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The linear regression model is widely used in empirical work in economics, statistics, and many other disciplines. Researchers often include many covariates in their linear model specification in an attempt to control for confounders. We give inference methods that allow for many covariates and heteroscedasticity. Our results are obtained using high-dimensional approximations, where the number of included covariates is allowed to grow as fast as the sample size. We find that all of the usual versions of Eicker-White heteroscedasticity consistent standard error estimators for linear models are inconsistent under this asymptotics. We then propose a new heteroscedasticity consistent standard error formula that is fully automatic and robust to both (conditional) heteroscedasticity of unknown form and the inclusion of possibly many covariates. We apply our findings to three settings: parametric linear models with many covariates, linear panel models with many fixed effects, and semiparametric semi-linear models with many technical regressors. Simulation evidence consistent with our theoretical results is provided, and the proposed methods are also illustrated with an empirical application. Supplementary materials for this article are available online.

The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees-of-freedom adjustment), applied to the fixed-effects estimator for panel data with serially uncorrelated errors, is incon- sistent if the number of time periods T is fixed (and greater than 2) as the number of entities n increases. We provide a bias-adjusted HR estimator that is$\\sqrt{nT}$-consistent under any sequences (n, T) in which n and/or T increase to ∞. This estimator can be extended to handle serial correlation of fixed order.

In prevention science and related fields, large meta-analyses are common, and these analyses often involve dependent effect size estimates. Robust variance estimation (RVE) methods provide a way to include all dependent effect sizes in a single meta-regression model, even when the exact form of the dependence is unknown. RVE uses a working model of the dependence structure, but the two currently available working models are limited to each describing a single type of dependence. Drawing on flexible tools from multilevel and multivariate meta-analysis, this paper describes an expanded range of working models, along with accompanying estimation methods, which offer potential benefits in terms of better capturing the types of data structures that occur in practice and, under some circumstances, improving the efficiency of meta-regression estimates. We describe how the methods can be implemented using existing software (the “metafor” and “clubSandwich” packages for R), illustrate the proposed approach in a meta-analysis of randomized trials on the effects of brief alcohol interventions for adolescents and young adults, and report findings from a simulation study evaluating the performance of the new methods.

OpenCap, a smartphone- and web-based markerless system, has shown acceptable accuracy compared to marker-based systems, but lacks information on repeatability. This study fills this gap by evaluating the intersession repeatability of OpenCap and investigating the effects of clothing on gait kinematics. Twenty healthy volunteers participated in a test–retest study, performing walking and sit-to-stand tasks with minimal clothing and regular street wear. Segment lengths and lower-limb kinematics were compared between both sessions and for both clothing conditions using the root-mean-square-deviation (RMSD) for entire waveforms and the standard error of measurement (SEM) and minimal detectable change (MDC) for discrete kinematic parameters. In general, the RMSD test–retest values were 2.8 degrees (SD: 1.0) for walking and 3.3 degrees (SD: 1.2) for sit-to-stand. The highest intersession variability was observed in the trunk, pelvis, and hip kinematics of the sagittal plane. SEM and MDC values were on average 2.2 and 6.0 degrees, respectively, for walking, and 2.4 and 6.5 degrees for sit-to-stand. Clothing had minimal effects on kinematics by adding on average less than one degree to the RMSD values for most variables. The segment lengths showed moderate to excellent agreement between both sessions and poor to moderate agreement between clothing conditions. The study highlights the reliability of OpenCap for markerless motion capture, emphasizing its potential for large-scale field studies. However, some variables showed high MDC values above 5 degrees and thus warrant further enhancement of the technology. Although clothing had minimal effects, it is still recommended to maintain consistent clothing to minimize overall variability.

Adsorption is considered to be one of the most effective technologies widely used in global environmental protection areas. Modeling of experimental adsorption isotherm data is an essential way for predicting the mechanisms of adsorption, which will lead to an improvement in the area of adsorption science. In this paper, we employed three isotherm models, namely: Langmuir, Freundlich, and Dubinin-Radushkevich to correlate four sets of experimental adsorption isotherm data, which were obtained by batch tests in lab. The linearized and non-linearized isotherm models were compared and discussed. In order to determine the best fit isotherm model, the correlation coefficient (r2) and standard errors (S.E.) for each parameter were used to evaluate the data. The modeling results showed that non-linear Langmuir model could fit the data better than others, with relatively higher r2 values and smaller S.E. The linear Langmuir model had the highest value of r2, however, the maximum adsorption capacities estimated from linear Langmuir model were deviated from the experimental data.

The Sarcopenia Quality of Life (SarQoL) questionnaire, a sarcopenia-specific patient-reported outcome measure, evaluates quality of life with 55 items. It produces 7 domain scores and 1 overall quality of life score, all between 0 and 100 points. This study aims to contribute to the interpretation of the SarQoL scores by calculating the standard error of measurement (SEM) and smallest detectable change (SDC) in a sample of subjects from 9 studies. Subjects from 9 studies (conducted in Belgium, Brazil, Czech Republic, England, Greece, Lithuania, Poland and Spain) were included. The SEM, a measure of the error in the scores that is not due to true changes, was calculated by dividing the standard deviation of the difference between test and retest scores (SDdiff) by √2. The SDC, defined as change beyond measurement error, was calculated by multiplying SDdiff by 1.96. Bland-Altman plots were assessed for the presence of systematic errors. A total of 278 sarcopenic subjects, aged 77.67 ± 7.64 years and 61.5% women, were included. The SEM for the overall SarQoL score ranged from 0.18 to 4.20 points for the individual studies, and was 2.65 points when all subjects were analyzed together. The SDC for the overall score ranged from 0.49 to 11.65 points for the individual studies, and was 7.35 points for all subjects. The Bland-Altman plots revealed no systematic errors in the questionnaire. This study shows that, for individual subjects, a change in overall quality of life of at least 7.35 points (on a scale from 0 to 100) would have to be observed to confirm that a true change, beyond measurement error, has occurred. It also demonstrated that the SarQoL questionnaire is a precise instrument, with the observed scores within less than 3 points of the theoretical \"true score\".

Context effects, where a characteristic of an upper-level unit or cluster (e.g., a country) affects outcomes and relationships at a lower level (e.g., that of the individual), are a primary object of sociological inquiry. In recent years, sociologists have increasingly analyzed such effects using quantitative multilevel modeling. Our review of multilevel studies in leading sociology journals shows that most assume the effects of lower-level control variables to be invariant across clusters, an assumption that is often implausible. Comparing mixed-effects (random-intercept and slope) models, cluster-robust pooled OLS, and two-step approaches, we find that erroneously assuming invariant coefficients reduces the precision of estimated context effects. Semi-formal reasoning and Monte Carlo simulations indicate that loss of precision is largest when there is pronounced cross-cluster heterogeneity in the magnitude of coefficients, when there are marked compositional differences among clusters, and when the number of clusters is small. Although these findings suggest that practitioners should fit more flexible models, illustrative analyses of European Social Survey data indicate that maximally flexible mixed-effects models do not perform well in real-life settings. We discuss the need to balance parsimony and flexibility, and we demonstrate the encouraging performance of one prominent approach for reducing model complexity.

Kriging has been more and more widely used as a method to construct surrogate models in a variety of areas within the engineering field. The universal Kriging is less appealing than the ordinary Kriging in the case that an informed decision could be hardly made to select the variables for capturing the global trends in responses. The Penalized Blind Kriging (PBK) systematically carries out model selection with penalizing the likelihood function, which leads to improving the predictive performance of a universal Kriging model. However, the PBK demands the execution of an iterative algorithm, which involves repeatedly solving a possibly time-consuming optimization problem to find a varying optimal solution to the correlation coefficient vector. In this paper, the Lasso Kriging (LK) is proposed to not only improve the predictive performance but avoid the iterative computation. The LK selects the important variables fundamentally by solving a Lasso problem using the LARS algorithm with CV. The one-standard error rule is employed to compensate for less penalizing the regression coefficients than the PBK does. Given the selected important variables, unknown Kriging parameters are estimated in the same manner as in the universal Kriging. A linear and a nonlinear mathematical problem and seven highly nonlinear benchmark problems are used to demonstrate the effectiveness of the LK concerning the model selection and predictive performance as well as the computational efficiency. The LK proves to be an effective approach that both improves predictive accuracy as much as the PBK does and requires a little more computational complexity than the universal Kriging.

In panel data models and other regressions with unobserved effects, fixed effects estimation is often paired with cluster-robust variance estimation (CRVE) to account for heteroscedasticity and un-modeled dependence among the errors. Although asymptotically consistent, CRVE can be biased downward when the number of clusters is small, leading to hypothesis tests with rejection rates that are too high. More accurate tests can be constructed using bias-reduced linearization (BRL), which corrects the CRVE based on a working model, in conjunction with a Satterthwaite approximation for t-tests. We propose a generalization of BRL that can be applied in models with arbitrary sets of fixed effects, where the original BRL method is undefined, and describe how to apply the method when the regression is estimated after absorbing the fixed effects. We also propose a small-sample test for multiple-parameter hypotheses, which generalizes the Satterthwaite approximation for t-tests. In simulations covering a wide range of scenarios, we find that the conventional cluster-robust Wald test can severely over-reject while the proposed small-sample test maintains Type I error close to nominal levels. The proposed methods are implemented in an R package called clubSandwich . This article has online supplementary materials.

The objective of this study was to compare the predictions of the protein contents and hardness values by partial least squares regression (PLSR) and principal components regression (PCR) models for bulk samples of Canadian wheat, which were obtained from different locations and crop years. Wheat samples of Canada Western Red Spring (CWRS), Canada Western Hard White Spring (CWHWS), Canada Western Soft White Spring (CWSWS), and Canada Prairie Spring Red (CPSR) classes were obtained from nearby agricultural farms in the main wheat growing locations in the Provinces of Alberta, Saskatchewan, and Manitoba from 2007, 2008, and 2009 crop years. Wheat samples were conditioned to moisture levels of 13, 16, and 19 % (wet basis) and pooled together for developing the regression models. A database of the near-infrared (NIR) hyperspectral image cubes of bulk samples of wheat classes was created in the wavelength region of 960–1,700 nm with 10 nm intervals. Reference protein contents and hardness values were determined using the Dumatherm method and single kernel characterization system (SKCS), respectively. A tenfold cross-validation was used for the ten-factor partial least squares regression (PLSR) and principal components regression (PCR) models for prediction purposes. Prediction performances of regression models were assessed by calculating the estimated mean square errors of prediction (MSEP), standard error of cross-validation (SECV), and correlation coefficient (r). Using the full data set in the protein prediction study, the ten-component PLSR model gave 1.76, 1.33, and 0.68 for the estimated MSEP, SECV, and r, respectively, which were better than the results for the ten-component PCR model (2.02, 1.42, and 0.62, respectively). For the hardness prediction, the estimated MSEP, SECV, and r values were 147.7, 12.15, and 0.82, respectively, for the ten-component PLSR model using the full data set. The PLSR models prediction performances outperformed the PCR models for predicting protein contents and hardness of wheat.