The most common measure of association between two continuous variables is the Pearson correlation (Maronna et al. in Safari an OMC. Robust statistics, 2019. ...https://login.proxy.bib.uottawa.ca/login?url=https://learning.oreilly.com/library/view/-/9781119214687/?ar&orpq&email=^u). When outliers are present, Pearson does not accurately measure association and robust measures are needed. This article introduces three new robust measures of correlation: Taba (T), TabWil (TW), and TabWil rank (TWR). The correlation estimators T and TW measure a linear association between two continuous or ordinal variables; whereas TWR measures a monotonic association. The robustness of these proposed measures in comparison with Pearson (P), Spearman (S), Quadrant (Q), Median (M), and Minimum Covariance Determinant (MCD) are examined through simulation. Taba distance is used to analyze genes, and statistical tests were used to identify those genes most significantly associated with Williams Syndrome (WS).
Based on the root mean square error (RMSE) and bias, the three proposed correlation measures are highly competitive when compared to classical measures such as P and S as well as robust measures such as Q, M, and MCD. Our findings indicate TBL2 was the most significant gene among patients diagnosed with WS and had the most significant reduction in gene expression level when compared with control (P value = 6.37E-05).
Overall, when the distribution is bivariate Log-Normal or bivariate Weibull, TWR performs best in terms of bias and T performs best with respect to RMSE. Under the Normal distribution, MCD performs well with respect to bias and RMSE; but TW, TWR, T, S, and P correlations were in close proximity. The identification of TBL2 may serve as a diagnostic tool for WS patients. A Taba R package has been developed and is available for use to perform all necessary computations for the proposed methods.
•Three correlation coefficients of hydration heat and strength are compared.•Linear and nonparametric correlation analysis is used quantitatively.•More variables are considered, the greater of the ...multiple correlation coefficient.
Analysis of linear and nonlinear dependencies of hydration characteristics and strength development is of interest for reliable and cost-effective designs. In this paper, the statistical assessment of linear and nonparametric correlation analysis model is used to investigate the association of these properties quantitatively. The bivariate correlation of early hydration characteristics within 72 h and compressive strength at different curing ages is evaluated by Pearson’s, Spearman’s rho and Kendall’s tau correlation coefficient, respectively. Assessment results of various methods show that early hydration characteristics and compressive strength have a strong correlation coefficient. Furthermore, the coefficient fitted by Spearman’s rho correlation analysis is higher than those by Pearson’s and Kendall’s tau analyses. The calculated correlation coefficients of middle and long curing ages (e.g. 28 d and 56 d) are higher than those in the early curing ages (e.g. 3 d and 7 d). For multiple correlation analysis, the correlation coefficients between heat release characteristics and mechanical properties undergo a fundamental change. The more variables of hydration characteristic are considered, the greater the multiple correlation coefficient of compressive strength, and the coefficients of middle and long curing age strength have a narrower range than early age compressive strength. Hence, the linear and nonparametric correlation model is a useful quantitative evaluation method for assessing the relationship between the early hydration characteristics and compressive strength for multi-composite blends.
Knowledge of spatial correlations of precipitation is important for the generation of grid‐based surface precipitation data sets, deployment of data collection, selection of downscaling strategies, ...and interpretation of paleoclimate reconstructions. Spatial correlations of daily precipitation in China were analyzed based on a daily precipitation data set from 1951 through 2014 for 2,208 stations by dividing them into 13 regions. Interstation Pearson correlation coefficient r for the daily precipitation series and the corresponding interstation distance d were calculated for each region. The exponential spatial correlation model (rd=c0×exp−d/d0s0+1−c0) was fitted by the r‐d pairs, in which c0, d0 and s0 were the parameter variance, scale and shape, respectively. The results showed that: (a) The determination coefficient R2 of the correlation model varied from 0.54 to 0.96, with a mean of 0.82 and the regional maximum correlation distance d0 varied from 102.2 to 201.7 km, with a mean of 155.2 km. Western regions generally had smaller d0 than eastern regions, which indicates rain events in the western regions were more local; (b) The goodness‐of‐fit of the model was improved by dividing samples into West‐East (W‐E) and North‐South (N‐S) directions. The average of d0 for all regions (190.2 km) for the W‐E direction is larger than that for the N‐S direction (142.9 km); (c) The correlation distances in summer and dry years are shorter than those in winter and wet years. However, the difference of correlation distance between dry and wet years was subtle compared with those between summer and winter, and between W‐E and N‐S directions. Seven regions were divided based on the spatial correlations of daily precipitation and different spatial models were suggested to be used for different regions, seasons and directions when the interpolation of daily precipitation is conducted for the generation of gridded surface precipitation data sets.
Spatial correlations of daily precipitation in China were analyzed by fitting exponential spatial correlation models between the interstation Pearson correlation coefficient for daily precipitation series and the corresponding interstation distance based on the daily precipitation data from 1951 through 2014 for 2,208 stations. Seven regions were divided based on the spatial correlations of daily precipitation and different spatial correlation models were suggested to be used for different regions, seasons and directions when the interpolation of daily precipitation is conducted.
In equation (1a) in function f(), the subscript for the first term within the brackets should be 1k,t, not ik,t. Please view the correct equation here: A general requirement for the stability of this ...equilibrium is thatd/e > a(R0 – K)/(R0 + K)" Citation: Ruokolainen L (2013) Correction: Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities.
To evaluate binary classifications and their confusion matrices, scientific researchers can employ several statistical rates, accordingly to the goal of the experiment they are investigating. Despite ...being a crucial issue in machine learning, no widespread consensus has been reached on a unified elective chosen measure yet. Accuracy and F
score computed on confusion matrices have been (and still are) among the most popular adopted metrics in binary classification tasks. However, these statistical measures can dangerously show overoptimistic inflated results, especially on imbalanced datasets.
The Matthews correlation coefficient (MCC), instead, is a more reliable statistical rate which produces a high score only if the prediction obtained good results in all of the four confusion matrix categories (true positives, false negatives, true negatives, and false positives), proportionally both to the size of positive elements and the size of negative elements in the dataset.
In this article, we show how MCC produces a more informative and truthful score in evaluating binary classifications than accuracy and F
score, by first explaining the mathematical properties, and then the asset of MCC in six synthetic use cases and in a real genomics scenario. We believe that the Matthews correlation coefficient should be preferred to accuracy and F
score in evaluating binary classification tasks by all scientific communities.
The probabilistic linguistic term set (PLTS) is a powerful technique in representing linguistic evaluations of individuals or groups in the process of decision making. The aim of this paper is to ...propose a strongly robust method to solve multiexperts multicriteria decision making problems with linguistic evaluations. To enrich the computation and to improve the measures of PLTS, we first define an expectation function of it. In addition, we advance three kinds of probabilistic linguistic distance measures reflecting on the difference of linguistic terms and probabilities at the same time to make up for the defects of the existing distance measures, and then propose the similarity and correlation measures. Integrating the subjective opinions with the correlation coefficients between criteria, we put forward a combined weight determining method. The robustness of the ranking method, MULTIMOORA, is enhanced by the improved Borda rule. Based on these research findings, a probabilistic linguistic MULTIMOORA method is proposed. Finally, the developed method is applied to an empirical example concerning the selection of shared karaoke television brands. The effectiveness of the proposed method is verified by some comparative analyses.
The problem of determining optimal designs for least squares estimation is considered in the common linear regression model with correlated observations. The approach is based on the determination of ...anearlya universally optimal designs, even in the case where the universally optimal design does not exist. For this purpose, a new optimality criterion which reflects the distance between a given design and an ideal universally optimal design is introduced. A necessary condition for the optimality of a given design is established. Numerical methods for constructing these designs are proposed and applied for the determination of optimal designs in a number of specific instances. The results indicate that the new anearlya universally optimal designs have good efficiencies with respect to common optimality criteria.
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