Subsample Size Research Articles

Canadian Library Human Resources Short-Term Supply and Demand Crisis Is Averted, But a Significant Long-Term Crisis Must Be Addressed

Canadian Library Human Resources Short-Term Supply and Demand Crisis Is Averted, But a Significant Long-Term Crisis Must Be Addressed

Logistic Regression with Exposure Biomarkers and Flexible Measurement Error

Regression calibration, refined regression calibration, and conditional scores estimation procedures are extended to a measurement model that is motivated by nutritional and physical activity epidemiology. Biomarker data, available on a small subset of a study cohort for reasons of cost, are assumed to adhere to a classical measurement error model, while corresponding self-report nutrient consumption or activity-related energy expenditure data are available for the entire cohort. The self-report assessment measurement model includes a person-specific random effect, the mean and variance of which may depend on individual characteristics such as body mass index or ethnicity. Logistic regression is used to relate the disease odds ratio to the actual, but unmeasured, dietary or physical activity exposure. Simulation studies are presented to evaluate and contrast the three estimation procedures, and to provide insight into preferred biomarker subsample size under selected cohort study configurations.

Variables influençant l’épaisseur du liège dans les forêts de chênes-lièges espagnoles: une proposition de modélisation

In this study, we evaluate the influence of different variables on cork thickness in cork oak forests. For this purpose, first we fitted a multilevel linear mixed model for predicting average cork thickness, and then identified the explanatory covariates by studying their possible correlation with random effects. The model for predicting average cork thickness is described as a stochastic process, where a fixed, deterministic model, explains the mean value, while unexplained residual variability is described and modelled by including random parameters acting at plot, tree, plot × cork harvest and residual within-tree levels, considering the spatial covariance structure between trees within the same plot. Calibration is carried out by using the best linear unbiased predictor (BLUP) theory. Different alternatives were tested to determine the optimum subsample size which was found to be appropriate at four trees. Finally, the model was applied and its performance in the estimation of cork production was tested and compared with the cork weight model traditionally used in Spain.

Effects of a reduced subsampling protocol on calculation of growth and body condition indices

The impact of a reduced subsampling protocol on growth and body condition calculations was examined for bluegill, white, and black crappie. A maximum of 5 fish per 10-mm length group were randomly subsampled from 9 years of survey data collected under a maximum of 10 fish per 10-mm length group subsampling protocol (referred to as P10). The new protocol (referred to as P5) reduced age and growth subsample size by an average of 26, 23, and 21 fish for bluegill, white, and black crappie surveys, respectively. Significant relationships were observed between P5 and P10 results for mean length-at-age (MLA), coefficients of variation associated with MLA (CV), Von Bertlanffy growth constants (K), mean relative weight for stock-length and greater fish (Wr-S), and CV values associated with Wr-S. Estimates of MLA were statistically different between P5 and P10 designs for all species, however, the differences were 3 mm or less in 90% or more of the time. Based on the results of this study, reducing the stratified subsampling protocol from a maximum of 10 fish to a maximum of 5 fish per 10-mm length group would have minimal effect on fishery management decisions based on standard growth and body condition parameters for these three species in Nebraska.

Sampling Almonds for Aflatoxin, Part I: Estimation of Uncertainty Associated with Sampling, Sample Preparation, and Analysis

Domestic and international regulatory limits have been established for aflatoxin in almonds and other tree nuts. It is difficult to obtain an accurate and precise estimate of the true aflatoxin concentration in a bulk lot because of the uncertainty associated with the sampling, sample preparation, and analytical steps of the aflatoxin test procedure. To evaluate the performance of aflatoxin sampling plans, the uncertainty associated with sampling lots of shelled almonds for aflatoxin was investigated. Twenty lots of shelled almonds were sampled for aflatoxin contamination. The total variance associated with measuring B1 and total aflatoxins in bulk almond lots was estimated and partitioned into sampling, sample preparation, and analytical variance components. All variances were found to increase with an increase in aflatoxin concentration (both B1 and total). By using regression analysis, mathematical expressions were developed to predict the relationship between each variance component (total, sampling, sample preparation, and analysis variances) and aflatoxin concentration. Variance estimates were the same for B1 and total aflatoxins. The mathematical relationships can be used to estimate each variance for a given sample size, subsample size, and number of analyses other than that measured in the study. When a lot with total aflatoxins at 15 ng/g was tested by using a 10 kg sample, a vertical cutter mixer type of mill, a 100 g subsample, and high-performance liquid chromatography analysis, the sampling, sample preparation, analytical, and total variances (coefficient of variation, CV) were 394.7 (CV, 132.4%), 14.7 (CV, 25.5%), 0.8 (CV, 6.1%), and 410.2 (CV, 135.0%), respectively. The percentages of the total variance associated with sampling, sample preparation, and analytical steps were 96.2, 3.6, and 0.2, respectively.

Sampling Hazelnuts for Aflatoxin: Uncertainty Associated with Sampling, Sample Preparation, and Analysis

The variability associated with the aflatoxin test procedure used to estimate aflatoxin levels in bulk shipments of hazelnuts was investigated. Sixteen 10 kg samples of shelled hazelnuts were taken from each of 20 lots that were suspected of aflatoxin contamination. The total variance associated with testing shelled hazelnuts was estimated and partitioned into sampling, sample preparation, and analytical variance components. Each variance component increased as aflatoxin concentration (either B1 or total) increased. With the use of regression analysis, mathematical expressions were developed to model the relationship between aflatoxin concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific aflatoxin concentration. The sampling, sample preparation, and analytical variances associated with estimating aflatoxin in a hazelnut lot at a total aflatoxin level of 10 ng/g and using a 10 kg sample, a 50 g subsample, dry comminution with a Robot Coupe mill, and a high-performance liquid chromatographic analytical method are 174.40, 0.74, and 0.27, respectively. The sampling, sample preparation, and analytical steps of the aflatoxin test procedure accounted for 99.4, 0.4, and 0.2% of the total variability, respectively.

Development of a standardized large river bioassessment protocol (LR‐BP) for macroinvertebrate assemblages

AbstractEfforts to develop benthic macroinvertebrate sampling protocols for the bioassessment of lotic ecosystems have been focused largely on wadeable systems. As these methods became increasingly refined and accepted, a growing number of monitoring agencies expanded their work and are now developing sampling protocols for non‐wadeable large rivers. Large rivers can differ from wadeable streams in many ways that preclude the use of some wadeable stream sampling protocols. Hence, resource managers need clear and consistent large river bioassessment protocols for measuring ecological integrity that are cost effective, logistically feasible, and meet or are adaptable to the multi‐purpose sampling needs of researchers and managers. We conducted a study using an experimental macroinvertebrate sampling method that was designed to overcome limitations of several methods currently in use. Our objectives were to: (1) determine the appropriate number of sampling points needed; (2) determine an appropriate laboratory subsample size to use and (3) examine how varying reach length affects assemblage characteristics. For six reaches in each of two large rivers, we sampled the macroinvertebrates of both banks at 12 transects separated by increasingly larger distances using a multi‐habitat, semi‐quantitative technique. Interpretation of results relied on the values attained for nine benthic macroinvertebrate assemblage metrics. Results from Monte Carlo methods indicated that, using the sampling methods described herein, a representative sample of the assemblage was collected by sampling both banks on 6 transects. Across all sites, we did not observe a consistent relationship between transect spacing (i.e. total reach length) and metric values, indicating that our sampling protocol was relatively robust with respect to variation in reach length. Therefore, flexibility exists that permits the study reach length to be dictated by the spatial scale (e.g. repeating geomorphic units) in question. For those preferring to use a fixed reach length, we recommend that transects be spaced at a minimum of 100 m intervals over a 500 m distance. We recommend that the field method be coupled with a fixed laboratory subsample size of 300 organisms for bioassessment purposes, with the recognition that a subsample size of 500 organisms may be needed to meet the objectives of more rigorous studies. It is likely this approach will over‐sample sites of uniform composition, but the goal was to develop a robust sampling protocol that would perform well across sites of differing habitat composition. Possible modifications to the method to streamline its future application in the field are provided. Published in 2006 by John Wiley & Sons, Ltd.

Comparison of Separable Components in Different Samples

Abstract. Imagine we have two different samples and are interested in doing semi‐ or non‐parametric regression analysis in each of them, possibly on the same model. In this paper, we consider the problem of testing whether a specific covariate has different impacts on the regression curve in these two samples. We compare the regression curves of different samples but are interested in specific differences instead of testing for equality of the whole regression function. Our procedure does allow for random designs, different sample sizes, different variance functions, different sets of regressors with different impact functions, etc. As we use the marginal integration approach, this method can be applied to any strong, weak or latent separable model as well as to additive interaction models to compare the lower dimensional separable components between the different samples. Thus, in the case of having separable models, our procedure includes the possibility of comparing the whole regression curves, thereby avoiding the curse of dimensionality. It is shown that bootstrap fails in theory and practice. Therefore, we propose a subsampling procedure with automatic choice of subsample size. We present a complete asymptotic theory and an extensive simulation study.

Structural segregation and scales of spatial dependency in Abies amabilis forests

AbstractQuestion: Is a mosaic structure apparent in the spatial distribution of trees in old‐growth Abies amabilis forests?Location: Montane forests of the western Cascade Range, Washington, USA.Methods: Maps of tree locations were created for study areas located in two, 300‐year old stands and a single 600‐year old stand. Stand structure parameters were calculated using several subsample quadrats sizes (56.25 ‐ 306.25 m2), which were drawn randomly with replacement at a density of 250 quadrats per ha from the stem maps in the computing environment. Spatial cross‐covariance functions between different canopy strata were estimated using the spline cross‐correlogram.Results: Negative spatial correlation (segregation) between subcanopy tree density and areas of high overstorey occupancy was detected. Understorey and midstorey tree densities were positively spatially correlated. These general trends were apparent across the range of observational scales investigated. Significant spatial correlation between canopy strata was observed at spatial scales of 12 ‐ 44 m and extended to the largest scales in the 600‐year old stand.Conclusion: The observed spatial segregation between canopy strata supports the hypothesis that old A. amabilis forests form fine‐scale structural mosaics. Structural segregation at small scales may be due to competitive interactions as well as exogenous forcing of tree locations (e.g. by mortality due to pathogens or disturbance), however segregation at large scales in the 600‐year old stand is likely due to exogenous factors alone. This study reinforces the idea that horizontal heterogeneity is an emergent property of old‐growth forests.

Structural segregation and scales of spatial dependency in Abies amabilis forests

Question: Is a mosaic structure apparent in the spatial distribution of trees in old-growth Abies amabilis forests? Location: Montane forests of the western Cascade Range, Washington, USA. Methods: Maps of tree locations were created for study areas located in two, 300-year old stands and a single 600-year old stand. Stand structure parameters were calculated using several subsample quadrats sizes (56.25 - 306.25 m 2 ), which were drawn randomly with replacement at a density of 250 quadrats per ha from the stem maps in the computing environment. Spatial cross-covariance functions between different canopy strata were estimated using the spline cross-correlogram. Results: Negative spatial correlation (segregation) between subcanopy tree density and areas of high overstorey occupancy was detected. Understorey and midstorey tree densities were positively spatially correlated. These general trends were apparent across the range of observational scales investigated. Significant spatial correlation between canopy strata was observed at spatial scales of 12 - 44 m and extended to the largest scales in the 600-year old stand. Conclusion: The observed spatial segregation between canopy strata supports the hypothesis that old A. amabilis forests form fine-scale structural mosaics. Structural segregation at small scales may be due to competitive interactions as well as exogenous forcing of tree locations (e.g. by mortality due to pathogens or disturbance), however segregation at large scales in the 600-year old stand is likely due to exogenous factors alone. This study reinforces the idea that horizontal heterogeneity is an emergent property of old-growth forests.

Consistent Testing for Stochastic Dominance under General Sampling Schemes

We propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of Stochastic Dominance of arbitrary order in the general K-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate general dependence amongst the prospects which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for conditional ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some N−1/2 local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentring the test statistic and using full-sample bootstrap methods. We compare the two methods in theory and in practice.

On optimal spatial subsample size for variance estimation

We consider the problem of determining the optimal block (or subsample) size for a spatial subsampling method for spatial processes observed on regular grids. We derive expansions for the mean square error of the subsampling variance estimator, which yields an expression for the theoretically optimal block size. The optimal block size is shown to depend in an intricate way on the geometry of the spatial sampling region as well as characteristics of the underlying random field. Final expressions for the optimal block size make use of some nontrivial estimates of lattice point counts in shifts of convex sets. Optimal block sizes are computed for sampling regions of a number of commonly encountered shapes. Numerical studies are performed to compare subsampling methods as well as procedures for estimating the theoretically best block size.

Variation of Analytical Results for Peanuts in Energy Bars and Milk Chocolate

Peanuts contain proteins that can cause severe allergic reactions in some sensitized individuals. Studies were conducted to determine the percentage of recovery by an enzyme-linked immunosorbent assay (ELISA) method in the analysis for peanuts in energy bars and milk chocolate and to determine the sampling, subsampling, and analytical variances associated with testing energy bars and milk chocolate for peanuts. Food products containing chocolate were selected because their composition makes sample preparation for subsampling difficult. Peanut-contaminated energy bars, noncontaminated energy bars, incurred milk chocolate containing known levels of peanuts, and peanut-free milk chocolate were used. A commercially available ELISA kit was used for analysis. The sampling, sample preparation, and analytical variances associated with each step of the test procedure to measure peanut protein were determined for energy bars. The sample preparation and analytical variances were determined for milk chocolate. Variances were found to be functions of peanut concentration. Sampling and subsampling variability associated with energy bars accounted for 96.6% of the total testing variability. Subsampling variability associated with powdered milk chocolate accounted for >60% of the total testing variability. The variability among peanut test results can be reduced by increasing sample size, subsample size, and number of analyses. For energy bars the effect of increasing sample size from 1 to 4 bars, subsample size from 5 to 20 g, and number of aliquots quantified from 1 to 2 on reducing the sampling, sample preparation, and analytical variance was demonstrated. For powdered milk chocolate, the effects of increasing subsample size from 5 to 20 g and number of aliquots quantified from 1 to 2 on reducing sample preparation and analytical variances were demonstrated. This study serves as a template for application to other foods, and for extrapolation to different sizes of samples and subsamples as well as numbers of analyses.

Testing Green Coffee for Ochratoxin A, Part I: Estimation of Variance Components

The variability associated with testing lots of green coffee beans for ochratoxin A (OTA) was investigated. Twenty-five lots of green coffee were tested for OTA contamination. The total variance associated with testing green coffee was estimated and partitioned into sampling, sample preparation, and analytical variances. All variances increased with an increase in OTA concentration. Using regression analysis, mathematical expressions were developed to model the relationship between OTA concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific OTA concentration. Testing a lot with 5 microg/kg OTA using a 1 kg sample, Romer RAS mill, 25 g subsamples, and liquid chromatography analysis, the total, sampling, sample preparation, and analytical variances were 10.75 (coefficient of variation [CV] = 65.6%), 7.80 (CV = 55.8%), 2.84 (CV = 33.7%), and 0.11 (CV = 6.6%), respectively. The total variance for sampling, sample preparation, and analytical were 73, 26, and 1%, respectively.

A Monte Carlo Simulation of Biotic Metrices as a Function of Subsample Size

ABSTRACT A Monte Carlo simulation was performed to explore the effect of subsample size selection on the numeric value and variation of eleven common macroinvertebrate metrices. A test species list was constructed from real-world freshwater stream samples possessing a densely populated, highly diverse lognormal species distribution. Metrics were classified into one of three groups based upon the relation of the median of replicates of successively larger subsamples to the “true” value obtained from the entire sample, and changes in variance about the median as a function of increasing subsample size. Variance was considerable in all cases where the size of the subsample was small compared to the size of the sample population. Results provide insight into the effect of increasing level of effort on the power to quantity between sample differences.

Interregional nonlinear height–diameter model with random coefficients for stone pine in Spain

An individual-tree height–diameter model was developed for stone pine (Pinus pinea L.) in Spain. Five biparametric nonlinear equations were fitted and evaluated based on a data set consisting of 8614 trees from 455 plots located in the four most important regions where the species occurs in Spain. Because of the problem of high correlation among observations taken from the same sampling unit, a mixed-model approach, including random coefficients, is proposed. Several stand variables, such as density, dominant height, or diametric distribution percentiles, were included in the model as covariates to explain among plot variability. To determine interregional variability among the regions studied, regional effects were included in the model using fixed dummy variables. Two models, one for inland regions and one for coastal regions, were found to be sufficient to explain regional variability in the height–diameter relationship for the species in Spain. Mixed models allow predictive role in two ways: a typical response, including only fixed effects, and a calibrated response, where random effects are predicted and included in the model from the prior measurement of the height in a subsample of trees. Different alternatives were tested to determine optimum subsample size. Measurement of the height of the 20% largest trees in the plot has been shown to be a useful approach.

Sample preparation and presampling of pistachios.

A theory has been developed to quantify the reduction of subsample variance of aflatoxin contamination, which is observed when granular materials are wet slurried, rather than dry ground, during subsample homogenization. A coefficient of variation, based on particle size distribution, subsample size, and probability of contamination, is predicted. The theory is tested with dry ground and with wet slurried pistachios, and excellent quantitative agreement is obtained. A 32% increase in the mean aflatoxin level is observed as well when wet slurrying is applied. Although no statistical explanation for this effect can be found, it is suggested that it is related to physiochemical binding between the nut matrix, which is (partly) broken by wet slurrying, and aflatoxin, making the extraction of more toxin possible. Other parameters that may affect slurrying results have been investigated as well.

A longitudinal exploration of alcohol use and problems comparing managerial and nonmanagerial men and women

The purpose of the present study was to compare the job attitude and drinking context correlates of alcohol beliefs, consumption, and problems between managerial and nonmanagerial women and men. Using longitudinal, self-report data from 1244 workers in a large manufacturing organization, we found that managerial women reported significantly higher levels of alcohol problems on a number of measures on both Times 1 and 2 surveys. Using partial correlations and controlling for Time 1 levels of the alcohol-related dependent variables, we found that few work attitudes predicted the outcomes of escape drinking reasons, alcohol consumption, and alcohol problems. However, those correlations that were significant reflected a differential pattern for managerial women as compared to managerial men and nonmanagerial women and men. Due to the small subsample size of managerial women, we regard these findings as suggestive only. We discuss the findings in terms of the stress-reduction hypothesis of alcohol consumption.

Distributional properties of estimated capability indices based on subsamples

AbstractUnder the assumption of normality, the distribution of estimators of a class of capability indices, containing the indices $C_p$, $C_{pk}$, $C_{pm}$ and $C_{pmk}$, is derived when the process parameters are estimated from subsamples. The process mean is estimated using the grand average and the process variance is estimated using the pooled variance from subsamples collected over time for an in‐control process. The derived theory is then applied to study the use of hypothesis testing to assess process capability. Numerical investigations are made to explore the effect of the size and number of subsamples on the efficiency of the hypothesis test for some indices in the studied class. The results for $C_{pm}$ and $C_{pk}$ indicate that, even when the total number of sampled observations remains constant, the power of the test decreases as the subsample size decreases. It is shown how the power of the test is dependent not only on the subsample size and the number of subsamples, but also on the relative location of the process mean from the target value. As part of this investigation, a simple form of the cumulative distribution function for the non‐central $\chi^2$‐distribution is also provided. Copyright © 2003 John Wiley & Sons, Ltd.

Boosted leave-many-out cross-validation: the effect of training and test set diversity on PLS statistics.

It is becoming increasingly common in quantitative structure/activity relationship (QSAR) analyses to use external test sets to evaluate the likely stability and predictivity of the models obtained. In some cases, such as those involving variable selection, an internal test set--i.e., a cross-validation set--is also used. Care is sometimes taken to ensure that the subsets used exhibit response and/or property distributions similar to those of the data set as a whole, but more often the individual observations are simply assigned 'at random.' In the special case of MLR without variable selection, it can be analytically demonstrated that this strategy is inferior to others. Most particularly, D-optimal design performs better if the form of the regression equation is known and the variables involved are well behaved. This report introduces an alternative, non-parametric approach termed 'boosted leave-many-out' (boosted LMO) cross-validation. In this method, relatively small training sets are chosen by applying optimizable k-dissimilarity selection (OptiSim) using a small subsample size (k = 4, in this case), with the unselected observations being reserved as a test set for the corresponding reduced model. Predictive errors for the full model are then estimated by aggregating results over several such analyses. The countervailing effects of training and test set size, diversity, and representativeness on PLS model statistics are described for CoMFA analysis of a large data set of COX2 inhibitors.