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Studies analyzing clustered data sets using both multilevel models (MLMs) and ordinary least squares (OLS) regression have generally concluded that resulting point estimates, but not the standard errors, are comparable with each other. However, the accuracy of the estimates of OLS models is important to consider, as several alternative techniques (e.g., bootstrapping) used when analyzing clustered data sets only make adjustments to standard errors but not to the regression coefficients. Using a Monte Carlo simulation, we analyzed 54,000 data sets using both MLM and OLS under varying conditions and we show that coefficients of not just OLS models, but MLMs as well, may be biased when relevant higher-level variables are omitted from a model, a situation that is likely to occur when using large-scale, secondary data sets. However, we demonstrate that by including aggregated level-one variables at the higher level, the resulting bias can be effectively removed.

We analyzed the combined 142 years sunspot-group data from Greenwich Photoheliograpic Results (GPR) and Debrecen Photoheliographic Data (DPD) and determined the yearly mean residual rotation rate and the meridional velocity of sunspot groups in different 5 ∘ latitude intervals. We find that there exists a considerable latitude–time dependence in both the residual rotation and the meridional motion. The residual rotation rate is found to be −120 m s −1 to 80 m s −1 . In a large number of solar cycles, the rotation is to some extent weaker during maxima than that of during minima. There exist alternate bands of equatorward and poleward meridional motions. The equatorward motion is dominant mostly around the maxima of solar cycles with velocity 8–12 m s −1 , whereas the poleward motion is dominant mostly around the minima but with a relatively weak velocity, only 4–6 m s −1 . The analysis of the data during Solar Cycles 12–24 that are folded according to the years from their respective epochs of maxima suggests the existence of equatorward migrating alternate bands of slower and faster than average rotation within the activity belt. This analysis suggests no clear equatorward or poleward migrating bands of meridional motions. A statistically significant anticorrelation exists between the meridional motion and residual rotation. The corresponding linear-least-squares best-fit is found to be reasonably good (slope, − 0.028 ± 0.008 , is about 3.5 times larger than its standard deviation). As per the sign convention used for the meridional motions, the significant negative value of the slope indicates the existence of a strong angular momentum transport toward the equator. The cross-correlation between the slopes determined from the data in 3-year moving time intervals and yearly mean sunspot number (SN) suggests that the slope leads SN by about 4 and 9 years. The Morlet wavelet spectrum of the slope suggests the existence of ≈11-year periodicity in the slope almost throughout the data window, but it was very weak during 1920–1940. We have also done cross-wavelet, wavelet-coherence, and wavelet-phase difference analyses of the slope and SN. Overall the results suggest there exists a strong relationship between the slope and amount of activity during a solar cycle. However, the correlation between the cycle-to-cycle modulations in the slope and the amplitude of solar cycle is found to be insignificant, indicating that there is no relationship between the slope and strength of activity on a long-time scale (longer than 11-year period).

This study investigates the effectiveness of combining the Group Method of Data Handling (GMDH) models and Kriging to reduce errors in groundwater salinity estimation. The study uses two datasets of electrical conductivity (EC) values collected from 109 observation wells in an agricultural region of Iran. The methodology comprises a two-step process. Initially, GMDH models were trained and validated to estimate groundwater EC values at any desired location based on the observed EC values from surrounding wells. Subsequently, these models were employed to expand the EC datasets, followed by using the Kriging interpolation approach to investigate the spatial variability of groundwater EC across the study area. During the cross-validation phase, the GMDH models achieved robust results. For the first dataset, the model maintained an average R-squared value of 0.81, with a corresponding root mean square error (RMSE) of 0.61 dS/m. Similarly, for the second dataset, the model performed well with an R-squared value of 0.84 and RMSE of 0.72 dS/m. The findings also indicated that employing GMDH to extend the original datasets improves the results provided by Kriging, particularly when the original datasets are increased by 40%. On average, for the first dataset, employing the integrated approach decreased the RMSE of Kriging by 18.34%, while for the second dataset, the decrease in RMSE was 19.21%. Overall, the findings suggest that expanding datasets can enhance the accuracy of estimating water quality variables, which has important implications for environmental monitoring and management.

The reference equations and diagnostic criteria play a critical role in the interpretation of pulmonary function tests (PFTs). The aim was to investigate the impacts of different reference equations and diagnostic criteria on the frequency of airway obstruction in adult people of a large teaching hospital of North China. The spirometry data of all adult people who underwent PFTs in Qilu hospital from April 2012 to November 2015 were collected. Two spirometry reference equations, namely, Zhongshan-2011 and Global Lung Function Initiative 2012 (GLI-2012) were compared. The frequency of airway obstruction using different spirometry prediction equations and diagnostic criteria including forced expiratory volume in 1 s (FEV1)/forced vital capacity (FVC) <92% of predicted value and FEV1/FVC 

Journal Article

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