduziert wird.' (Autorenreferat)'This paper describes an implementation of the method of multiple imputation in the database of surveys in the International Social Science Programme. Since missing values occur for most variables, with a wide range of patterns, the imputations are carried out in stages, starting with background variables which, in general, have fewer missing values. For blocks of questionnaire items only their total scores are imputed, making the imputation task manageable without substantial loss of utility of the database, and reducing the size of the data files added to the database by the imputation procedure.' (author's abstract)

Estimation of origin-destination matrices from traffic counts: theoretical and operational development

This thesis deals with the o-d estimation problem from indirect measures, addressing two main aspects of the problem: the identification of the set of indirect measures that provide the maximum information with a resulting reduction of the uncertainty on the estimate; once defined the set of measures, the choice of an estimator to identify univocally and as much reliable as possible the estimate. As regards the former aspect, an innovative and theoretically founded methodology is illustrated, explicitly accounting for the reliability of the o-d matrix estimate. The proposed approach is based on a specific measure, named Synthetic Dispersion Measure (SDM), related to the trace of the dispersion matrix of the posterior demand estimate conditioned to a given set of sensors locations. Under the mild assumption of multivariate normal distribution for the prior demand estimate, the proposed SDM does not depend on the specific values of the counted flows – unknown in the planning stage – but just on the locations of such sensors. The proposed approach is applied to real contexts, leading to results outperforming the other methods currently available in the literature. In addition, the proposed methodology allows setting a formal budget allocation problem between surveys and counts in the planning stage, in order to maximize the overall quality of the demand estimation process. As regard the latter aspect, a “quasi-dynamic” framework is proposed, under the assumption that o-d shares are constant across a reference period, whilst total flows leaving each origin vary for each sub-period within the reference period. The advantage of this approach over conventional within-day dynamic estimators is that of reducing drastically the number of unknowns given the same set of observed time-varying traffic counts. The quasi-dynamic assumption is checked by means of empirical and statistical tests and the performances of the quasi-dynamic estimator - whose formulation is also given – are compared with other dynamic estimators