scholarly journals SYMMETRY MODEL BASED ON BIVARIATE NORMAL DISTRIBUTION FOR SQUARE CONTINGENCY TABLES WITH ORDERED CATEGORIES

2016 ◽  
Vol 15 (2) ◽  
pp. 71-84
Keyword(s):  
Normal Distribution ◽  
Contingency Tables ◽  
Bivariate Normal Distribution ◽  
Ordered Categories ◽  
Bivariate Normal ◽  
Model Based ◽  
Symmetry Model

scholarly journals Log-normal Distribution Type Symmetry Model for Square Contingency Tables with Ordered Categories

2018 ◽  
Vol 47 (3) ◽  
pp. 39-48
Author(s):  
Kiyotaka Iki
Keyword(s):  
Normal Distribution ◽  
Contingency Tables ◽  
Ordered Categories ◽  
Symmetry Model ◽  
Proposed Model ◽  
Type Symmetry ◽  
The Difference ◽  
Log Normal ◽  
Distribution Type ◽  
Log Normal Distribution

For the analysis of square contingency tables with the same row and column ordinal classications, this article proposes a new model which indicates that the log-ratios of symmetric cell probabilities are proportional to the difference between log-row category and log-column category. The proposed model may be appropriate for a square ordinal table if it is reasonable to assume an underlying bivariate log-normal distribution. Also, this article gives the decomposition of the symmetry model using the proposed model with the orthogonality of test statistics. Examples are given. The simulation studies based on bivariate log-normal distribution are given.

scholarly journals Ridit Score Type Quasi-Symmetry and Decomposition of Symmetry for Square Contingency Tables with Ordered Categories

2016 ◽  
Vol 38 (3) ◽  
Author(s):  
Kiyotaka Iki ◽  
Kouji Tahata ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Ordered Categories ◽  
Marginal Distributions ◽  
Model Based ◽  
Symmetry Model ◽  
Proposed Model ◽  
Log Odds ◽  
The Difference ◽  
Mean Equality

For square contingency tables with the same row and column ordinal classifications, this paper proposes the quasi-symmetry model based on the marginal ridits. The model indicates that the log-odds that an observation will fall in the (i; j) cell instead of in the (j; i) cell, i < j, is proportional to the difference between the average ridit score of row and column marginal distributions for category j and that for category i. This paper also gives atheorem such that the symmetry model holds if and only if both the proposed model and the marginal mean equality model hold. Examples are given.

A note on the generalization of bivariate normal quadrant probabilities to bivariate elliptical distributions

2018 ◽  
Author(s):  
Oscar Lorenzo Olvera Astivia
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Elliptical Distributions ◽  
Bivariate Normal ◽  
Geometric Argument

I present a geometric argument to show that the quadrant probability for the bivariate normal distribution can be generalized to the case of all elliptical distributions.

scholarly journals PSIII-5 Comparison of Bivariate Machine Learning and Linear Model for Genomic Prediction with Different Heritability, QTL and SNP Panel Scenarios

2020 ◽  
Vol 98 (Supplement_4) ◽  
pp. 230-231
Author(s):  
Sunday O Peters ◽  
Mahmut Sinecan ◽  
Kadir Kizilkaya ◽  
Milt Thomas
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Normal Distribution ◽  
Genomic Prediction ◽  
Network Models ◽  
Bivariate Normal Distribution ◽  
Snp Markers ◽  
Neural Network Models ◽  
Bivariate Normal ◽  
Artificial Neural

Abstract This simulation study used actual SNP genotypes on the first chromosome of Brangus beef cattle to simulate 0.50 genetically correlated two traits with heritabilities of 0.25 and 0.50 determined either by 50, 100, 250 or 500 QTL and then aimed to compare the accuracies of genomic prediction from bivariate linear and artificial neural network with 1 to 10 neurons models based on G genomic relationship matrix. QTL effects of 50, 100, 250 and 500 SNPs from the 3361 SNPs of 719 animals were sampled from a bivariate normal distribution. In each QTL scenario, the breeding values (Σgijβj) of animal i for two traits were generated by using genotype (gij) of animal i at QTL j and the effects (βj) of QTL j from a bivariate normal distribution. Phenotypic values of animal i for traits were generated by adding residuals from a bivariate normal distribution to the breeding values of animal i. Genomic predictions for traits were carried out by bivariate Feed Forward MultiLayer Perceptron ANN-1–10 neurons and linear (GBLUP) models. Three sets of SNP panels were used for genomic prediction: only QTL genotypes (Panel1), all SNP markers, including the QTL (Panel2), and all SNP markers, excluding the QTL (Panel3). Correlations from 10-fold cross validation for traits were used to assess predictive ability of bivariate linear (GBLUP) and artificial neural network models based on 4 QTL scenarios with 3 Panels of SNP panels. Table 1 shows that the trait with high heritability (0.50) resulted in higher correlation than the trait with low heritability (0.25) in bivariate linear (GBLUP) and artificial neural network models. However, bivariate linear (GBLUP) model produced higher correlation than bivariate neural network. Panel1 performed the best correlations for all QTL scenarios, then Panel2 including QTL and SNP markers resulted in better prediction than Panel3.

Tables of the Integral of the Elliptical Bivariate Normal Distribution over Offset Circles.

1962 ◽  
Vol 16 (77) ◽  
pp. 116
Author(s):  
Author's Summary ◽  
G. W. Rosenthal ◽  
J. J. Rodden
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal
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