This study investigates the compromise allocation of multivariate stratified sampling with complete response and nonresponse. We have formulated a multivariate stratified sampling problem as a mathematical programming problem to estimate p-population means with complete response and nonresponse for a fixed cost. Then, the compromise allocations for sample designs are determined by implementing intuitionistic fuzzy programming using optimistic and pessimistic solution strategies. A simulation study is carried out using the Stratify R software program to demonstrate the complete solution process. In wildlife, agricultural and marketing-related surveys, the study could be helpful. Also, the national planning policies related to surveys in such cases this study could be helpful. This study is an attempt to solve the sampling optimization problem using the Lingo-18 optimization program.

Data related to the strata and their characteristics for the nonresponse case.

Data related to strata and their characteristics for the complete response case.

Allocation of trace value with incurred survey cost for complete response case.

Allocation of trace values with incurred survey cost for the nonresponse case.

BackgroundTo address the limitations of commonly used cross-validation methods, the linear regression method (LR) was proposed to estimate population accuracy of predictions based on the implicit assumption that the fitted model is correct. This method also provides two statistics to determine the adequacy of the fitted model. The validity and behavior of the LR method have been provided and studied for linear predictions but not for nonlinear predictions. The objectives of this study were to 1) provide a mathematical proof for the validity of the LR method when predictions are based on conditional means, regardless of whether the predictions are linear or non-linear 2) investigate the ability of the LR method to detect whether the fitted model is adequate or inadequate, and 3) provide guidelines on how to appropriately partition the data into training and validation such that the LR method can identify an inadequate model.ResultsWe present a mathematical proof for the validity of the LR method to estimate population accuracy and to determine whether the fitted model is adequate or inadequate when the predictor is the conditional mean, which may be a non-linear function of the phenotype. Using three partitioning scenarios of simulated data, we show that the one of the LR statistics can detect an inadequate model only when the data are partitioned such that the values of relevant predictor variables differ between the training and validation sets. In contrast, we observed that the other LR statistic was able to detect an inadequate model for all three scenarios.ConclusionThe LR method has been proposed to address some limitations of the traditional approach of cross-validation in genetic evaluation. In this paper, we showed that the LR method is valid when the model is adequate and the conditional mean is the predictor, even when it is a non-linear function of the phenotype. We found one of the two LR statistics is superior because it was able to detect an inadequate model for all three partitioning scenarios (i.e., between animals, by age within animals, and between animals and by age) that were studied.

The intercept here is meaningful and tells us the level of True Overplacement when all other variables are 0, i.e. True Overplacement in empathy, before taking the test, without incentives for accuracy. We control for common variance from repeated measures using random intercepts for participants.

Meaning of mathematical symbols in decomposition formula.

We control for common variance from repeated measures using random intercepts for participants.

The values based on an S sampling scheme under non-response utilizing Population I

The structured sampling design for the estimation of MSE through simulation under non-response utilizing Population I

This study focuses on estimating a finite population cumulative distribution function (CDF) using two-stage and three-stage cluster sampling under non-response. This work is then extended to estimate the finite population CDF under non-response using stratified two-stage and three-stage cluster sampling. We propose two distinct families of CDF estimators, specifically designed for these complex surveys, namely classical ratio/product-type and exponential ratio/product-type. Furthermore, we introduce a difference estimator for the CDF under non-response, utilizing ancillary information about the variances and covariances of the estimators under these complex schemes. We provide mathematical expressions for the biases and mean squared errors of the proposed CDF estimators, based on first-order approximation. To evaluate the performance of the proposed estimators, we conduct extensive simulations and assess their efficiency. The simulation results demonstrate that the proposed families of estimators perform well under different sampling scenarios. Our findings indicate that difference CDF estimators are more explicit than the other estimators discussed. We support our theoretical claims by analyzing real datasets.

Evaluating REs of proposed CDF estimator of G(y) under non-response relative to utilizing Population I

Mathematical details of the computation of the means, variances, and covariance of the nonstationary Gompertz process.

Extensive research work has been done for the estimation of population mean using bivariate auxiliary information based on conventional measures. Conventional measures of the auxiliary variables provide suspicious results in the presence of outliers/extreme values. However, non-conventional measures of the auxiliary variables include quartile deviation, mid-range, inter-quartile range, quartile average, tri-mean, Hodge-Lehmann estimator etc. give efficient results in case of extreme values. Unfortunately, non-conventional measures are not used by survey practitioners to enhance the estimation of unknown population parameters using bivariate auxiliary information. In this article, difference-cum-exponential-type estimators for population mean utilizing bivariate auxiliary information based on non-conventional measures under simple and stratified random sampling schemes have been suggested. Mathematical properties such as bias and mean squared error are derived. To support theoretical findings, various real-life applications are used to confirm the superiority of the suggested estimators as compared to the competing estimators under study.

Extensive research work has been done for the estimation of population mean using bivariate auxiliary information based on conventional measures. Conventional measures of the auxiliary variables provide suspicious results in the presence of outliers/extreme values. However, non-conventional measures of the auxiliary variables include quartile deviation, mid-range, inter-quartile range, quartile average, tri-mean, Hodge-Lehmann estimator etc. give efficient results in case of extreme values. Unfortunately, non-conventional measures are not used by survey practitioners to enhance the estimation of unknown population parameters using bivariate auxiliary information. In this article, difference-cum-exponential-type estimators for population mean utilizing bivariate auxiliary information based on non-conventional measures under simple and stratified random sampling schemes have been suggested. Mathematical properties such as bias and mean squared error are derived. To support theoretical findings, various real-life applications are used to confirm the superiority of the suggested estimators as compared to the competing estimators under study.

Parental environmental effects can be a rapid and effective means for clonal plants in response to temporally or spatially varying environments. However, few studies have quantitatively measured the ecological significance of parental effects in aquatic clonal plants. In this study, we developed a two-generation (parent-offspring) growth model to examine the parental effects of nitrogen (N) conditions on summed and mean performance of clonal offspring of one wetland species Alternanthera philoxeroides. We also examined the role of survival status and developmental stage of clonal offspring in the consequence of parental effects in aquatic clonal plants. Our results indicated direct evidence that (1) there were significant non-linear correlations between the performance of parental plants and initial status of clonal offspring (i.e., the mass and number of clonal propagules); (2) parental N effects on the summed performance of clonal offspring were content-dependent (i.e., there were significant interactions between parental and offspring N effects), while parental effects on the mean performance of offspring were independent of offspring conditions; (3) parental effects mainly occurred at the early development stage of clonal offspring, and then gradually declined at the late stage; (4) the context-dependent parental effects on the summed performance of clonal offspring gradually strengthened when offspring survival was high. The mathematical models derived from the experimental data may help researchers to not only deeply explore the ecological significance of parental environmental effects in aquatic clonal plants, but also to reveal the importance of potential factors that have been often neglected in empirical studies.

Mesenchymal stem cell dynamics involve cell proliferation and cell differentiation into cells of distinct functional type, such as osteoblasts, adipocytes, or chondrocytes. Electrically active implants influence these dynamics for the regeneration of the cells in damaged tissues. How applied electric field influences processes of individual stem cells is a problem mostly unaddressed. The mathematical approaches to study stem cell dynamics have focused on the stem cell population as a whole, without resolving individual cells and intracellular processes. In this paper, we present a theoretical framework to describe the dynamics of a population of stem cells, taking into account the processes of the individual cells. We study the influence of the applied electric field on the cellular processes. We test our mean-field theory with the experiments from the literature, involving in vitro electrical stimulation of stem cells. We show that a simple model can quantitatively describe the experimentally observed time-course behavior of the total number of cells and the total alkaline phosphate activity in a population of mesenchymal stem cells. Our results show that the stem cell differentiation rate is dependent on the applied electrical field, confirming published experimental findings. Moreover, our analysis supports the cell density-dependent proliferation rate. Since the experimental results are averaged over many cells, our theoretical framework presents a robust and sensitive method for determining the effect of applied electric fields at the scale of the individual cell. These results indicate that the electric field stimulation may be effective in promoting bone regeneration by accelerating osteogenic differentiation.

Several members of the suggested families of CDF estimators under non-response

MSE of all the estimators based on simulation studies under SRS.