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Covariance modeling
Published in Atanu Bhattacharjee, Bayesian Approaches in Oncology Using R and OpenBUGS, 2020
There are different covariance patterns available. It is difficult to choose the appropriate one. The approach is to select the most suitable one that fits with the data. It also generated with standard error with fixed effect. Sometimes the presence of more covariance parameters may increase the chance of overfitting. Likelihood testing is useful to explore the amount of overfitting. Different types of covariance patterns are available. It is not easy to select an appropriate one. It is suitable to define the best covariance by fitting the data. The standard error for the fixed effects model estimate is useful to understand the covariance pattern. The model diagnostic criteria are useful to test the best covariance structure. It is defined as
Statistics for Genomics
Published in Altuna Akalin, Computational Genomics with R, 2020
In the equation above, is the covariance; this is again a measure of how much two variables change together, like correlation. If two variables show similar behavior, they will usually have a positive covariance value. If they have opposite behavior, the covariance will have a negative value. However, these values are boundless. A normalized way of looking at covariance is to divide covariance by the multiplication of standard errors of X and Y. This bounds the values to -1 and 1, and as mentioned above, is called Pearson correlation coefficient. The values that change in a similar manner will have a positive coefficient, the values that change in an opposite manner will have a negative coefficient, and pairs that do not have a linear relationship will have 0 or near 0 correlation. In Figure 3.17, we are showing R2, the correlation coefficient, and covariance for different scatter plots.
Fundamentals
Published in Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam, Introduction to Computational Health Informatics, 2019
Arvind Kumar Bansal, Javed Iqbal Khan, S. Kaisar Alam
Another important factor in a statistical analysis is the correlation of two variables x and y. If a variable y varies in the same direction as an independent variable x, then the variable y is positively correlated with variable x. It is used to study the relationship between independent variables and dependent variables in regression analysis. Independent variables are controlled parameters in an experiment. Dependent variables are the measured outcomes. The metrics to study the correlation of two variables x and y is called covariance. Covariance measures the spread of the points in a two-dimensional plane and is defined as the average deviation of all the points from the centroid given by (μx, μy) as shown in Equation 2.12.
Clustering pedestrians’ perceptions towards road infrastructure and traffic characteristics
Published in International Journal of Injury Control and Safety Promotion, 2023
Aditya Saxena, Ankit Kumar Yadav
After the collection of samples, data analysis was undertaken using SPSS version 22. The data obtained for the selected 14 parameters were then subjected to factor analysis (a dimension reduction method) using the principal component analysis technique with varimax rotation. Varimax rotation involves using a mathematical algorithm that maximizes high- and low-value factor loadings and minimizes mid-value factor loadings. Using factor analysis, factor loadings were obtained which were used to derive the number of factors to be considered for dimension reduction. Factors with an eigenvalue above 1 were only retained. Four factors were acquired from component variances. The correlation between factors and parameters was found from component loading and only those parameters were retained whose correlation value was above 0.5 (Jolliffe & Cadima, 2016; Maskey et al., 2018; Venkatramanan et al., 2019). The following equation was used for computing covariance (Mishra et al., 2017):
Boundaries tuned support vector machine (BT-SVM) classifier for cancer prediction from gene selection
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2022
The proposed work explores that the feature extraction process for the dataset will be grouped into three as mean, worst and standard error. All these three values are considered and a matrix is constructed. During matrix construction, one set of the vector is transformed into another with respect to their covariance and variance. Analysis of eigenvalue and eigenvector is done using covariance matrix. This leads to equivalent fitting of data variance’s principal component lines. To find the Eigen value the factorization is done for covariance value. The identity matrix is updated as Eigenvector and covariance updated as Eigenvalue. Generation of principal component is needed which helps to identify the direction of principle. Linear transformation of data is utilised by the principal component into a latent space. Factor analysis is contained in linear techniques and is same as PCA. Modelling correlations are focussed rather than focussing on covariance. Feature extraction is possible through these linear methods. The principal components are generated based on the maximum Eigenvalue and Eigenvector. The following Table 2 depicts the notations and descriptions employed in the proposed methodology.
Directional monitoring and diagnosis for covariance matrices
Published in Journal of Applied Statistics, 2022
Hongying Jing, Jian Li, Kaizong Bai
However, the true shift direction usually remains unknown in reality. In other words, we don't know which pair of variables have shifting covariance. To be safe, it requires considering each pair of variables. Therefore, without loss of generality, we suppose 7) should be extended to 8), we can devise our proposed directional covariance matrix monitoring scheme. By the definition of generalised LRT, the LRT statistic for testing hypothesis (8) should be the maximum of the LRT statistics for testing hypothesis (7) over all 7) requires the ML estimate of the shift magnitude k, denoted by 1), we employ the Newton-Raphson algorithm to calculate the ML estimate 1) with respect to B is true and 0 otherwise. The initial value for estimating