scholarly journals Asymmetry models based on ordered score and separations of symmetry model for square contingency tables

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Shuji Ando
Keyword(s):  
Asymmetry Parameter ◽  
Contingency Tables ◽  
Real Data ◽  
Symmetry Model ◽  
Th Cell ◽  
Proposed Model ◽  
Log Odds ◽  
The Difference ◽  
Mean Equality ◽  
Column Variable

Summary This study proposes two original asymmetry models based on ordered scores for square contingency tables with the same row and column ordinal classifications. The proposed models can be applied to cases in which the scores of all categories are known or unknown. In the proposed models, the log odds for an observation falling in the (i, j)th cell instead of the (j, i)th cell are inversely proportional to the difference of the ordered scores corresponding to categories i and j. The asymmetry parameter of the proposed model can be useful for inferring whether the row variable is stochastically greater than the column variable or vice versa. The proposed models constantly hold when the symmetry model holds, but the converse is not necessarily true. This study also examines what is necessary for a model, in addition to the proposed models, to satisfy the symmetry model, and gives separations of the symmetry model using the proposed and marginal mean equality models. We apply real data to show the utility of the proposed models. The proposed models provide a better fit than that of the existing models.

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.

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 Capacity Estimation for On-Ramp Merging Section of Urban Expressway Based on Time Headway Loss

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Xing-jian Xue ◽  
Feng Shi ◽  
Qun Chen
Keyword(s):  
Real Data ◽  
Efficient Solutions ◽  
Optimal Time ◽  
Lane Changing ◽  
Time Headway ◽  
Urban Expressway ◽  
Proposed Model ◽  
The Difference ◽  
Capacity Drop ◽  
Gap Acceptance Theory

This paper proposes a model for estimating capacity of on-ramp merging section of urban expressway based on dynamics and gap acceptance theory, considering lane-changing processes and time headway loss. Survey data were collected from on-ramp merging sections of shanghai urban expressway system and showed that capacity drop of on-ramp merging section is caused by drivers’ lane-changing which may lead to unsteady speed of vehicles and so prolonged time headway compared to the minimum time headway corresponding to the maximum capacity. Three parameters (optimal time headway, time headway loss, and interference quantity of lane-changing) are given and a methodology by accumulating time headway loss due to lane-changing is developed to estimate the capacity drop. Results’ comparisons between real data and microsimulation of on-ramp merging sections and sensitivity analysis show that the proposed model can produce reliable and accurate results. This study also reveals that ramp flow and the difference between the optimal speed and the lane-changing speed of fleet have a great impact on capacity drop. This study is beneficial to evaluate congestion levels, to understand complex traffic phenomena, and so to find efficient solutions.

scholarly journals A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

2021 ◽  
Vol 50 (5) ◽  
pp. 115-126
Author(s):  
Shuji Ando
Keyword(s):  
Asymmetry Parameter ◽  
Confidence Region ◽  
Contingency Tables ◽  
Real Data ◽  
Data Sets ◽  
Index Vector ◽  
Direction Of Departure ◽  
Reverse Circulation ◽  
The Asymmetry

This study proposes a bivariate index vector to concurrently analyze both the degree and direction of departure from the quasi-symmetry (QS) model for ordinal square contingency tables. The QS model and extended QS (EQS) models identify the symmetry and asymmetry between the probabilities of normal circulation and reverse circulation when the order exists for arbitrary three categories. The asymmetry parameter of the EQS model implies the degree of departure from the QS model; the EQS model is equivalent to the QS model when the asymmetry parameter equals to one. The structure of the EQS model differs depending on whether the asymmetry parameter approaches zero or infinity. Thus, the asymmetry parameter of the EQS model also implies the direction of departure from the QS model. The proposed bivariate index vector is constructed by combining existing and original sub-indexes that represent the degree of departure from the QS model and its direction. These sub-indexes are expressed as functions of the asymmetry parameter under the EQS model. We construct an estimator of the proposed bivariate index vector and an approximate confidence region for the proposed bivariate index vector. Using real data, we show that the proposed bivariate index vector is important to compare degrees of departure from the QS model for plural data sets.

scholarly journals Diagonal Exponent Conditional Symmetry Model for Square Contingency Tables with Ordered Categories

2016 ◽  
Vol 5 (4) ◽  
pp. 38
Author(s):  
Kiyotaka Iki ◽  
Akira Shibuya ◽  
Sadao Tomizawa
Keyword(s):  
Contingency Tables ◽  
Main Diagonal ◽  
Test Statistics ◽  
Conditional Symmetry ◽  
Exponential Form ◽  
Ordered Categories ◽  
Expected Frequency ◽  
Symmetry Model ◽  
Proposed Model ◽  
New Models

For square contingency tables with ordered categories, this article proposes new models which indicate that in addition to the structure of asymmetry of the probabilities with respect to the main diagonal of the table, the expected frequency has an exponential form along every subdiagonal of the table. Also it gives the new three kinds of decompositions using the proposed model and proves the orthogonality of the test statistics.

scholarly journals Measure of departure from cumulative local symmetry for square contingency tables having ordered categories

2020 ◽  
Vol 57 (1) ◽  
pp. 23-35
Author(s):  
Yusuke Saigusa ◽  
Tomomasa Takada ◽  
Aki Ishii ◽  
Tomoyuki Nakagawa ◽  
Sadao Tomizawa
Keyword(s):  
Diversity Index ◽  
Contingency Tables ◽  
Local Symmetry ◽  
Women Patients ◽  
Ordered Categories ◽  
Case Examples ◽  
Symmetry Model ◽  
Proposed Model ◽  
Nominal Categories ◽  
Table Data

SummaryFor square contingency tables with nominal categories, a local symmetry model which indicates the symmetric structure of probabilities for only one pair of symmetric cells is proposed. For ordinal square tables, the present paper proposes (1) another local symmetry model for cumulative probabilities from the upper-right and lower-left corners of the table, and (2) a measure to represent the degree of departure from the proposed model. The measure has the form of a weighted harmonic mean of the diversity index, which includes the Shannon entropy as a special case. Examples are given in which the proposed method is applied to square table data on decayed teeth in Japanese women patients.

scholarly journals Orthogonal decomposition of the sum-symmetry model for square contingency tables with ordinal categories: Use of the exponential sum-symmetry model

2021 ◽  
Vol 58 (2) ◽  
pp. 95-104
Author(s):  
Shuji Ando
Keyword(s):  
Contingency Tables ◽  
Decomposition Theorem ◽  
Real Data ◽  
Exponential Sum ◽  
Orthogonal Decomposition ◽  
Global Symmetry ◽  
Asymptotic Equivalence ◽  
Artificial Data ◽  
Test Statistic ◽  
Symmetry Model

Summary In the existing decomposition theorem, the sum-symmetry model holds if and only if both the exponential sum-symmetry and global symmetry models hold. However, this decomposition theorem does not satisfy the asymptotic equivalence for the test statistic. To address the aforementioned gap, this study establishes a decomposition theorem in which the sum-symmetry model holds if and only if both the exponential sum-symmetry and weighted global-sum-symmetry models hold. The proposed decomposition theorem satisfies the asymptotic equivalence for the test statistic. We demonstrate the advantages of the proposed decomposition theorem by applying it to datasets comprising real data and artificial data.

scholarly journals Two-Dimensional Index of Departure from the Symmetry Model for Square Contingency Tables with Nominal Categories

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2031
Author(s):  
Tomotaka Momozaki ◽  
Tomoyuki Nakagawa ◽  
Aki Ishii ◽  
Yusuke Saigusa ◽  
Sadao Tomizawa
Keyword(s):  
Numerical Experiments ◽  
Diversity Index ◽  
Contingency Tables ◽  
Real Data ◽  
The Other ◽  
Two Dimensional ◽  
Measures Of Association ◽  
Log Odds ◽  
Nominal Categories ◽  
Power Divergence

In the analysis of two-way contingency tables, the degree of departure from independence is measured using measures of association between row and column variables (e.g., Yule’s coefficients of association and of colligation, Cramér’s coefficient, and Goodman and Kruskal’s coefficient). On the other hand, in the analysis of square contingency tables with the same row and column classifications, we are interested in measuring the degree of departure from symmetry rather than independence. Over past years, many studies have proposed various types of indexes based on their power divergence (or diversity index) to represent the degree of departure from symmetry. This study proposes a two-dimensional index to measure the degree of departure from symmetry in terms of the log odds of each symmetric cell with respect to the main diagonal of the table. By measuring the degree of departure from symmetry in terms of the log odds of each symmetric cell, the analysis results are easier to interpret than existing indexes. Numerical experiments show the utility of the proposed two-dimensional index. We show the usefulness of the proposed two-dimensional index by using real data.

scholarly journals Modeling the Effects of Implementation of Alternative Ways of Vehicle Powering

Fuels ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 487-500
Author(s):  
Andrzej L. Wasiak
Keyword(s):  
Carbon Dioxide Emissions ◽  
Energy Demand ◽  
Electric Propulsion ◽  
Technology Development ◽  
Real Data ◽  
Previous Generation ◽  
Vehicle Operation ◽  
Vehicle Registration ◽  
Proposed Model ◽  
The Difference

The trend to replace traditional fossil fuel vehicles is becoming increasingly apparent. The replacement concerns the use of pure biofuels or in blends with traditional fuels, the use of hydrogen as an alternative fuel and, above all, the introduction of electric propulsion. The introduction of new types of vehicle propulsion affects the demand for specific fuels, the needs for new infrastructure, or the nature of the emissions to the environment generated by fuel production and vehicle operation. The article presents a mathematical model using the difference of two logistic functions, the first of which describes the development of the production of a specific type of vehicle, and the second, the withdrawal of this type of vehicle from traffic after its use. The model makes it possible to forecast both the number of vehicles of each generation as a function of time, as well as changes in energy demand from various sources and changes in exhaust emissions. The results of the numerical simulation show replacing classic vehicles with alternative vehicles increases the total energy demand if the generation of the next generation occurs earlier than the decay of the previous generation of vehicles and may decrease in the case of overlapping or delays in the creation of new vehicles compared to the course of the decay function of the previous generation. For electric vehicles, carbon dioxide emissions are largely dependent on the emissions from electricity generation. The proposed model can be used to forecast technology development variants, as well as analyze the current situation based on the approximation of real data from Vehicle Registration Offices.

A new load forecasting model considering planned load shedding effect

2019 ◽  
Vol 13 (1) ◽  
pp. 149-165
Author(s):  
Esam A. Hashim Alkaldy ◽  
Maythem A. Albaqir ◽  
Maryam Sadat Akhavan Hejazi
Keyword(s):  
Load Forecasting ◽  
Real Data ◽  
Load Shedding ◽  
Forecasting Model ◽  
Load Curve ◽  
Content Type ◽  
Electrical Grid ◽  
Four Seasons ◽  
Proposed Model ◽  
The Difference

PurposeLoad forecasting is important to any electrical grid, but for the developing and third-world countries with power shortages, load forecasting is essential. When planed load shedding programs are implemented to face power shortage, a noticeable distortion to the load curves will happen, and this will make the load forecasting more difficult.Design/methodology/approachIn this paper, a new load forecasting model is developed that can detect the effect of planned load shedding on the power consumption and estimate the load curve behavior without the shedding and with different shedding programs. A neuro-Fuzzy technique is used for the model, which is trained and tested with real data taken from one of the 11 KV feeders in Najaf city in Iraq to forecast the load for two days ahead for the four seasons. Load, temperature, time of the day and load shedding schedule for one month before are the input parameters for the training, and the load forecasting data for two days are estimated by the model.FindingsTo verify the model, the load is forecasted without shedding by the proposed model and compared to real data without shedding and the difference is acceptable.Originality/valueThe proposed model provides acceptable forecasting with the load shedding effect available and better than other models. The proposed model provides expected behavior of load with different shedding programs an issue helps to select the appropriate shedding program. The proposed model is useful to estimate the real demands by assuming load shedding hours to be zero and forecast the load. This is important in places suffer from grid problems and cannot supply full loads to calculate the peak demands as the case in Iraq.

Sign in / Sign up

Export Citation Format

Share Document