Selection Of Auxiliary Variables Research Articles

Multiple imputation using auxiliary imputation variables that only predict missingness can increase bias due to data missing not at random

BackgroundEpidemiological and clinical studies often have missing data, frequently analysed using multiple imputation (MI). In general, MI estimates will be biased if data are missing not at random (MNAR). Bias due to data MNAR can be reduced by including other variables (“auxiliary variables”) in imputation models, in addition to those required for the substantive analysis. Common advice is to take an inclusive approach to auxiliary variable selection (i.e. include all variables thought to be predictive of missingness and/or the missing values). There are no clear guidelines about the impact of this strategy when data may be MNAR.MethodsWe explore the impact of including an auxiliary variable predictive of missingness but, in truth, unrelated to the partially observed variable, when data are MNAR. We quantify, algebraically and by simulation, the magnitude of the additional bias of the MI estimator for the exposure coefficient (fitting either a linear or logistic regression model), when the (continuous or binary) partially observed variable is either the analysis outcome or the exposure. Here, “additional bias” refers to the difference in magnitude of the MI estimator when the imputation model includes (i) the auxiliary variable and the other analysis model variables; (ii) just the other analysis model variables, noting that both will be biased due to data MNAR. We illustrate the extent of this additional bias by re-analysing data from a birth cohort study.ResultsThe additional bias can be relatively large when the outcome is partially observed and missingness is caused by the outcome itself, and even larger if missingness is caused by both the outcome and the exposure (when either the outcome or exposure is partially observed).ConclusionsWhen using MI, the naïve and commonly used strategy of including all available auxiliary variables should be avoided. We recommend including the variables most predictive of the partially observed variable as auxiliary variables, where these can be identified through consideration of the plausible casual diagrams and missingness mechanisms, as well as data exploration (noting that associations with the partially observed variable in the complete records may be distorted due to selection bias).

Interfacial dynamic impermeable crack analysis in dissimilar piezoelectric materials by a new interaction integral

Dynamic intensity factors (IFs) provide an important parameter for assessing the failure risk of an interfacial crack for piezoelectric composites exposed to electromechanical impact loadings. In the present research, a new dynamic interaction integral (I-integral) is built for computing the dynamic stress IFs (SIFs) and electric displacement IF (EDIF) of an interfacial crack located in dissimilar inhomogeneous piezoelectric media. Through proper selection of auxiliary variables, the domain expression of I-integral for the inhomogeneous piezoelectric bi-materials does not need to take into account any derivative term for any piezoelectric material property. Further, after rigorous theoretical derivation, the resulting I-integral is still valid for complex models where the integration domain contains other multiple interfaces, regardless of whether the extra materials are straight or curved. Incorporating the modified extended finite element approach, the accuracy is confirmed by checking the dynamic IFs extracted from the I-integral with referenced results. The domain-independence is tested by varying ranges of integration domains for inhomogeneous piezoelectric bi-materials and multi-interface piezoelectric composites. Finally, typical examples are employed to discuss the influences of the direction and magnitude of electric impact loading, combination of polarizations, inhomogeneous degree of piezoelectric bi-materials and complex distribution of diverse material properties on the dynamic IFs.

Random forest analysis and lasso regression outperform traditional methods in identifying missing data auxiliary variables when the MAR mechanism is nonlinear (p.s. Stop using Little's MCAR test).

The selection of auxiliary variables is an important first step in appropriately implementing missing data methods such as full information maximum likelihood (FIML) estimation or multiple imputation. However, practical guidelines and statistical tests for selecting useful auxiliary variables are somewhat lacking, leading to potentially biased estimates. We propose the use of random forest analysis and lasso regression as alternative methods to select auxiliary variables, particularly in situations in which the missing data pattern is nonlinear or otherwise complex (i.e., interactive relationships between variables and missingness). Monte Carlo simulations demonstrate the effectiveness of random forest analysis and lasso regression compared to traditional methods (t-tests, Little's MCAR test, logistic regressions), in terms of both selecting auxiliary variables and the performance of said auxiliary variables when incorporated in an analysis with missing data. Both techniques outperformed traditional methods, providing a promising direction for improvement of practical methods for handling missing data in statistical analyses.

Twinning quality sensors in wastewater treatment process via optimized echo state network-based soft sensors

The presence of a large amount of quality-related but hard-to-measure variables usually makes effective monitoring of industrial processes difficult, and even impossible. Soft computing techniques and digital twins can revolutionize standard approaches to solve this issue, even though industrial data are frustrated by nonlinearity, disturbances, and dynamic behaviors. In this light, this paper proposes a data-driven soft sensor with the help of the Fourier amplitude sensitivity test (FAST) and improved probabilistic regularized echo state network (IPRESN), then to twin the quality hardware sensors. Within this framework, the initial step is to rely on the FAST method to measure the collaborated importance of multiple process variables with respect to each quality variable. This quantification facilitates the selection of auxiliary variables for the training of IPRESN. Furthermore, a probabilistic regularization method is learned to improve the robust performance of the echo state network (ESN) by re-designing a new objective function to minimize the mean and variance of the modeling error. Additionally, the whale optimization algorithm (WOA) is improved and then used to optimize the critical hyper-parameters of ESN, thus mitigating the risks associated with suboptimal hyperparameter selection. The effectiveness of the proposed method is verified through a Benchmark Simulation Model 2 (BSM2) and a full-scale wastewater treatment plant data set. The findings show the potential of the proposed method in facilitating digital twin implementations for hardware sensors.

A comparison of strategies for selecting auxiliary variables for multiple imputation.

Multiple imputation (MI) is a popular method for handling missing data. Auxiliary variables can be added to the imputation model(s) to improve MI estimates. However, the choice of which auxiliary variables to include is not always straightforward. Several data-driven auxiliary variable selection strategies have been proposed, but there has been limited evaluation of their performance. Using a simulation study we evaluated the performance of eight auxiliary variable selection strategies: (1, 2) two versions of selection based on correlations in the observed data; (3) selection using hypothesis tests of the "missing completely at random" assumption; (4) replacing auxiliary variables with their principal components; (5, 6) forward and forward stepwise selection; (7) forward selection based on the estimated fraction of missing information; and (8) selection via the least absolute shrinkage and selection operator (LASSO). A complete case analysis and an MI analysis using all auxiliary variables (the "full model") were included for comparison. We also applied all strategies to a motivating case study. The full model outperformed all auxiliary variable selection strategies in the simulation study, with the LASSO strategy the best performing auxiliary variable selection strategy overall. All MI analysis strategies that we were able to apply to the case study led to similar estimates, although computational time was substantially reduced when variable selection was employed. This study provides further support for adopting an inclusive auxiliary variable strategy where possible. Auxiliary variable selection using the LASSO may be a promising alternative when the full model fails or is tooburdensome.

Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method

Model-based estimation of small area means can lead to reliable estimates when the area sample sizes are small. This is accomplished by borrowing strength across related areas using models linking area means to related covariates and random area effects. The effective selection of variables to be included in the linking model is important in small area estimation. The main purpose of this paper is to extend the earlier work on variable selection for area level and two-fold subarea level models to three-fold sub-subarea models linking sub-subarea means to related covariates and random effects at the area, sub-area, and sub-subarea levels. The proposed variable selection method transforms the sub-subarea means to reduce the linking model to a standard regression model and applies commonly used criteria for variable selection, such as AIC and BIC, to the reduced model. The resulting criteria depend on the unknown sub-subarea means, which are then estimated using the sample sub-subarea means. Then, the estimated selection criteria are used for variable selection. Simulation results on the performance of the proposed variable selection method relative to methods based on area level and two-fold subarea level models are also presented.

Application GIS and remote sensing for soil organic carbon mapping in a farm-scale in the hilly area of central Vietnam

Soil Organic Carbon (SOC) influences many soil properties including nutrient and water holding capacity, nutrient cycling and stability, improved water infiltration and aeration. It also is an essential parameter in the assessment of soil quality, especially for agricultural production. However, SOC mapping is a complicated process that is costly and time-consuming due to the physical challenges of the natural conditions that is being surveyed. The best model for SOC mapping is still in debate among many researchers. Recently, the development of machine learning and Geographical Information Systems (GIS) has provided the potential for more accurate spatial prediction of SOC content. This research was conducted in a relatively small-scale capacity in the Central Vietnam region. The aim of this study is to compare the accuracy of Inverse Distance Weighting (IDW), Ordinary Kriging (OK), and Random Forest (RF) methods for SOC interpolation, with a dataset of 47 soil samples for an area of 145 hectares. Three environmental variables including elevation, slope, and the Normalized Difference Vegetation Index (NDVI) were used for the RF model. In the RF model, the values of the number of variables randomly sampled as candidates at each split, (mtry), and the number of bootstrap replicates, (ntree), were determined in terms of 1 and 1,000 respectively The results at our research site showed that using IDW is the most accurate method for SOC mapping, followed by the methods of RF and OK respectively. Concerning SOC mapping based-on auxiliary variables, in areas where there is human activity, the selection of auxiliary variables should be carefully considered because the variation in the SOC may not only be due to environmental variables but also by farming technologies.

A Comparison of Model-Assisted Estimators, With and Without Data-Driven Transformations of Auxiliary Variables, With Application to Forest Inventory

Forest information is requested at many levels and for many purposes. Sampling-based national forest inventories (NFIs) can provide reliable estimates on national and regional levels. By combining expensive field plot data with different sources of remotely sensed information, from airplanes and/or satellite platforms, the precision in estimators of forest variables can be improved. This paper focuses on the design-based model-assisted approach to using NFI data together with remotely sensed data to estimate forest variables for small areas, where the variables studied are total growing stock volume, volume of Norway spruce (Picea abies), and volume of broad-leaved trees. Remote sensing variables may be highly correlated with one another and some may have poor predictive ability for target forest variables, and therefore model selection and/or coefficient shrinkage may be appropriate to improve the efficiency of model-assisted estimators of forest variables. For this purpose, one can use modern shrinkage estimators based on lasso, ridge, and elastic net regression methods. In a simulation study using real NFI data, Sentinel 2 remote-sensing data, and a national airborne laser scanning (ALS) campaign, we show that shrinkage estimators offer advantages over the (weighted) ordinary least-squares (OLS) estimator in a model-assisted setting. For example, for a sample size n of about 900 and with 72 auxiliary variables, the RMSE was up to 41% larger when based on OLS. We propose a data-driven method for finding suitable transformations of auxiliary variables, and show that it can improve estimators of forest variables. For example, when estimating volume of Norway spruce, using a smaller expert selection of auxiliary variables, transformations reduced the RMSE by up to 10%. The overall best results in terms of RMSE were obtained using shrinkage estimators and a larger set of 72 auxiliary variables. However, for this larger set of variables, the use of transformations yielded at most small improvements of RMSE, and at worst large increases of RMSE, except in combination with ridge and elastic net regression.

Improved cube-attack-like cryptanalysis of reduced-round Ketje-Jr and Keccak-MAC

At EUROCRYPT 2015, Dinur et al. proposed cube-attack-like cryptanalysis on reduced-round Keccak. The process of recovering the key is divided into the preprocessing and the online phase. The preprocessing phase is setting a look-up table by computing the cube sum of involved key bits. The online phase is computing the cube sum of auxiliary variables and recording the matching values in the table as candidates. Auxiliary variables help balance the complexity of the two phases by reducing the number of involved key bits. Following this idea, a series of works has been presented, mainly focusing on a better selection of cube variables, auxiliary variables and involved key bits.We provide new methods to select auxiliary variables and involved key bits. The first step is to get a precise algebraic expression of each bit after one round permutation. Then, combined with the corresponding constraints on these variables, we can construct a Mixed-integer Linear Programming (MILP) model. Secondly, unlike the previous idea that auxiliary variables are chosen to satisfy the CP-kernel property just for the consideration of controlling diffusion, we cancel this restriction and adopt a more skilled selection of auxiliary variables. Based on these two steps, we improve the cube-attack-like cryptanalysis in terms of the complexity.

An improved GM(1,3) model combining terrain factors and neural network error correction for urban land subsidence prediction

Urban land subsidence is a slow-density geology disaster caused by the withdrawal of groundwater or the application of water at the land surface. Developing a method of effectively monitoring, predicting and preventing land subsidence has become an urgent urban disaster issue and a great challenge. Traditional mathematical statistics prediction models lack physical meaning. Thus, in this paper, an improved third-order gray prediction GM(1, 3) model that combines terrain factors and neural network error corrections is proposed for urban land subsidence prediction. First, the correlation between land subsidence and terrain factors is verified through a correlation analysis. Second, a geospatial weight matrix based on the terrain factors is presented for auxiliary variable selection. Finally, a neural network is used to model the prediction errors to improve the model accuracy. Precision levelling data for Haiyan County, Zhejiang Province, China from 1999 to 2016 are used as the experimental data. The results show that the proposed method can achieve the same accuracy level as precision levelling. The average absolute error of three-phrase prediction is less than 10 mm, and the relative error can reach 0.4%. The proposed method can be expected to replace precision levelling for the prediction of long-term land subsidence and provide decision support for urban settlement disaster prevention.

Prediction of Soil Organic Carbon based on Landsat 8 Monthly NDVI Data for the Jianghan Plain in Hubei Province, China

High-precision maps of soil organic carbon (SOC) are beneficial for managing soil fertility and understanding the global carbon cycle. Digital soil mapping plays an important role in efficiently obtaining the spatial distribution of SOC, which contributes to precision agriculture. However, traditional soil-forming factors (i.e., terrain or climatic factors) have weak variability in low-relief areas, such as plains, and cannot reflect the spatial variation of soil attributes. Meanwhile, vegetation cover hinders the acquisition of the direct information of farmland soil. Thus, useful environmental variables should be utilized for SOC prediction and the digital mapping of such areas. SOC has an important effect on crop growth status, and remote sensing data can record the apparent spectral characteristics of crops. The normalized difference vegetation index (NDVI) is an important index reflecting crop growth and biomass. This study used NDVI time series data rather than traditional soil-forming factors to map SOC. Honghu City, located in the middle of the Jianghan Plain, was selected as the study region, and the NDVI time series data extracted from Landsat 8 were used as the auxiliary variables. SOC maps were estimated through stepwise linear regression (SLR), partial least squares regression (PLSR), support vector machine (SVM), and artificial neural network (ANN). Ordinary kriging (OK) was used as the reference model, while root mean square error of prediction (RMSEP) and coefficient of determination of prediction (R2P) were used to evaluate the model performance. Results showed that SOC had a significant positive correlation in July and August (0.17, 0.29) and a significant negative correlation in January, April, and December (−0.23, −0.27, and −0.23) with NDVI time series data. The best model for SOC prediction was generated by ANN, with the lowest RMSEP of 3.718 and highest R2P of 0.391, followed by SVM (RMSEP = 3.753, R2P = 0.361) and PLSR (RMSEP = 4.087, R2P = 0.283). The SLR model was the worst model, with the lowest R2P of 0.281 and highest RMSEP of 3.930. ANN and SVM were better than OK (RMSEP = 3.727, R2P = 0.372), whereas PLSR and SLR were worse than OK. Moreover, the prediction results using single-data NDVI or short time series NDVI showed low accuracy. The effect of the terrain factor on SOC prediction represented unsatisfactory results. All these results indicated that the NDVI time series data can be used for SOC mapping in plain areas and that the ANN model can maximally extract additional associated information between NDVI time series data and SOC. This study presented an effective method to overcome the selection of auxiliary variables for digital soil mapping in plain areas when the soil was covered with vegetation. This finding indicated that the time series characteristics of NDVI were conducive for predicting SOC in plains.

Empirical Analysis for Crop Yield Forecasting in India

Several factors, including weather vagaries, possess a serious threat to agricultural crop production in India and also are noteworthy risks to the economy. Crop yield depends on nutrition level of soils, fertilizer availability and cost, pest control, agro-meteorological input parameters like temperature, rainfall and other factors. Further, each particular crop needs specific growing weather conditions. Therefore, prognosticating crop yield is a challenging task for every nation. Statistical models are the most commonly used tools to forecast the crop yield, whereas statistical forecasting model for predicting dynamic behavior of crop yield should be able to take advantage not only of historical data of crop yield, but also the impact of various driving forces of the external environment. This paper describes both the linear regression and time-series models to predict crop yield efficiently and precisely. In particular, Bajra yield data for Alwar district of Rajasthan have been considered for empirical fitting of the models. Additionally, the selection of auxiliary variables, based on the knowledge of crop growth stages, has mediated the outperformance of time-series model.

Structured Genome-Wide Association Studies with Bayesian Hierarchical Variable Selection.

It becomes increasingly important in using genome-wide association studies (GWAS) to select important genetic information associated with qualitative or quantitative traits. Currently, the discovery of biological association among SNPs motivates various strategies to construct SNP-sets along the genome and to incorporate such set information into selection procedure for a higher selection power, while facilitating more biologically meaningful results. The aim of this paper is to propose a novel Bayesian framework for hierarchical variable selection at both SNP-set (group) level and SNP (within group) level. We overcome a key limitation of existing posterior updating scheme in most Bayesian variable selection methods by proposing a novel sampling scheme to explicitly accommodate the ultrahigh-dimensionality of genetic data. Specifically, by constructing an auxiliary variable selection model under SNP-set level, the new procedure utilizes the posterior samples of the auxiliary model to subsequently guide the posterior inference for the targeted hierarchical selection model. We apply the proposed method to a variety of simulation studies and show that our method is computationally efficient and achieves substantially better performance than competing approaches in both SNP-set and SNP selection. Applying the method to the Alzheimers Disease Neuroimaging Initiative (ADNI) data, we identify biologically meaningful genetic factors under several neuroimaging volumetric phenotypes. Our method is general and readily to be applied to a wide range of biomedical studies.

Application of Ordinary Kriging and Regression Kriging Method for Soil Properties Mapping in Hilly Region of Central Vietnam

Soil property maps are essential resources for agricultural land use. However, soil properties mapping is costly and time-consuming, especially in the regions with complicated topographic conditions. This study was conducted in a hilly region of Central Vietnam with the following objectives: (i) to evaluate the best environmental variables to estimate soil organic carbon (SOC), total nitrogen (TN), and soil reaction (pH) with a regression kriging (RK) model, and (ii) to compare the accuracy of the ordinary kriging (OK) and RK methods. SOC, TN, and soil pH data were measured at 155 locations within the research area with a sampling grid of 2 km × 2 km for a soil layer from 0 to 30 cm depth. From these samples, 117 were used for interpolation, and the 38 randomly remaining samples were used for evaluating accuracy. The chosen environmental variables are land use type (LUT), topographic wetness index (TWI), and transformed soil adjusted vegetation index (TSAVI). The results indicate that the LUT variable is more effective than TWI and TSAVI for determining TN and pH when using the RK method, with a variance of 7.00% and 18.40%, respectively. In contrast, a combination of the LUT and TWI variables is the best for SOC mapping with the RK method, with a variance of 14.98%. The OK method seemed more accurate than the RK method for SOC mapping by 3.33% and for TN mapping by 10% but the RK method was found more precise than the OK method for soil pH mapping by 1.81%. Further selection of auxiliary variables and higher sampling density should be considered to improve the accuracy of the RK method.

Resource optimization and power allocation in in-band full duplex-enabled non-orthogonal multiple access networks

In this paper, the problem of uplink (UL) and downlink (DL) resource optimization, mode selection, and power allocation is studied for wireless cellular networks under the assumption of in-band full duplex base stations, non-orthogonal multiple access (NOMA) operation, and queue stability constraints. The problem is formulated as a network utility maximization problem for which a Lyapunov framework is used to decompose it into two disjoint subproblems of auxiliary variable selection and rate maximization. The latter is further decoupled into a user association and mode selection (UAMS) problem and a UL/DL power optimization (UDPO) problem that are solved concurrently. The UAMS problem is modeled as a many-to-one matching problem whose goal is to associate users to small cell base stations and select transmission mode (half-/full-duplex and orthogonal/NOMA). Then, an algorithm is proposed to solve the problem by finding a pairwise stable matching. Subsequently, the UDPO problem is formulated as a sequence of convex problems and is solved using the concave–convex procedure. Simulation results demonstrate that the proposed scheme is effective in allocating UL and DL power levels after dynamically selecting the operating mode and the served users, under different traffic intensity conditions, network density, and self-interference cancellation capability. The proposed scheme is shown to achieve up to 63% and 73% of gains in UL and DL packet throughput, and 21% and 17% in UL and DL cell edge throughput, respectively, compared with the existing baseline schemes.

Event sustainability and transportation policy: A model-based cluster analysis for a cross-comparison of hallmark events

Transportation is one of the main topics in the wide-ranging theme of event sustainability. The aim of this article is to make a contribution towards the evaluation of the sustainable transportation policies implemented by the organizers of hallmark events, to establish an accurate and objective methodology for a cross-comparison. The organizers, policy makers and the host community are the main stakeholders interested in an evaluation of the degree of sustainability implicit in the mobility policy of an event. A non-hierarchical model-based clustering is performed, using a sample of periodical Italian hallmark events, and then examined to determine whether there is a difference in the distribution of a selection of auxiliary variables among the clusters. The results show that neither visitor number, nor the number of inhabitants in the host city, is associated with the cluster membership. However, the theme of the event appears to be associated with the estimated partition.

How auxiliary variables and plant data collection affect closed-loop performance of inferential control

The design of property estimators for inferential control is addressed in this paper, and the effects of the auxiliary variables (estimator’s inputs) and of the approach to collect plant data, used to compute the model coefficients, are investigated. The concept of steady-state closed-loop consistency, which is the ability of an estimator to guarantee low offset in the unmeasured controlled variables, is adopted and theoretical results about this property are derived. It is shown how the selection of auxiliary variables represents the most crucial design step that determines the final closed-loop performance of an inferential control system. When this selection is done on a steady-state closed-loop consistency basis, the closed-loop performance is satisfactory, and it is secondary how the dataset is built. On the other hand, when “inconsistent” inputs are used, the performance is, in general, poor and may be significantly affected (in positive or in negative) by the dataset characteristics.