First-phase Sample Research Articles

Chain ratio and product estimators for population mode using two-phase sampling scheme

Background: For skewed datasets, the mode is utilized as a more appropriate measure of location. We formed chain ratio and product estimators for the population mode using two types of auxiliary information under the two-phase sampling scheme. Methods: Expressions for biases and mean square errors for the formed estimators up to the first order of approximation are obtained. The confidence intervals of the estimators are obtained and the aspects related to fixed cost and fixed variance are also studied. A simulation study is performed to support the theoretical outcomes. A real dataset is also provided which was collected from the department of agriculture, United States. Results: The simulation results for the fixed first-phase sample size and the second-phase sample size show that the mean square error is 0.035, the bias is 0.012, the confidence interval is 2.67-3.15, and the cost of the survey under the fixed variance is ₹ 194.67 of the proposed estimator , which is lower than 0.039, 0.055, 2.70-3.20, and ₹ 247.37 of the ratio estimator and 0.078, 0.041, 2.57-3.31, and ₹ 268.73 of the naive estimator . Conclusions: The simulation results show that the proposed estimator performs better than the ratio estimator and the naive estimator .

Design and analysis of two-phase studies with multivariate longitudinal data.

Two-phase studies are crucial when outcome and covariate data are available in a first-phase sample (e.g., a cohort study), but costs associated with retrospective ascertainment of a novel exposure limit the size of the second-phase sample, in whom the exposure is collected. For longitudinal outcomes, one class of two-phase studies stratifies subjects based on an outcome vector summary (e.g., an average or a slope over time) and oversamples subjects in the extreme value strata while undersampling subjects in the medium-value stratum. Based on the choice of the summary, two-phase studies for longitudinal data can increase efficiency of time-varying and/or time-fixed exposure parameter estimates. In this manuscript, we extend efficient, two-phase study designs to multivariate longitudinal continuous outcomes, and we detail two analysis approaches. The first approach is a multiple imputation analysis that combines complete data from subjects selected for phase two with the incomplete data from those not selected. The second approach is a conditional maximum likelihood analysis that is intended for applications where only data from subjects selected for phase two are available. Importantly, we show that both approaches can be applied to secondary analyses of previously conducted two-phase studies. We examine finite sample operating characteristics of the two approaches and use the Lung Health Study (Connett etal. (1993), Controlled Clinical Trials, 14, 3S-19S) to examine genetic associations with lung function decline overtime.

Variance estimation for mean growth from successive double sampling for stratification

Double sampling for stratification (2SS) is a sampling design that is widely used for forest inventories. We present the mathematical derivation of two appropriate variance estimators for mean growth from repeated 2SS with updated stratification on each measurement occasion. Both estimators account for substratification based on the transition of sampling units among the strata due to the updated allocation. For the first estimator, sizes of the substrata were estimated from the second-phase sample (sample plots), whereas the respective sizes in the second variance estimator relied on the larger first-phase sample. The estimators were empirically compared with a modified version of Cochran’s well-known 2SS variance estimator that ignores substratification. This was done by performing bootstrap resampling on data from two German forest districts. The major findings were as follows: (i) accounting for substratification, as implemented in both new estimators, has substantial impact in terms of significantly smaller variance estimates and bias compared with the estimator without substratification, and (ii) the second estimator with substrata sizes being estimated from the first-phase sample shows a smaller bias than the first estimator.

A New Estimator of Mean Using Double Sampling

Abstract In this paper, we consider the problem of estimation of population mean of a study variable by making use of first-phase sample mean and first-phase sample median of the auxiliary variable at the estimation stage. The proposed new estimator of the population mean is compared to the sample mean estimator, ratio estimator and the difference type estimator for the fixed cost of the survey by using the concept of two-phase sampling. The magnitude of the relative efficiency of the proposed new estimator has been investigated through simulation study.

Influence of footprint size and geolocation error on the precision of forest biomass estimates from space-borne waveform LiDAR

Space-borne LiDAR systems can potentially assist large-area assessments of forest resources, in particular when a subset of the acquired LiDAR footprints is combined with field surveys of forest stand characteristics at footprint location. When combined, space-borne LiDAR geolocation error and the footprint size may however have considerable effects on the estimation accuracy of forest stand variables, such as aboveground biomass (AGB). The aim of this study was to draw recommendations for future space-borne LiDAR systems, which should deliver data for unbiased AGB assessments. The recommendations were drawn from AGB estimations based on space-borne LiDAR waveforms simulated over a 1300ha large study site in southern Sweden. Large-footprint, nadir-looking satellite waveforms were simulated by stacking individual small-footprint, airborne LiDAR waveforms observed near a predefined sampling pattern. The stacked waveforms, represented by their metrics, were used as input for a two-phase systematic sampling in combination with model-assisted estimation or hybrid inference for estimating AGB and its variance. The second-phase sample included 264 inventory plots, whereas the first-phase sample included 1010 sample locations, where satellite waveforms were simulated. After simulating satellite waveforms with different footprint sizes and analyzing the AGB variance, the recommendation is to have a footprint size that is similar to the size of the field plots used for collecting reference data, i.e. 20m diameter in our case. For the optimal footprint size, AGB was estimated with a precision of 2.9Mg per hectare (2.9% of the average). The results also showed that variance estimates increased constantly with increasing geolocation error. For a geolocation error of 14m, variance estimates increased by 17%, which justifies investing additional efforts in minimizing it.

Variance estimation of DEE and regression estimator when a first-phase cluster sample is restratified

ABSTRACTWe consider a variance estimation when a stratified single stage cluster sample is selected in the first phase and a stratified simple random element sample is selected in the second phase. We propose explicit formulas of (asymptotically), we propose explicit formulas of (asymptotically) unbiased variance estimators for the double expansion estimator and regression estimator. We perform a small simulation study to investigate the performance of the proposed variance estimators. In our simulation study, the proposed variance estimator showed better or comparable performance to the Jackknife variance estimator. We also extend the results to a two-phase sampling design in which a stratified pps with replacement cluster sample is selected in the first phase.

Validation of Attitudes and Beliefs on Classroom Control Inventory among Beginning Teachers in Singapore Schools

Teachers’ attitudes and beliefs on classroom management contribute significantly to student learning and development. Despite its importance, research in this aspect, however, has still been stymied by the difficulty of measuring teachers’ classroom management attitudes and beliefs. Psychometrically sound instruments to measure teachers’ classroom management attitudes and beliefs are still unavailable for use in Asian classrooms. In view of such reality, this study was intended to evaluate the psychometric properties of the Attitudes and Beliefs of Classroom Control Inventory-Adapted (ABCC-A) in Singapore schools. Construct validation of ABCC-A was conducted in three studies. Participants’ responses to the 27-item ABCC inventory from the first-phase data collection (N = 512) were used in study 1 and study 2. Participants and their responses to the revised ABCC-A inventory from the second-phase data collection were used in study 3. In study 1, half of the first-phase data collection sample (N 1 = 259) was randomly selected for the exploratory factor analysis and reliability test. In the study 2, the other half of first-phase sample (N 2 = 253) will be used for the confirmatory factor analysis (CFA) test. In study 3, participants (N 3 = 41) who completed the revised ABCC-A, teacher efficacy scale, and questionnaire on teacher interaction questionnaires in the second-phase data collection will be used for convergent and discriminate validity tests. The CFA of ABCC-A revealed a good model fit of instruction management and people management subscales and acceptable evidence of invariance among different groups of beginning teachers in Singapore primary and secondary schools.

Estimating multiple treatment effects using two-phase semiparametric regression estimators

We propose a semiparametric two-phase regression estimator with a semiparametric generalized propensity score estimator for estimating average treatment effects in the presence of the first-phase sampling. The proposed estimator can be easily extended to any number of treatments and does not rely on a prespecified form of the response or outcome functions. The proposed estimator is shown to reduce bias found in standard estimators that ignore the first-phase sample design, and can have improved efficiency compared to the inverse propensity weighted estimators. Results from simulation studies and from an empirical study of NHANES are presented.

Estimating the proportions of closely related species: Performance of the two-phase ratio estimator

In many ecological field contexts, accurately classifying closely related species based on phenotypic characteristics may be difficult. In such cases, definitive classification of species may require expensive genetic analysis of tissues or extensive quantitative measurements. If inexpensive phenotype-based species classifications are highly correlated with expensive but definitive classifications, however, then estimating the proportion of a target species in a mixed species complex using a two-phase ratio estimator may prove cost-efficient. In two-phase ratio estimation, a first-phase sample is randomly selected, and phenotype is used to classify all individuals in the sample. A smaller, second-phase sample is then randomly selected from the first-phase sample, and a definitive method is used to classify the individuals in this subsample. Net relative efficiency (i.e., cost-effectiveness) of the optimally allocated two-phase ratio estimator of a proportion depends on the relative costs of classification at the first and second phases, on the phenotypic classification accuracy for the target species (sensitivity) and nontarget species (specificity), and on the magnitude of the target species proportion. Results are presented that allow assessment of the circumstances in which this two-phase estimation approach can be recommended over an equal-cost single-phase approach based only on expensive but definitive classification. An illustrative application of these methods is provided using an example of two closely related, sympatric, anadromous salmonid species: steelhead (Oncorhynchus mykiss) and coastal cutthroat trout (O. clarki clarki).

VARIANCE ESTIMATION IN TWO-PHASE SAMPLING

Two-phase sampling is often used for estimating a population total or mean when the cost per unit of collecting auxiliary variables, x, is much smaller than the cost per unit of measuring a characteristic of interest, y. In the first phase, a large sample s1 is drawn according to a specific sampling design p(s1), and auxiliary data x are observed for the units i∈s1. Given the first-phase sample s1, a second-phase sample s2 is selected from s1 according to a specified sampling design {p(s2∣s1) }, and (y, x) is observed for the units i∈s2. In some cases, the population totals of some components of x may also be known. Two-phase sampling is used for stratification at the second phase or both phases and for regression estimation. Horvitz–Thompson-type variance estimators are used for variance estimation. However, the Horvitz–Thompson (Horvitz & Thompson, J. Amer. Statist. Assoc. 1952) variance estimator in uni-phase sampling is known to be highly unstable and may take negative values when the units are selected with unequal probabilities. On the other hand, the Sen–Yates–Grundy variance estimator is relatively stable and non-negative for several unequal probability sampling designs with fixed sample sizes. In this paper, we extend the Sen–Yates–Grundy (Sen, J. Ind. Soc. Agric. Statist. 1953; Yates & Grundy, J. Roy. Statist. Soc. Ser. B 1953) variance estimator to two-phase sampling, assuming fixed first-phase sample size and fixed second-phase sample size given the first-phase sample. We apply the new variance estimators to two-phase sampling designs with stratification at the second phase or both phases. We also develop Sen–Yates–Grundy-type variance estimators of the two-phase regression estimators that make use of the first-phase auxiliary data and known population totals of some of the auxiliary variables.

Jackknife method for estimating the variance of the age composition using two-phase sampling with an application to commercial catches of swordfish ( Xiphias gladius)

An estimate of the age composition of a commercial swordfish catch and its variance was obtained using the replicate full jackknife estimator for two-phase sampling where the sampling units in the first phase are clusters (vessel-trips) and the units of the second phase are individual fishes. The jackknife variance estimator was compared with an analytical estimator of variance commonly used in fisheries studies which ignores the clustering, and assumes simple random sampling of individual fish. The application of these naïve estimators to the Chilean South Pacific swordfish fishery results in an underestimation of the variance. This is a consequence of using an inappropriate primary sampling unit of analysis in the first-phase sample where the vessel-trip unit is replaced by an individual fish unit, thus ignoring the intra-cluster correlation in age samples. The jackknife estimator of variance is an alternative useful for complex two-phase sampling designs.

A Comparative Analysis of Economics Graduates' Learning Attitudes: Implications for Teaching

We report on the results of a two-phase survey aiming to explore the learning preferences of graduates in economics, compare the findings with graduates in other disciplines, and identify the determinant dimensions of their developed learning preferences. Economics graduates are compared against business administration, engineering, accounting-finance-banking, trading-maritime-marketing, maths-stats-informatics, and public administration graduates. A group of miscellaneous graduates is also included for graduates not-classifiable in the aforementioned groups. Kolb's LSIv3 has been utilized in identifying student learning styles. First-phase sample consists of 288 graduates and second-phase sample consists of 496 graduates. All these graduates attended post-graduate programs classes at nine Greek major universities. Both samples are relatively balanced as regards gender participation with a small female prevalence over males. Results show assimilating types to be the prevailing group, followed by converging, diverging, and accommodating types for both phases. Economics graduates are predominantly assimilators, while significant differences are found mainly in the perceiving dimension of learning ((AC-CE) dimension in Kolb's model) between them and same learning style type graduates in other disciplines. A grid presentation of individual scores for all participants reveals a higher concentration of assimilating types for the second phase sample, while accommodating types are in relative scarcity in both phases. Factor analyses reveal that processing and transforming of information and experience into knowledge ((AE-RO) dimension in Kolb's model) is the most significant determinant dimension in student learning for all groups of graduates for both phases. Overall, results have implications for teaching of economics. The impact of selecting and implementing teaching strategies based on lectures is discussed and we argue in favor of active student engagement in the teaching-learning procedure. Finally, we put forward some propositions for further research.

Replication Variance Estimation for Two-Phase Stratified Sampling

In two-phase sampling, the second-phase sample is often a stratified sample based on the information observed in the first-phase sample. For the total of a population characteristic, either the double-expansion estimator or the reweighted expansion estimator can be used. Given a consistent first-phase replication variance estimator, we propose a consistent variance estimator that is applicable to both the double-expansion estimator and the reweighted expansion estimator. The proposed method can be extended to multiphase sampling.

Minmax designs for planning the second phase in a two‐phase case–control study

Two-phase designs, in which a subsample with validation or complete information data is sampled stratified both on outcome and covariate from a first-phase study with incomplete data, have been proposed over 10 years ago and have been proven to result in efficient estimates with respect to standard designs. The efficiency depends, however, on the sampling fractions within each stratum. Our aim is to present a strategy for obtaining an optimized design, i.e. sampling fractions, that makes use of available phase-one data of an existing case-control study considered as the first-phase sample when the focus is on estimating a parameter vector. No global optimal design exists and local optimal designs depend on scenarios comprising the true disease model and the association between the phase-one and phase-two information. We develop an admissibility test that rejects scenarios inconsistent with the phase-one data and, for the selected scenarios, determine a minmax D- or A-optimal design that protects against worst-case scenarios. This work is applied on two examples.

Adaptive cluster double sampling

We present a multi-phase variant of adaptive cluster sampling which allows the sampler to control the number of measurements of the variable of interest. A first-phase sample is selected using an adaptive cluster sampling design based on an inexpensive auxiliary variable associated with the survey variable. Then the network structure of the adaptive cluster sample is used to select an ordinary one-phase or two-phase subsample of units and the values of the survey variable associated with those units are recorded. The population mean is estimated by either a regression-type estimator or a Horvitz–Thompson-type estimator. The results of a simulation study show good performance of the proposed design, and suggest that in many real situations this design might be preferred to the ordinary adaptive cluster sampling design.

Variance estimation for two-phase stratified sampling

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Bayesian Sequential Two-Phase Sampling

Abstract We propose a sequential two-phase sample design to accommodate applications where conventional two-phase sampling cannot be used. First, we derive the optimal, the optimal myopic, and several approximate optimal myopic sequential decision procedures for subsampling a first-phase sample. Then we compare our procedure to that of the optimal (nonsequential) conventional two-phase sample design. In our application, the objective is inference about the age distribution of a population of fish using data on covariates (e.g., length, weight) obtained from all members of the first-phase sample and data on age obtained from the fish in the second-phase subsample.

Two-Phase Sampling of Tax Records for Business Surveys

A two-phase design used to sample tax records of businesses to obtain annual estimates of Canadian economic production is described. Classification information obtained from units in the first-phase sample is used during stratification for selection of the second-phase sample. Bernoulli sampling is employed. Given multiple precision constraints, optimal allocation requires solution of a convex programming problem. An approximate method is described and compared to the optimal approach. The efficiency of the two-phase design relative to one-phase alternatives is examined.

Ranked Set Sampling with Size-Biased Probability of Selection

Ranked set sampling as suggested by McIntyre (1952, Journal of Agricultural Research 3, 385-390) and Takahasi and Wakimoto (1968, Annals of the Institute of Statistical Mathematics 20, 1-31) may be combined with size-biased probability of selection. We assume that the natural first-phase sample is collected with probability of selection proportional to size for each unit. The objective is then to use the ranked set sampling procedure to obtain a second-phase sample and increase the efficiency of estimators relative to simple random sampling. Estimators of the population mean and the population size are considered. Computer simulated results are given, and an example using line-intercept sampling of vegetation is provided to illustrate computations. Finally, ranked set sampling with errors in ranking is considered with probability of selection proportional to size.