Number Of Strata Research Articles

Accounting for differences in costs among sampling locations in optimal stratification

SummaryIn areas with marked differences in accessibility, the cost efficiency of design‐based sampling strategies for estimating the population mean or total can be increased by accounting for these differences in the selection of the sampling locations. This can be achieved by stratified random sampling. The question then is how to construct the strata. Existing optimal stratification methods such as cum stratification assume a constant cost among the sampling units, and therefore can be suboptimal when this assumption is violated. A simulated annealing algorithm is proposed for simultaneous optimization of the stratum breaks and the sample size under optimal allocation of the sample size, given a chosen maximum for the expected total costs. The proposed stratification method is tested in a study area of 5900 km2 in Anhui province, China. Optimal stratum breaks were computed for estimating the population mean of the soil organic matter content (SOM). Predictions of SOM from a multiple linear regression model were used as a stratification variable. The optimal stratum breaks differed markedly from the cum breaks. The variance of the estimated mean of SOM using the optimal stratification was about 8 to 29% smaller than with the cum stratification, depending on the number of strata. This large gain in precision can be explained by the moderately strong correlation of the point‐wise costs and the stratification variable. Smaller gains are expected when this correlation is weaker or the variation in costs among the units are smaller. The proposed algorithm can also be used when no ancillary variable related to the variable of interest is available, accounting for differences in costs among the sampling units only. An R script with functions is provided as supporting information.HighlightsA method is proposed to compute optimal strata that accounts for differences in costs among sampling locations Simulated annealing is used to optimize stratum breaks and total sample size under a total costs constraint The variance of estimated mean of SOM with proposed method was 8 to 29% smaller than with cum method Proposed algorithm can also be used when no stratification variable is available (optimal costs stratification)

Systems with Parameters, or Efficiently Solving Systems of Polynomial Equations: 33 Years Later. I

Consider a system of polynomial equations with parametric coefficients over an arbitrary ground field. We show that the variety of parameters can be represented as a union of strata. For values of the parameters from each stratum, the solutions of the system are given by algebraic formulas depending only on this stratum. Each stratum is a quasiprojective algebraic variety with degree bounded from above by a subexponential function in the size of the input data. The number of strata is also subexponential in the size of the input data. Thus, here we avoid double exponential upper bounds on the degrees and solve a long-standing problem

Sample allocation balancing overall representativeness and stratum precision

PurposeIn large-scale surveys, it is often necessary to distribute a preset sample size among a number of strata. Researchers must make a decision between prioritizing overall representativeness or precision of stratum estimates. Hence, I evaluated different sample allocation strategies based on stratum size. MethodsThe strategies evaluated herein included allocation proportional to stratum population; equal sample for all strata; and proportional to the natural logarithm, cubic root, and square root of the stratum population. This study considered the fact that, from a preset sample size, the dispersion index of stratum sampling fractions is correlated with the population estimator error and the dispersion index of stratum-specific sampling errors would measure the inequality in precision distribution. Identification of a balanced and efficient strategy was based on comparing those both dispersion indices. ResultsBalance and efficiency of the strategies changed depending on overall sample size. As the sample to be distributed increased, the most efficient allocation strategies were equal sample for each stratum; proportional to the logarithm, to the cubic root, to square root; and that proportional to the stratum population, respectively. ConclusionsDepending on sample size, each of the strategies evaluated could be considered in optimizing the sample to keep both overall representativeness and stratum-specific precision.

Optimal Stratification and Allocation for the June Agricultural Survey

Abstract A computational approach to optimal multivariate designs with respect to stratification and allocation is investigated under the assumptions of fixed total allocation, known number of strata, and the availability of administrative data correlated with thevariables of interest under coefficient-of-variation constraints. This approach uses a penalized objective function that is optimized by simulated annealing through exchanging sampling units and sample allocations among strata. Computational speed is improved through the use of a computationally efficient machine learning method such as K-means to create an initial stratification close to the optimal stratification. The numeric stability of the algorithm has been investigated and parallel processing has been employed where appropriate. Results are presented for both simulated data and USDA’s June Agricultural Survey. An R package has also been made available for evaluation.

Development of the Hand Assessment for Infants: evidence of internal scale validity.

The aim of this study was to develop a descriptive and evaluative assessment of upper limb function for infants aged 3 to 12 months and to investigate its internal scale validity for use with infants at risk of unilateral cerebral palsy. The concepts of the test items and scoring criteria were developed. Internal scale validity and aspects of reliability were investigated on the basis of 156 assessments of infants at 3 to 12 months corrected age (mean 7.2mo, SD 2.5) with signs of asymmetric hand use. Rasch measurement model analysis and non-parametric statistics were used. The new test, the Hand Assessment for Infants (HAI), consists of 12 unimanual and five bimanual items, each scored on a 3-point rating scale. It demonstrated a unidimensional construct and good fit to the Rasch model requirements. The excellent person reliability enabled person separation to six significant ability strata. The HAI produced an interval-level measure of bilateral hand use as well as unimanual scores of each hand, allowing a quantification of possible asymmetry expressed as an asymmetry index. The HAI can be considered a valid assessment tool for measuring bilateral hand use and quantifying side difference between hands among infants at risk of developing unilateral cerebral palsy. The Hand Assessment for Infants (HAI) measures the use of both hands and quantifies a possible asymmetry of hand use. HAI is valid for infants at 3 to 12 months corrected age at risk of unilateral cerebral palsy.

Statistical investigation through stratified random sampling for apple production in Himachal Pradesh

The present study focuses on standardization of sampling technique and comparison of different types of sample allocation methods in combination with various stratification tools (optimum strata boundaries, number of strata and optimum sample size etc.) for obtaining efficient estimators of area and production of apple in Himachal Pradesh. Forth is purpose, various aspects involved in optimum stratification with reference todata collected from the selected or chardists in district Shimla, during the year 2011-12 have been analyzed. The variable "Area under Apple" was chosen as the stratification variable as it had high correlation(r=0.96) with the estimation variable "Production of Apple". Four methods of construction of strata viz., equalization of strata total, equalization of cumulative of ?f(y) , equalization of cumulative of ½{r(y)+f(y)} and equalization of cumulative of were used and their relative efficiencies for estimating total production of apple in the study district of the state have been analyzed. The critical examination of the result revealed that with the increase in number of strata from 2 to 4 and sample size from 10 to 40, equalization of cumulative of method along with Neyman allocation resulted in least variance (0.89) and maximum percentage gain in efficiency (20418.16). Thus, equalization of cumulative of method with L>2 can profitably be applied for the estimation of apple production in the study district of the state Himachal Pradesh, India.

Efficient Absolute Factorization of Polynomials with Parametric Coefficients

Consider a polynomial with parametric coefficients. We show that the variety of parameters can be represented as a union of strata. For values of the parameters from each stratum, the decomposition of this polynomial into absolutely irreducible factors is given by algebraic formulas depending only on the stratum. Each stratum is a quasiprojective algebraic variety. This variety and the corresponding output are given by polynomials of degrees at most D with D = d′d O(1) where d′, d are bounds on the degrees of the input polynomials. The number of strata is polynomial in the size of the input data. Thus, here we avoid double exponential upper bounds for the degrees and solve a long-standing problem.

Long-term clinical outcomes for bifurcation treatment using a provisional T-stenting and double proximal optimization technique with Absorb bioresorbable scaffolds

Aim. The article presents long-term outcomes of treatment of coronary artery bifurcation lesions by using bioresorbable vascular scaffolds and provisional T-stenting combined with double proximal optimization. Methods. 14 patients aged 44-80 years (mean age 61±6 years) including 8 (57.14 %) males underwent endovascular treatment of coronary artery bifurcation lesions by using Absorb bioresorbable vascular scaffolds (BVS). Clinical/instrumental analysis was carried out after 23.7±4.12 months. Angiographic examination was performed in 12 cases (85.71 %). 7 patients (50 %) underwent optical coherent tomography. Results. 11 patients (78.57) were free of angina during long-term follow-up. 1 patient (7.14 %) developed BVS thrombosis and received a drug-eluting stent. A neointimal layer of the main branch increased during long-term follow-up to 29.23±7.82%, that of the lateral branch – up to 19.2±7.48%. Optical coherence tomography (OCT) shows that all strata are fully covered with neointima, the number of strata with malappositions is minimal and the loss of the main branch diameter (16.9±4.9%) is insignificant. Conclusion. The use of Absorb bioresorbable vascular scaffolds implanted by means of provisional T-stenting combined with double proximal optimization when treating coronary artery bifurcation lesions is a safe and efficient procedure.Received 2 February 2017. Accepted 10 March 2017.Financing: The study did not have sponsorship.Conflict of interest: The authors declare no conflict of interest.

Improved estimates of opium cultivation in Afghanistan using imagery-based stratification

ABSTRACTThe United Nations Office on Drugs and Crime and the US Government make extensive use of remote sensing to quantify and monitor trends in Afghanistan’s illicit opium production. Cultivation figures from their independent annual surveys can vary because of systematic differences in survey methodologies relating to spectral stratification and the addition of a pixel buffer to the agricultural area. We investigated the effect of stratification and buffering on area estimates of opium poppy using SPOT5 imagery covering the main opium cultivation area of Helmand province and sample data of poppy fields interpreted from very high resolution satellite imagery. The effect of resolution was investigated by resampling the original 10 m pixels to 20, 30, and 60 m, representing the range of available imagery. The number of strata (1, 4, 8, 13, 23, 40) and sample fraction (0.2–2%) used in the estimate were also investigated. Stratification reduced the confidence interval by improving the precision of estimates. Cultivation estimates of poppy using 40 spectral strata and a sample fraction of 1.1% had a similar precision to direct expansion estimates using a 2% sample fraction. Stratified estimates were more robust to changes in sample size and distribution. The mapping of the agricultural area had a significant effect on poppy cultivation estimates in Afghanistan, where the area of total agricultural production can vary significantly between years. The findings of this research explain differences in cultivation figures of the opium monitoring programmes in Afghanistan and recommendations can be applied to improve resource monitoring in other geographic areas.

Choosing a covariate-adaptive randomization procedure in practice

ABSTRACTPocock and Simon’s minimization method is a very popular covariate-adaptive randomization procedure intended to balance the allocations of two treatments across a set of covariates without compromising randomness. Additional covariate-adaptive schemes have been proposed in the literature, such as Atkinson’s -optimum Biased Coin Design and the Covariate-Adaptive Biased Coin Design (CA-BCD), and their properties were analyzed and compared in terms of imbalance and predictability. The aim of this paper is to push forward these comparisons by also taking into account other randomization methods, such as the Permuted Block Design, the Big Stick Design, a generalization of the CA-BCD that can be implemented when the covariate distribution is unknown, and the Covariate-Adaptive Dominant Biased Coin Design, which is a new class of stratified randomization methods that forces the balance increasingly as the joint imbalance grows and improves the degree of randomness as the size of every stratum increases. The performance of covariate-adaptive procedures is strictly related to the considered factors and the number of patients in the trial as well, which makes it hard to find a dominant rule, namely a design that is more balanced and less predictable with respect to other schemes. In general, stratified randomization methods perform very well when the number of strata is small, showing also some dominance structure with respect to the other designs. Nevertheless, the evolution and the performance of stratified designs are strictly related to the random entries of the subjects. Thus, these rules become less efficient in the case of both (i) limited samples and (ii) large number of factors/levels.

Estimation of Sensitive Attributes Using a Stratified Kuk Randomization Device

This paper suggests a stratified Kuk model to estimate the proportion of sensitive attributes of a population composed by a number of strata; this is undertaken by applying stratified sampling to the adjusted Kuk model. The paper estimates sensitive parameters when the size of the stratum is known by taking proportional and optimal allocation methods into account and then extends to the case of an unknown stratum size, estimating sensitive parameters by applying stratified double sampling and checking the two allocation methods. Finally, the paper compares the efficiency of the proposed model to that of the Su, Sedory and Singh model and the adjusted Kuk model in terms of the estimator variance.

A SAS Macro for Covariate-Constrained Randomization of General Cluster-Randomized and Unstratified Designs

Ivers et al. (2012) have recently stressed the importance to both statistical power and face validity of balancing allocations to study arms on relevant covariates. While several techniques exist (e.g., minimization, pair-matching, stratification), the covariate-constrained randomization (CCR) approach proposed by Moulton (2004) is favored when clusters can be recruited prior to randomization. CCRA V1.0, a macro published by Chaudhary and Moulton (2006), provides a SAS implementation of CCR for a particular subset of possible designs (those with two arms, small numbers of strata and clusters, an equal number of clusters within each stratum, and constraints that can be expressed as absolute mean differences between arms). This paper presents a more comprehensive macro, CCR, that is applicable across a wider variety of designs and provides statistics describing the range of possible allocations meeting the constraints in addition to performing the actual random assignment.

The number of strata in propensity score stratification for abinary outcome.

IntroductionNon-interventional and other observational studies have become important in medical research. In such observational, non-randomized studies, groups usually differ in some baseline covariates. Propensity scores are increasingly being used in the statistical analysis of these studies. Stratification, also called subclassification, based on propensity scores is one of the possible methods. There is the quasi-standard of using five strata. In this paper we focus on a binary outcome and evaluate the above-mentioned standard of using five strata.Material and methodsBias and power for different numbers of strata are investigated with a simulation study. The methods are illustrated using data from a study where patients with diabetes mellitus and triple vessel disease undergoing coronary artery bypass surgery with and without previous percutaneous coronary intervention were compared.ResultsWe show that more than five strata can be more powerful and give less biased results. However, using more than ten strata hardly gives any further benefit.ConclusionsWhen applying a stratification, more than five strata may be preferable, especially because of increased power. Our simulation study does not show a clear winner; hence a useful strategy could be to work with five as well as with ten strata.

School Delay of Child in Brazzaville (Congo)

The aim of this study was to determine the prevalence of school delay in school age children and to identify its determinants in Brazzaville. A case-control study, comparing school age children with a school delay (Group 1 or cases) to those who had not school delay (Group 2 or control), was carried out between February and July 2013. It included students of CM2 (primary 6) and those of 3ème (form 4) of both public and private schools of Brazzaville. The sample selection was made according to a random survey by strata, the number of strata was set to 2. The sample consisted of 2064 pupils including 1138 girls (55.1%). A total of 2064 students (1138 male/926 female), 792 of them had a school delay, with a prevalence of 38.3%. It was 27% in the private sector and 46.9% in the public one; 28.2% in primary education compared to 48.1% in the college; 27.8% in girls and 48.8% in boys (p p p < 0.05). The prevalence of school delay was high in Brazzaville (38.3%), boys were more affected than girls. The kindergarten program attendance was found to have a positive effect on later school performances, while parent’s low level of education and low socioeconomic status of the family significantly influenced the rate of school delay in children in Brazzaville. The high prevalence of school delay in child in Brazzaville imposed substantial actions, in addition to the efforts already made.

Using discrete‐return airborne laser scanning to quantify number of canopy strata across diverse forest types

SummaryThe vertical arrangement of forest canopies is a key descriptor of canopy structure, a driver of ecosystem function and indicative of forest successional stage. Yet techniques to attribute for canopy vertical structure across large and potentially heterogeneously forested areas remain elusive.This study introduces a new technique to estimate the Number of Strata (NoS) that comprise a canopy profile, using discrete‐return Airborne Laser Scanning (ALS) data. Vertically resolved gap probability (Pgap) aggregated over a plot is generalized with a nonparametric cubic spline regression (Ps). Subsequently a count of the positive zero‐crossings of second derivative of 1 −Psis used to estimateNoS.Comparison with inventory derived estimates at 24 plots across three diverse study areas shows a good agreement between the two techniques (RMSE = 0·41 strata). Furthermore, this is achieved without altering model parameters, indicating the transferability of the technique across diverse forest types.NoSvalues ranged from 0 to 4 at a further 239 plots, emphasizing the need for a method to quantify canopy vertical structure across forested landscapes. Comparison ofNoSwith other commonly derived ALS descriptors of canopy structure (canopy height, canopy cover and return height coefficient of determination) returned only a moderate correlation (r2 &lt; 0·4).It is proposed the presented method provides a primary descriptor of canopy structure to complement canopy height and cover, as well as a candidate Ecological Biodiversity Variable for characterizing habitat structure.

Farm-scale soil carbon auditing

A novel method for soil carbon auditing at farm scale based on data value is presented. Using a map of carbon content with associated uncertainty, it optimizes stratified random sampling: number of strata, stratum boundaries, total sample size and sample sizes within strata. The optimization maximizes the expected profit for the farmer on the basis of sequestered carbon price, sampling costs, and a trading parameter that balances farmer's and buyer's risks due to uncertainty of the estimated amount of sequestered carbon. The stratification is optimized by a novel method (Ospats), an iterative procedure that re-allocates grid points to strata on the basis of pairwise differences between predictions and covariances of prediction errors. Optimal sample sizes are calculated from variance predictions by Ospats. An application on an Australian farm has shown that soil carbon changes across farms and regions can be audited effectively using the proposed method. It is concluded that sample bulking and returning to the same sites in subsequent sampling rounds are not recommendable.

Tone-Mapped Mean-Shift Based Environment Map Sampling.

In this paper, we present a novel approach for environment map sampling, which is an effective and pragmatic technique to reduce the computational cost of realistic rendering and get plausible rendering images. The proposed approach exploits the advantage of adaptive mean-shift image clustering with aid of tone-mapping, yielding oversegmented strata that have uniform intensities and capture shapes of light regions. The resulted strata, however, have unbalanced importance metric values for rendering, and the strata number is not user-controlled. To handle these issues, we develop an adaptive split-and-merge scheme that refines the strata and obtains a better balanced strata distribution. Compared to the state-of-the-art methods, our approach achieves comparable and even better rendering quality in terms of SSIM, RMSE and HDRVDP2 image quality metrics. Experimental results further show that our approach is more robust to the variation of viewpoint, environment rotation, and sample number.

Did Elijah Show Respect to Royalty?

At the end of the description of the dramatic event at Mount Carmel, Kings relates that after the heavy downpour began Elijah ran before the king to Jezreel. Elijah’s running was already understood in the Tannaitic sources as a gesture meant to show respect to royalty. This interpretation, which is not consistent with the characterization of Elijah as zealous that emerges from the biblical narrative, was accepted by both medieval and modern biblical commentators. The article discusses this interpretive tradition in its textual and historical contexts and reveals the conceptual stance that it expresses. At the center of the discussion is a passage from Mekilta de-Rabbi Ishmael, in which this interpretive tradition first appears. The article indicates a number of strata in the Mekilta text, each of which expresses a different ideological approach to the question of the proper attitude to “royalty.” The article proposes that Mekilta reflects different positions on the question of the proper attitude to the Roman authorities, and reveals an ideological-educational conflict over the image and heritage of biblical characters as part of the struggle over the fashioning of the collective Jewish historical and political memory.

Cumulative Point—L1 Between Two Positively Charged Plasma Structures (3-D Strata)

Values of a cathode potential drop (CD) are estimated in nanosecond argon discharges with a hollow cathode over total number of strata in the discharge gap ( $n \sim 10$ ). The CD dependence on the discharge parameters has been studied. The structurization of this discharge in experiments is analytically analyzed. It is proved that the strata in the nanosecond discharges are caused by the electron drift and the electron impact direct ionization forming the ionization—drift waves. The drift removal of electrons leads to formation of positively charged layers of a space charge, a significant increase of the peripheral ionization. At that the cumulation of the electron flow in to the plasma focuses takes place similar to cumulation of neural particle flows in to the Lagrange–Euler libration points $L_{1}$ . The cumulative points $L_{1}$ arise between the attractors of any nature.

Habitat selection of endemic birds in temperate forests in a biodiversity "Hotspot"

Aim of study: Our objective was to find habitat associations at a microhabitat level for two endemic birds in a Chilean temperate forest (biodiversity “hotspots”), in order to integrate biodiversity into forest planning.Area of study: Nahuelbuta Range, Chile.Material and methods: The two birds studied were Scelorchilus rubecula (Chucao Tapaculo) and Scytalopus magellanicus (Magellanic Tapaculo), both belonging to the Rhinocryptidae family. Presence or absence of the two species was sampled in 57 census spots. Habitat was categorized according to presence/absence results. We assessed the influence of abiotic variables (altitude, exposure, slope) and vegetation structure (percentage of understory cover, number of strata) using a statistical cluster analysis.Main results: The two bird species selected the habitat. Most frequent presence was detected at a range of 600-1100 masl, but Magellanic Tapaculo was associated to more protected sites in terms of vegetation structure (50-75% for understory cover and 2-3 strata). Slope was the most relevant abiotic variable in habitat selection due to its linkage to vegetation traits in this area.Research highlights: Our results can help managers to integrate biodiversity (endemic fauna species) into forest planning by preserving certain traits of the vegetation as part of a habitat (at a microhabitat level) selected by the fauna species. That planning should be implemented with both an adequate wood harvesting cuts system and specific silvicultural treatments.Key words: Chile; Nahuelbuta; rhinocryptidae; cluster analysis; rorest planning; vegetation structure.