scholarly journals Permutation tests for comparative data

2020 ◽  
Author(s):  
James G. Saulsbury
Keyword(s):  
Least Squares ◽  
Permutation Test ◽  
Phylogenetic Signal ◽  
Cyclic Permutation ◽  
Permutation Tests ◽  
Generalized Least Squares ◽  
Comparative Data ◽  
Least Squares Regression ◽  
Data Points ◽  
Restricted Permutation

AbstractThe analysis of patterns in comparative data has come to be dominated by least-squares regression, mainly as implemented in phylogenetic generalized least-squares (PGLS). This approach has two main drawbacks: it makes relatively restrictive assumptions about distributions and can only address questions about the conditional mean of one variable as a function of other variables. Here I introduce two new non-parametric constructs for the analysis of a broader range of comparative questions: phylogenetic permutation tests, based on cyclic permutations and permutations conserving phylogenetic signal. The cyclic permutation test, an extension of the restricted permutation test that performs exchanges by rotating nodes on the phylogeny, performs well within and outside the bounds where PGLS is applicable but can only be used for balanced trees. The signal-based permutation test has identical statistical properties and works with all trees. The statistical performance of these tests compares favorably with independent contrasts and surpasses that of a previously developed permutation test that exchanges closely related pairs of observations more frequently. Three case studies illustrate the use of phylogenetic permutations for quantile regression with non-normal and heteroscedastic data, testing hypotheses about morphospace occupation, and comparative problems in which the data points are not tips in the phylogeny.

scholarly journals A comparison between generalized least squares regression and top-kriging for homogeneous cross-correlated flood regions

2021 ◽  
Author(s):  
Simone Persiano ◽  
Jose Luis Salinas ◽  
Jery Russell Stedinger ◽  
William H. Farmer ◽  
David Lun ◽  
...  
Keyword(s):  
Least Squares ◽  
Generalized Least Squares ◽  
Least Squares Regression

Incorrect least-squares regression coefficients in method-comparison analysis.

1979 ◽  
Vol 25 (3) ◽  
pp. 432-438 ◽  
Author(s):  
P J Cornbleet ◽  
N Gochman
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Line ◽  
Method Comparison ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Data Set ◽  
Data Points ◽  
Regression Slopes

Abstract The least-squares method is frequently used to calculate the slope and intercept of the best line through a set of data points. However, least-squares regression slopes and intercepts may be incorrect if the underlying assumptions of the least-squares model are not met. Two factors in particular that may result in incorrect least-squares regression coefficients are: (a) imprecision in the measurement of the independent (x-axis) variable and (b) inclusion of outliers in the data analysis. We compared the methods of Deming, Mandel, and Bartlett in estimating the known slope of a regression line when the independent variable is measured with imprecision, and found the method of Deming to be the most useful. Significant error in the least-squares slope estimation occurs when the ratio of the standard deviation of measurement of a single x value to the standard deviation of the x-data set exceeds 0.2. Errors in the least-squares coefficients attributable to outliers can be avoided by eliminating data points whose vertical distance from the regression line exceed four times the standard error the estimate.

scholarly journals An Improvised SIMPLS Estimator Based on MRCD-PCA Weighting Function and Its Application to Real Data

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2211
Author(s):  
Siti Zahariah ◽  
Habshah Midi ◽  
Mohd Shafie Mustafa
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Weighting Function ◽  
Real Data ◽  
Least Squares Regression ◽  
Regression Problem ◽  
Leverage Points ◽  
Explanatory Variables ◽  
Diagnostic Plot ◽  
Data Points

Multicollinearity often occurs when two or more predictor variables are correlated, especially for high dimensional data (HDD) where p>>n. The statistically inspired modification of the partial least squares (SIMPLS) is a very popular technique for solving a partial least squares regression problem due to its efficiency, speed, and ease of understanding. The execution of SIMPLS is based on the empirical covariance matrix of explanatory variables and response variables. Nevertheless, SIMPLS is very easily affected by outliers. In order to rectify this problem, a robust iteratively reweighted SIMPLS (RWSIMPLS) is introduced. Nonetheless, it is still not very efficient as the algorithm of RWSIMPLS is based on a weighting function that does not specify any method of identification of high leverage points (HLPs), i.e., outlying observations in the X-direction. HLPs have the most detrimental effect on the computed values of various estimates, which results in misleading conclusions about the fitted regression model. Hence, their effects need to be reduced by assigning smaller weights to them. As a solution to this problem, we propose an improvised SIMPLS based on a new weight function obtained from the MRCD-PCA diagnostic method of the identification of HLPs for HDD and name this method MRCD-PCA-RWSIMPLS. A new MRCD-PCA-RWSIMPLS diagnostic plot is also established for classifying observations into four data points, i.e., regular observations, vertical outliers, and good and bad leverage points. The numerical examples and Monte Carlo simulations signify that MRCD-PCA-RWSIMPLS offers substantial improvements over SIMPLS and RWSIMPLS. The proposed diagnostic plot is able to classify observations into correct groups. On the contrary, SIMPLS and RWSIMPLS plots fail to correctly classify observations into correct groups and show masking and swamping effects.

A generalized least squares regression approach for computing effect sizes in single-case research: Application examples

2011 ◽  
Vol 49 (3) ◽  
pp. 301-321 ◽  
Author(s):  
Daniel M. Maggin ◽  
Hariharan Swaminathan ◽  
Helen J. Rogers ◽  
Breda V. O'Keeffe ◽  
George Sugai ◽  
...  
Keyword(s):  
Least Squares ◽  
Single Case ◽  
Generalized Least Squares ◽  
Effect Sizes ◽  
Least Squares Regression ◽  
Research Application ◽  
Case Research ◽  
Regression Approach ◽  
Single Case Research

A Novel Method for Determining Harmonic Emission Responsibilities at the Point of Common Coupling

2013 ◽  
Vol 448-453 ◽  
pp. 2380-2383
Author(s):  
Xiao Jun Zhu ◽  
Xiang Li ◽  
Bin Fu ◽  
Ang Fu ◽  
Min You Chen ◽  
...  
Keyword(s):  
Least Squares ◽  
Partial Least Squares Regression ◽  
Least Squares Regression ◽  
Harmonic Emission ◽  
Point Of Common Coupling ◽  
Practical Engineering ◽  
Data Points ◽  
Harmonic Voltage ◽  
Novel Method ◽  
Common Coupling

This paper presents a novel method for determining the harmonic emission responsibilities of utility and customer at the point of common coupling (PCC). The proposed approach is based on robust partial least squares regression (robust PLS), which estimates system harmonic impedance by utilizing the signals of harmonic voltage and current measured synchronously at PCC. Consequently the harmonic emission responsibilities are calculated. The presented method reduces or removes the effect of outlying data points. The simulation and the practical engineering results indicate that the proposed method is valid and feasible.

scholarly journals On the relationship between enamel band complexity and occlusal surface area in Equids (Mammalia, Perissodactyla)

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2181 ◽  
Author(s):  
Nicholas A. Famoso ◽  
Edward Byrd Davis
Keyword(s):  
Body Size ◽  
Least Squares ◽  
Surface Area ◽  
Phylogenetic Signal ◽  
Negative Relationship ◽  
Generalized Least Squares ◽  
Occlusal Surface ◽  
Last Common Ancestor ◽  
Occlusal Surfaces ◽  
The Relationship

Enamel patterns on the occlusal surfaces of equid teeth are asserted to have tribal-level differences. The most notable example compares the Equini and Hipparionini, where Equini have higher crowned teeth with less enamel-band complexity and less total occlusal enamel than Hipparionini. Whereas previous work has successfully quantified differences in enamel band shape by dividing the length of enamel band by the square root of the occlusal surface area (Occlusal Enamel Index, OEI), it was clear that OEI only partially removes the effect of body size. Because enamel band length scales allometrically, body size still has an influence on OEI, with larger individuals having relatively longer enamel bands than smaller individuals. Fractal dimensionality (D) can be scaled to any level, so we have used it to quantify occlusal enamel complexity in a way that allows us to get at an accurate representation of the relationship between complexity and body size. To test the hypothesis of tribal-level complexity differences between Equini and Hipparionini, we digitally traced a sample of 98 teeth, one tooth per individual; 31 Hipparionini and 67 Equini. We restricted our sampling to the P3-M2 to reduce the effect of tooth position. After calculating theDof these teeth with the fractal box method which uses the number of boxes of various sizes to calculate theDof a line, we performed at-test on the individual values ofDfor each specimen, comparing the means between the two tribes, and a phylogenetically informed generalized least squares regression (PGLS) for each tribe with occlusal surface area as the independent variable andDas the dependent variable. The slopes of both PGLS analyses were compared using at-test to determine if the same linear relationship existed between the two tribes. Thet-test between tribes was significant (p< 0.0001), suggesting differentDpopulations for each lineage. The PGLS for Hipparionini was a positive but not significant (p= 0.4912) relationship betweenDand occlusal surface area, but the relationship for Equini was significantly negative (p= 0.0177).λwas 0 for both tests, indicating no important phylogenetic signal is present in the relationship between these two characters, thus the PGLS collapses down to a non-phylogenetic generalized least squares (GLS) model. Thet-test comparing the slopes of the regressions was not significant, indicating that the two lineages could have the same relationship betweenDand occlusal surface area. Our results suggest that the two tribes have the same negative relationship betweenDand occlusal surface area but the Hipparionini are offset to higher values than the Equini. This offset reflects the divergence between the two lineages since their last common ancestor and may have constrained their ability to respond to environmental change over the Neogene, leading to the differential survival of the Equini.

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