Error Variance Components Research Articles

The appraisal of pedotransfer functions with legacy data; an example from southern Africa

Predictions of soil hydraulic properties by pedotransfer functions (PTFs) must be treated with caution when they are used in an application domain which differs from the domain of their original development and calibration. However, in some settings, scientists may have little alternative but to use PTFs calibrated elsewhere. In this paper we consider how legacy data can be used to evaluate PTFs in new regions, paying particular attention to the challenges that arise when, as is often the case, the legacy data are not obtained by independent random sampling, and may be clustered at multiple scales. We undertook this work in southern Africa (Zimbabwe, Zambia and Malawi) where PTFs have been little-used, despite the scarcity of direct measurements of the soil properties of interest. We evaluated the extent to which existing PTFs provide a useful tool for the prediction of soil moisture content at field-capacity (−33 kPa) and permanent wilting-point (−1500 kPa) at different spatial scales. Soil legacy data for Zambia, Zimbabwe and Malawi were collated from various sources and PTFs from temperate and tropical domains were evaluated. We examined error variance components of predictions at within-profile, within-site and between-site scales; and estimated their mean errors. In general the better-performing PTFs (with respect to bias and the size of the error variance components) were ones calibrated with data from a tropical domain. This was most apparent at −1500 kPa. However, not all PTFs calibrated with data on tropical soils performed well, and predictions from some PTFs calibrated over a temperate domain were better at −33 kPa. The observations were spatially clustered, with data from different depth intervals in the same profile, from profiles in the same experimental site or farm, and from clusters across the region. This enabled us to show, with an appropriate mixed model analysis, that PTFs which effectively capture regional-scale variation may be less useful for predicting variation within a profile. We propose that such studies, based on legacy data, and with a suitable linear mixed model, should be used to screen PTFs of any provenance before their wider application.

Benefits of Doing Generalizability Theory Analyses within Structural Equation Modeling Frameworks: Illustrations Using the Rosenberg Self-Esteem Scale

Although generalizability theory (GT) designs typically are analyzed using analysis of variance (ANOVA) procedures, they also can be integrated into structural equation models (SEMs). In this tutorial, we review basic concepts for conducting univariate and multivariate GT analyses and demonstrate advantages of doing such analyses within SEM frameworks using multi-occasion data from the Rosenberg Self-Esteem Scale. We show how GT-SEMs can reproduce variance components for both relative and absolute error obtained from ANOVA models, estimate effects of changes made to measurement procedures and universes of generalization, incorporate estimation methods to correct for scale coarseness, represent essential tau-equivalent or congeneric relationships, include additional method factors for negatively and positively worded items, incorporate bifactor designs, allow for formal tests of model fit when warranted, and derive Monte Carlo confidence intervals for key parameters of interest. We provide code for conducting the demonstrated analyses using several statistical packages in extended online Supplemental Material.

Performance, Variance Components, and Acceptability of Pro-vitamin A-Biofortified Sweetpotato in Southern Africa and Implications in Future Breeding.

In sub-Saharan Africa (SSA), vitamin A deficiency (VAD) is a major cause of blindness in children under 5 years. Sweetpotato (Ipomea batatas L.) is widely grown in this region, and pro-vitamin A varieties could help to combat such problems. Fourteen newly introduced orange-fleshed sweetpotato (OFSP) varieties from the International Potato Centre (CIP) and two local checks were evaluated at four environments using a 4 × 4 triple-lattice design for total tuber yield, marketable yield, unmarketable yield, total tuber numbers, marketable tuber numbers, unmarketable tuber numbers, dry matter content, and sensory characteristics on boiled sweetpotato. Since varieties were previously tested intensively by CIP under diverse conditions, the focus of the current study was to determine their acceptability by farmers. Across-environment ANOVA showed highly significant differences (P < 0.001) for environments, genotypes, and genotype × environment interaction (GE) for all traits studied. Variety Cecelia outperformed the rest in three environments. Cecelia, Erica, Ininda, and Lourdes were found to be the top four most stable and high-yielding varieties. Genetic gains of the top four varieties over the preferred local check Mai Chenje ranged from 135 to 184%, and across-environment broad-sense heritability was 60% for tuber yield. Furthermore, farmers accepted the dry matter content (which was >25%) and taste of all the introduced OFSP varieties. Since there was a high acceptability by farmers, introductions from CIP could help improve human nutrition. Despite the appropriate design, the error variance component was the highest for all traits, and proper field plot techniques were proposed in future breeding and testing activities.

Statistical modelling of measurement error in wet chemistry soil data

AbstractThere is a growing demand for high‐quality soil data. However, soil measurements are subject to many error sources. We aimed to quantify uncertainties in synthetic and real‐world wet chemistry soil data through a linear mixed‐effects model, including batch and laboratory effects. The use of synthetic data allowed us to investigate how accurately the model parameters were estimated for various experimental measurement designs, whereas the real‐world case served to explore if estimates of the random effect variances were still accurate for unbalanced datasets with few replicates. The variance estimates for synthetic data were unbiased, but limited laboratory information led to imprecise estimates. The same was observed for unbalanced synthetic datasets, where 20, 50 and 80% of the data were removed randomly. Removal led to a sharp increase of the interquartile range (IQR) of the variance estimates for batch effect and the residual. The model was also fitted to real‐world and total organic carbon (TOC) data, provided by the Wageningen Evaluating Programmes for Analytical Laboratories (WEPAL). For , the model yielded unbiased estimates with relatively small IQRs. However, the limited number of batches with replicate measurements (5.8%) caused the batch effect to be larger than expected. A strong negative correlation between batch effect and residual variance suggested that the model could not distinguish well between these two random effects. For TOC, batch effect was removed from the model as no replicates were available within batches. Again, unbiased model estimates were obtained. However, the IQRs were relatively large, which could be attributed to the smaller dataset with only a single replicate measurement. Our findings demonstrated the importance of experimental measurement design and replicate measurements in the quantification of uncertainties in wet chemistry soil data.Highlights Accurate uncertainty quantification depends on the experimental measurement design. Linear mixed‐effects models can be used as a tool to quantify uncertainty in wet chemistry soil data. Lack of replicate measurements leads to poor estimates of error variance components. Measurement error in wet chemistry soil data should not be ignored.

Estimating Measurement Errors and Score Dependability of NECO 2019 Mathematics Examination

This study estimated measurement error and score dependability in examinations using the Generalizability Theory. Scores obtained by the students (object of measurements) in examinations are affected by multiple sources of error (facets), and these scores are used in taking relative and absolute decisions about the students. There is, therefore, needed to estimate measurement error and score dependability to find the extent of the contributions of the facets to error in examination scores. Three research questions and one hypothesis were used to guide the study. The study population comprised 5,085 SS3 students of the 34 Government-owned senior secondary schools in Yenagoa LGA of Bayelsa State 2019/2020 academic session. 10 schools were selected using simple random sampling technic and the 1,525 SS3 students of the selected schools formed the sample. section A of the 2018 NECO Mathematics main paper and 2018 NECO Mathematics Marking Scheme were used to collect the data. EduG version 6.0-e based on ANOVA and Generalizability theory was used to answer the three research questions. A 95% confidence interval was computed using the standard error variance components to test the hypothesis. The findings of the study revealed that some hidden sources of error were at play in the study. the students’ facets (σ2S) made the highest contribution to measurement error in examination scores followed by the residual (σ2SIM). Also, the Students’ facet was significantly different (p&lt; 0.05) in its contributions to measurement error, while the other facets and their interactions were not significantly different in their contribution to measurement error. Hence, Ho1 was not accepted for the students’ facet but accepted for other facets. An increase in the level of markers from 1 to 4 with level of items 5 yielded an outcome of 0.84 to 0.91 respectively, a generalizability coefficient of 0.94 high enough to rank order students according to their relative abilities in examinations was obtained when the level of markers was at 2 with an increment in level of items to 10. An index of dependability of 0.93 that is high enough to maximize reliability was obtained when we have level of markers at 2 and the items at 10.

A Hierarchical Bayes Unit-Level Small Area Estimation Model for Normal Mixture Populations

National statistical agencies are regularly required to produce estimates about various subpopulations, formed by demographic and/or geographic classifications, based on a limited number of samples. Traditional direct estimates computed using only sampled data from individual subpopulations are usually unreliable due to small sample sizes. Subpopulations with small samples are termed small areas or small domains. To improve on the less reliable direct estimates, model-based estimates, which borrow information from suitable auxiliary variables, have been extensively proposed in the literature. However, standard model-based estimates rely on the normality assumptions of the error terms. In this research we propose a hierarchical Bayesian (HB) method for the unit-level nested error regression model based on a normal mixture for the unit-level error distribution. Our method proposed here is applicable to model cases with unit-level error outliers as well as cases where each small area population is comprised of two subgroups, neither of which can be treated as an outlier. Our proposed method is more robust than the normality based standard HB method (Datta and Ghosh, Annals Stat. 19, 1748–1770, 1991) to handle outliers or multiple subgroups in the population. Our proposal assumes two subgroups and the two-component mixture model that has been recently proposed by Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) to address outliers. To implement our proposal we use a uniform prior for the regression parameters, random effects variance parameter, and the mixing proportion, and we use a partially proper non-informative prior distribution for the two unit-level error variance components in the mixture. We apply our method to two examples to predict summary characteristics of farm products at the small area level. One of the examples is prediction of twelve county-level crop areas cultivated for corn in some Iowa counties. The other example involves total cash associated in farm operations in twenty-seven farming regions in Australia. We compare predictions of small area characteristics based on the proposed method with those obtained by applying the Datta and Ghosh (Annals Stat. 19, 1748–1770, 1991) and the Chakraborty et al. (Int. Stat. Rev. 87, 158–176, 2019) HB methods. Our simulation study comparing these three Bayesian methods, when the unit-level error distribution is normal, or t, or two-component normal mixture, showed the superiority of our proposed method, measured by prediction mean squared error, coverage probabilities and lengths of credible intervals for the small area means.

ADJUSTMENT OF CADASTRAL NETWORK USING LEAST-SQUARES VARIANCE COMPONENT ESTIMATION

Abstract. The role of the stochastic model very important in data processing of geodetic network since it describes the accuracy of the measurements and their correlation with each other. Knowledge of weights of the observables is required to provide a better understanding of the sources of errors and to model the error, hence the weights need to be determined correctly. This study concentrates on the estimation of variance components from different types of instruments used in the cadastral survey. The ideas are to combine the conventional and advanced instruments in a traverse network to enhance the estimated variance component in the stochastic model. Thus, Least Squares Variance Component Estimation (LS-VCE) method was used in this study because the method is simple, flexible and attractive due to the precision of variance estimators that can be directly obtained. Observation data come with several types of instruments such as chain measurement, Electronic Distance Measurement and total station were utilized. The findings showed that LS-VCE method was very reliable in cadastral network application. Besides, the results revealed that the estimated variance components for distance scale error, σp seem to become unrealistic for each data tested. It was found that the traverse network which included chain survey, showed the insignificant result to the precision of station coordinates when the measurements were combined.

Implications of correlations and genotype by environment interactions among cotton traits

The existence of negative correlations, coupled with significant genotype x environment interaction (GE) among cotton traits poses both opportunities and challenges in breeding. This study aimed at determining the existence of GE on seed cotton ( Gossypium hirsutum L.) yield, lint yield, earliness index, gin out turn ratio, 100 seed weight, split boll weight and fuzz grade and correlations, among these traits, as well as understanding the implications on variety evaluation and release. Ten genotypes from Cotton Research Institute, Zimbabwe, were evaluated across seven locations, during the 2012/13 and 2013/14 cropping years with three replications at each location. Seed cotton and lint yield, earliness index, gin out turn ratio, 100-seed weight, split boll weight and fuzz grade were measured on the genotypes at all locations. Analysis of variance for GE showed significant differences (P<0.05) on most traits, except earliness index. There were huge GE and error variance components on seed cotton yield and allied traits that reduced heritability and correlation among these traits. Seed cotton and lint yield were significantly correlated (P<0.001; r = 0.95) to each other; while split boll weight had significant correlation (P<0.004; r = 0.82) with 100-seed weight. The genotype plus GE biplot analysis showed that SZ 9523 had high and stable yield and desirable fuzz grade, which made it an ideal genotype for release. All locations belonged to one complex mega-environment with Chisumbanje Research Station more representative and most discriminating location which can be used in early generation testing of cotton. Key Words: Gossypium hirsutum , lint, mega-environments

The exchangeability of brief intelligence tests for children with intellectual giftedness: Illuminating error variance components’ influence on IQs

AbstractThis study examined the exchangeability of total scores (i.e., intelligent quotients [IQs]) from three brief intelligence tests. Tests were administered to 36 children with intellectual giftedness, scored live by one set of primary examiners and later scored by a secondary examiner. For each student, six IQs were calculated, and all 216 values were submitted to a generalizability theory analysis. Despite strong convergent validity and reliability evidence supporting brief IQs, the resulting dependability coefficient was only .80, which indicates relatively low exchangeability across tests and examiners. Although error variance components representing the effects of the examiner, examiner‐by‐examinee interaction, the examiner‐by‐test interaction, and the test contributed little to IQ variability, the component representing the test‐by‐examinee interaction contributed about one‐third of the variance in IQs. These findings hold implications for selecting and interpreting brief intelligence tests and general testing for intellectual giftedness.

A guide to analyzing biodiversity experiments

Aims: The aim of this guide is to provide practical help for ecologists who analyze data from biodiversity–ecosystem functioning experiments. Our approach differs from others in the use of least squares-based linear models (LMs) together with restricted maximum likelihood-based mixed models (MMs) for the analysis of hierarchical data. An original data set containing diameter and height of young trees grown in monocultures, 2- or 4-species mixtures under ambient light or shade is used as an example. Methods: Starting with a simple LM, basic features of model fitting and the subsequent analysis of variance (ANOVA) for significance tests are summarized. From this, more complex models are developed. We use the statistical software R for model fitting and to demonstrate similarities and complementarities between LMs and MMs. The formation of contrasts and the use of error (LMs) or random-effects (MMs) terms to account for hierarchical data structure in ANOVAs are explained. Important Findings: Data from biodiversity experiments can be analyzed at the level of entire plant communities (plots) and plant individuals. The basic explanatory term is species composition, which can be divided into contrasts in many ways depending on specific biological hypotheses. Typically, these contrasts code for aspects of species richness or the presence of particular species. For significance tests in ANOVAs, contrast terms generally are compared with remaining variation of the explanatory terms from which they have been ‘carved out’. Once a final model has been selected, parameters (e.g. means or slopes for fixed-effects terms and variance components for error or random-effects terms) can be estimated to indicate the direction and size of effects.

Improved uncertainty quantification in nondestructive assay for nonproliferation

This paper illustrates methods to improve uncertainty quantification (UQ) for non-destructive assay (NDA) measurements used in nuclear nonproliferation. First, it is shown that current bottom-up UQ applied to calibration data is not always adequate, for three main reasons: (1) Because there are errors in both the predictors and the response, calibration involves a ratio of random quantities, and calibration data sets in NDA usually consist of only a modest number of samples (3–10); therefore, asymptotic approximations involving quantities needed for UQ such as means and variances are often not sufficiently accurate; (2) Common practice overlooks that calibration implies a partitioning of total error into random and systematic error, and (3) In many NDA applications, test items exhibit non-negligible departures in physical properties from calibration items, so model-based adjustments are used, but item-specific bias remains in some data. Therefore, improved bottom-up UQ using calibration data should predict the typical magnitude of item-specific bias, and the suggestion is to do so by including sources of item-specific bias in synthetic calibration data that is generated using a combination of modeling and real calibration data. Second, for measurements of the same nuclear material item by both the facility operator and international inspectors, current empirical (top-down) UQ is described for estimating operator and inspector systematic and random error variance components. A Bayesian alternative is introduced that easily accommodates constraints on variance components, and is more robust than current top-down methods to the underlying measurement error distributions.

Dynamic Association Mapping based on a Kalman Filter Model using GAW 18 Data Set

Background Linear mixed model with pedigree information commonly employed to detect and correct for genetic relationship in cross sectional genomics research. Main aim of this study was to dynamic association mapping by using a random walk-Kalman filter approach for analyzing GAW18 dataset. We also extended the model to incorporate stationary process by auto regressive structure for dynamic gene and environmental effects. Methods We used random walk model and it is given below 22 1 , (0, ); , (0, ) t t t t e t t t t n y N NA α e e σ α α η η α σ + = + ∞ = + In (1) the first equation is called the observation equation and the second equation is called the state equation. We assumed that observations, t y , depends on unobservable quantity, t α , and our aim was to do statistical inference on t α (states) Results Error, genetic and permanent environmental variance components were predicted as 17.3 (0.0006), 10.9 (0.0007) and 8.2 (0.0006) using genomic relation matrix for and 18.0 (0.0007), 9.2 (0.0008) and 8.4(0.0006) using pedigree relation matrix for diastolic blood pressure. Rs 11711953 from time point 1, 2 and 3 is found to be associated with MAP4 gene. Conclusions Probably due to small number of time points the model did not detect all true genomic signals. Genomic relationship matrix gave better inflation factors. Random walk is a non stationary process and in this paper we extended the model for stationary case by tuning ∆ parameter. In genomic studies failing to taken into account of longitudinal gene and environmental effects over time may lead to either undetection of true signals and/ or may also lead to false positives due to stochastic errors.

The impact of metrology study sample size on uncertainty in IAEA safeguards calculations

Quantitative conclusions by the International Atomic Energy Agency (IAEA) regarding States' nuclear material inventories and flows are provided in the form of material balance evaluations (MBEs). MBEs use facility estimates of the material unaccounted for together with verification data to monitor for possible nuclear material diversion. Verification data consist of paired measurements (usually operators' declarations and inspectors' verification results) that are analysed one-item-at-a-time to detect significant differences. Also, to check for patterns, an overall difference of the operator-inspector values using a “D (difference) statistic” is used. The estimated DP and false alarm probability (FAP) depend on the assumed measurement error model and its random and systematic error variances, which are estimated using data from previous inspections (which are used for metrology studies to characterize measurement error variance components). Therefore, the sample sizes in both the previous and current inspections will impact the estimated DP and FAP, as is illustrated by simulated numerical examples. The examples include application of a new expression for the variance of the D statistic assuming the measurement error model is multiplicative and new application of both random and systematic error variances in one-item-at-a-time testing.

Bayesian Estimation of Genotypes Means, Precision, and Genetic Gain Due to Selection from Routinely Used Barley Trials

ABSTRACTBlock designs are normally used in evaluation of crop varieties. The responses or yield data arising from designed trials in a crop variety improvement program are generally analyzed using linear mixed models under the frequentist paradigm. Such analysis ignores information on the genotypic parameters available from previous similar trials. Another approach with a relatively wider inferential framework is Bayesian, which integrates the prior information with the likelihood of current data. While the Bayesian approach has been implemented in numerous situations, stepwise presentation of its application in routine crop variety trials is not available. Illustrated with a dataset from a resolvable incomplete block design, this study provides a working tool for Bayesian analysis based on priors available from a series of crop variety trials. The posterior estimates of predicted values of mean of genotypes and precision, coefficient of variation, heritability, and genetic gain due to selection were obtained. The a posteriori mean of experimental error variance, coefficient of variation, and genotypic variance were lower for the Bayesian than the frequentist approach. The precision of a posteriori means was higher than that of predicted means under the frequentist approach. Accounting for incomplete blocks, rather than ignoring them, using a Bayesian approach showed a large reduction in estimates of error variance components and large increases in heritability and genetic gain. The current a posteriori distributions also serve as updated priors for future analysis. The step‐by‐step procedure presented here is recommended for routine analysis of variety trials.

Joint prior distributions for variance parameters in Bayesian analysis of normal hierarchical models

In random effect models, error variance (stage 1 variance) and scalar random effect variance components (stage 2 variances) are a priori modeled independently. Considering the intrinsic link between the stages 1 and 2 variance components and their interactive effect on the parameter draws in Gibbs sampling, we propose modeling the variances of the two stages a priori jointly in a multivariate fashion. We use random effects linear growth model for illustration and consider multivariate distributions to model the variance components jointly including the recently developed generalized multivariate log gamma (G-MVLG) distribution. We discuss these variance priors as well as the independent variance priors exercised in the literature in different aspects including noninformativeness and propriety of the associated posterior density. We show through an extensive simulation experiment that modeling the variance components of different stages multivariately results in better estimation properties for the response and random effect model parameters compared to independent modeling. We scrutinize the sensitivity of response model coefficient estimates to the parameters of considered noninformative variance priors and find that their full conditional expectations are insensitive to noninformative G-MVLG prior parameters. We apply independent and joint models for analysis of a real dataset and find that multivariate priors for variance components lead to better fitted hierarchical model than the univariate variance priors.

Statistical calibration of qRT-PCR, microarray and RNA-Seq gene expression data with measurement error models

The accurate quantification of gene expression levels is crucial for transcriptome study. Microarray platforms are commonly used for simultaneously interrogating thousands of genes in the past decade, and recently RNA-Seq has emerged as a promising alternative. The gene expression measurements obtained by microarray and RNA-Seq are, however, subject to various measurement errors. A third platform called qRT-PCR is acknowledged to provide more accurate quantification of gene expression levels than microarray and RNA-Seq, but it has limited throughput capacity. In this article, we propose to use a system of functional measurement error models to model gene expression measurements and calibrate the microarray and RNA-Seq platforms with qRT-PCR. Based on the system, a two-step approach was developed to estimate the biases and error variance components of the three platforms and calculate calibrated estimates of gene expression levels. The estimated biases and variance components shed light on the relative strengths and weaknesses of the three platforms and the calibrated estimates provide a more accurate and consistent quantification of gene expression levels. Theoretical and simulation studies were conducted to establish the properties of those estimates. The system was applied to analyze two gene expression data sets from the Microarray Quality Control (MAQC) and Sequencing Quality Control (SEQC) projects.

Small Sample Properties of Bayesian Multivariate Autoregressive Time Series Models

The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.

Estimation of weaning age effects on growth performance in berkshire pigs.

Analysis for back fat thickness (BFAT) and daily body weight gains from birth to the end of a performance test were conducted to find an optimal method for estimation of weaning age effects and to ascertain impacts of weaning age on the growth performance of purebred Berkshire pigs from a closed population in Korea. Individual body weights were measured at birth (B), at weaning (W: mean, 22.9 d), at the beginning of the performance test (P: mean, 72.7 d), and at the end of the performance test (T: mean, 152.4 d). Further, the average daily gains in body weight (ADG) of 3,713 pigs were analyzed for the following periods: B to W (DGBW), W to P (DGWP), P to T (DGPT), B to P (DGBP), B to T (DGBT), and W to T (DGWT). Weaning ages ranged from 17 to 34 d, and were treated as fixed (WF), random with (WC) and random without (WU) consideration of an empirical relationship between weaning ages in the models. WF and WC produced the lowest AIC (Akaike Information Criterion) and least fractions of error variance components in multi-traits analysis, respectively. The fractions of variances due to diverse weaning age and the weaning age correlations among ADGs of different stages (when no overlapping allowed) by WC ranged from 0.09 to 0.35 and from −0.03 to 0.44, respectively. The maximum weaning age effects and optimal back fat thicknesses were attained at weaning ages of 27 to 32 d. With the exception of DGBW, the effects of weaning age on the ADGs increased (ranging from 1.50 g/d to 7.14 g/d) with increased weaning age. In addition, BFAT was reduced by 0.106 mm per increased day in weaning age. In conclusion, WC produced reasonable weaning age correlations, and improved the fitness of the model. Weaning age was one of crucial factors (comparable with heritability) influencing growth performance in Berkshire pigs. Further, these studies suggest that increasing weaning age up to 32 d can be an effective management strategy to improve growth performance. However, additional investigations of the costs and losses related to extension of the suckling period and on the extended range of weaning age are necessary to determine the productivity and safety of this practice in a commercial herd and production system.

Model-based inference for biomass estimation in a LiDAR sample survey in Hedmark County, NorwayThis article is one of a selection of papers from Extending Forest Inventory and Monitoring over Space and Time.

In forest inventories, regression models are often applied to predict quantities such as biomass at the level of sampling units. In this paper, we propose a model-based inference framework for combining sampling and model errors in the variance estimation. It was applied to airborne laser (LiDAR) data sets from Hedmark County, Norway, where the model error proportion of the total variance was found to be large for both scanning (airborne laser scanning) and profiling LiDAR when biomass was estimated. With profiling LiDAR, the model error variance component for the entire county was as large as 71% whereas for airborne laser scanning, it was 43% of the total variance. Partly, this reflects the better accuracy of the pixel-based regression models estimated from scanner data as compared with the models estimated from profiler data. The framework proposed in our study can be applied in all types of sample surveys where model-based predictions are made at the level of individual sampling units. Especially, it should be useful in cases where model-assisted inference cannot be applied due to the lack of a probability sample from the target population or due to problems of correctly matching observations of auxiliary and target variables.

Genetic relationships of body composition, serum leptin, and age at puberty in gilts12

Leptin produced by adipocytes acts through leptin receptors in the hypothalamus to control appetite and food intake and thus communicates information about degree of fatness. It is thought that a degree of body fat is required for initiation of puberty and maintenance of reproductive function in mammals. The objective of this study was to determine whether polymorphisms in the leptin (LEP), leptin receptor (LEPR), paired box 5 (PAX5), aldo-keto reductase (AKR), and pro-opiomelanocortin (POMC) genes were associated with age, leptin concentration, backfat as an indicator of body condition, or BW at puberty in 3 lines of gilts and to characterize genetic relationships among these traits. The first 2 lines, born in 2001, were formed by crossing maternal White Cross (Yorkshire x Maternal Landrace) gilts to Duroc (n = 210) or (lean) Landrace (n = 207) boars. The remaining line (n = 507), born in 2002, was formed by crossing progeny of the Duroc- and Landrace-sired lines. At first estrus, age, BW (BWP), and backfat (BFP) at puberty were recorded and blood was collected for leptin assays. Nine SNP were detected in candidate genes/regions: 1 in LEP, 3 in LEPR, 1 in PAX5, 2 in AKR, and 2 in POMC. Animals were genotyped for each of the SNP; genotypes were validated using GenoProb. The association model included fixed effects of farrowing group, covariates of SNP genotypic probabilities (from GenoProb), and random additive polygenic effects to account for genetic similarities between animals not explained by SNP. Variance components for polygenic effects and error were estimated using MTDFREML. Leptin concentrations were logarithmically transformed for data analysis. All 4 traits were moderately to highly heritable (0.38 to 0.48). Age and leptin at puberty had a significant (P < 0.01) genetic correlation at -0.63 +/- 0.097, and the genetic correlation between BWP and age at puberty was 0.65 +/- 0.083 (P < 0.01). Significant additive associations (a; P < 0.05) were detected at PAX5 for age at puberty (a = 3.2 d) and for BFP (a = 0.61 mm). One SNP in LEPR was associated with leptin concentration (a = 0.31 log units; P < 0.05). The associations from PAX5 correspond to a QTL peak for age at puberty detected on SSC1. Although not necessarily the causative mutation, this result implies that a QTL that can decrease age at puberty without increasing BFP and BWP at puberty may exist in this region in commercial pigs.