A Numerical Comparison of Iterative Algorithms for Inconsistency Reduction in Pairwise Comparisons

In this paper, we compare three methods for deriving a priority vector in the theoretical framework of pairwise comparisons—the Geometric Mean Method (GMM), Eigenvalue Method (EVM) and Best–Worst Method (BWM)—with respect to two features: sensitivity and order violation. As the research method, we apply One-Factor-At-a-Time (OFAT) sensitivity analysis via Monte Carlo simulations; the number of compared objects ranges from 3 to 8, and the comparison scale coincides with Saaty’s fundamental scale from 1 to 9 with reciprocals. Our findings suggest that the BWM is, on average, significantly more sensitive statistically (and thus less robust) and more susceptible to order violation than the GMM and EVM for every examined matrix (vector) size, even after adjustment for the different numbers of pairwise comparisons required by each method. On the other hand, differences in sensitivity and order violation between the GMM and EMM were found to be mostly statistically insignificant.

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Heteroscedastic Methods for Performing All Pairwise Comparisons of Regression Lines Associated With J Independent Groups

Methodology ◽

10.1027/1614-2241/a000097 ◽

2015 ◽

Vol 11 (3) ◽

pp. 110-115 ◽

Cited By ~ 2

Author(s):

Rand R. Wilcox ◽

Jinxia Ma

Keyword(s):

Least Squares ◽

Pairwise Comparisons ◽

Simple Extension ◽

Type I ◽

Type I Errors ◽

Well Elderly ◽

Using Data

Abstract. The paper compares methods that allow both within group and between group heteroscedasticity when performing all pairwise comparisons of the least squares lines associated with J independent groups. The methods are based on simple extension of results derived by Johansen (1980) and Welch (1938) in conjunction with the HC3 and HC4 estimators. The probability of one or more Type I errors is controlled using the improvement on the Bonferroni method derived by Hochberg (1988) . Results are illustrated using data from the Well Elderly 2 study, which motivated this paper.

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Exploring the Boundaries of the Number–Temporal Order Association

Experimental Psychology (formerly Zeitschrift für Experimentelle Psychologie) ◽

10.1027/1618-3169/a000285 ◽

2015 ◽

Vol 62 (3) ◽

pp. 198-205 ◽

Cited By ~ 3

Author(s):

Dana Ganor-Stern

Keyword(s):

Embodied Cognition ◽

Mental Representation ◽

Temporal Order ◽

Past Research ◽

Numerical Comparison ◽

Negative Number ◽

Comparison Task ◽

Negative Numbers ◽

The Past

Past research has shown that numbers are associated with order in time such that performance in a numerical comparison task is enhanced when number pairs appear in ascending order, when the larger number follows the smaller one. This was found in the past for the integers 1–9 ( Ben-Meir, Ganor-Stern, & Tzelgov, 2013 ; Müller & Schwarz, 2008 ). In the present study we explored whether the advantage for processing numbers in ascending order exists also for fractions and negative numbers. The results demonstrate this advantage for fraction pairs and for integer-fraction pairs. However, the opposite advantage for descending order was found for negative numbers and for positive-negative number pairs. These findings are interpreted in the context of embodied cognition approaches and current theories on the mental representation of fractions and negative numbers.

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Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15200 ◽

2002 ◽

Vol 7 (1) ◽

pp. 31-42

Author(s):

J. Šaltytė ◽

K. Dučinskas

Keyword(s):

Spatial Correlation ◽

Random Fields ◽

Data Augmentation ◽

Gaussian Random Fields ◽

Classification Rule ◽

Numerical Comparison ◽

First Order ◽

Bayesian Risk ◽

Correlation Models

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed.

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