Two-way Contingency Tables Research Articles

Combining deep neural network and spatio-temporal clustering to automatically assess rockburst and seismic hazard – Case study from Marcel coal mine in Upper Silesian Basin, Poland

Mine induced seismic events are a major safety concern in mining and require careful monitoring and management to reduce their effects. Therefore, an essential step in assessing seismic and rock burst hazards is the analysis of mine seismicity. Recently, deep neural networks have been used to automatically determine seismic wave arrival times, surpassing human performance and allowing their use in seismic data analysis such as seismic event location and seismic energy calculation. In order to properly automate the rockburst and seismic hazard assessment deep neural network phase picker and a spatio-temporal clustering method were utilized. Seismic and rockburst hazards were statistically quantified using two-way contingency tables for two categorical variables: seismic energy level of mine tremors and number of clusters. Correlations between several spatio-temporal clusters and a statistical association between two categorical variables: seismic energy level and cluster number indicate an increase of seismic hazard in the Marcel hard coal mine in Poland. A new automated tool has been elaborated to automatically identify high-stress areas in mines in the form of spatio-temporal clusters.

Correspondence Analysis for Assessing Departures from Perfect Symmetry Using the Cressie–Read Family of Divergence Statistics

Recently, Beh and Lombardo (2022, Symmetry, 14, 1103) showed how to perform a correspondence analysis on a two-way contingency table where Bowker’s statistic lies at the numerical heart of this analysis. Thus, we showed how this statistic could be used to visually identify departures from perfect symmetry. Interestingly, Bowker’s statistic is a special case of the symmetry version of the Cressie–Read family of divergence statistics. Therefore, this paper presents a new framework for visually assessing departures from perfect symmetry using a second-order Taylor series approximation of the Cressie–Read family of divergence statistics.

Cumulative ordinal quasi-symmetry model and its separation for square contingency tables with ordered categories

Summary This study deals with square contingency tables, which are two-way contingency tables in which the row and column variables consist of the same classification. When the categorical variables are grouped into ordered categories from quantitative variables by cut points, a score that approximates the distance between the midpoints of the quantitative scale categories may be used to reflect the characteristics of the data. As an asymmetry model based on scores, this study proposes the cumulative ordinal quasi-symmetry model and ordinal marginal homogeneity model based on cumulative probabilities. The asymmetric parameter in the proposed models would be useful for making inferences such as that a row variable is stochastically less than a column variable or vice versa. This study also gives a separation of the cumulative ordinal quasi-symmetry model, that is, the cumulative ordinal quasi-symmetry model holds if and only if both the cumulative quasi-symmetry and ordinal marginal homogeneity models hold. The usefulness of the proposed models and the proposed separation is demonstrated through real data analysis.

Geometric Mean Type of Proportional Reduction in Variation Measure for Two-Way Contingency Tables

Traditional analysis of two-way contingency tables with explanatory and response variables focuses on the independence of two variables. However, if the variables do not show independence or a clear relationship, the analysis shifts to the degree of association. Various measures have been proposed to calculate the degree of association. One is the proportional reduction in variation (PRV) measure. This measure describes the PRV from the marginal distribution to the conditional distribution of the response variable. Although conventional PRV measures can assess the association of the entire contingency table, they cannot accurately assess the association for each explanatory variable. In this paper, we propose a geometric mean type of PRV (geoPRV) measure, which aims to sensitively capture the association of each explanatory variable to the response variable. Our approach uses a geometric mean, and enabling analysis without underestimating the values when the cells in the contingency table are partially biased. The geoPRV measure can be constructed using any function that satisfies specific conditions. This approach has practical advantages, and in special cases, conventional PRV measures can be expressed as geometric mean types.

Generalized Cramér’s coefficient via f-divergence for contingency tables

AbstractVarious measures in two-way contingency table analysis have been proposed to express the strength of association between row and column variables in contingency tables. Tomizawa et al. (2004) proposed more general measures, including Cramér’s coefficient, using the power-divergence. In this paper, we propose measures using the f-divergence that has a wider class than the power-divergence. Unlike statistical hypothesis tests, these measures provide quantification of the association structure in contingency tables. The contribution of our study is proving that a measure applying a function that satisfies the condition of the f-divergence has desirable properties for measuring the strength of association in contingency tables. With this contribution, we can easily construct a new measure using a divergence that has essential properties for the analyst. For example, we conducted numerical experiments with a measure applying the $$\theta$$ θ -divergence. Furthermore, we can give further interpretation of the association between the row and column variables in the contingency table, which could not be obtained with the conventional one. We also show a relationship between our proposed measures and the correlation coefficient in a bivariate normal distribution of latent variables in the contingency tables.

The Applicability of Peer Teaching in a Post-Graduate Business Course

This study demonstrates the interrelation between peer teaching and six grading criteria used in a graduate business program. Twenty (20) enrolled post-graduate students in the Advanced Statistics course were assigned to five (5) peer groups participating in the study. The quantitative graphical method was used. Specifically, the Correspondence Analysis (CA) two-way contingency table describes the association between the level of peer-teaching and its applicability to the six grading criteria. Based on the CA result, there was a clear separation among the peer groupings and the six grading criteria. Peer group D find peer teaching applicable to written content and exam. Peer group B considered peer-teaching moderately applicable to research while highly applicable in language content. For students in peer group C, moderate peer teaching is highly applicable to oral content. However, peer group A regarded peer teaching as not applicable to written skills. The correspondence analysis provided valuable insights into the relationships between peer teaching and six grading criteria. This study confirms that the level of peer teaching possesses a specific level of applicability in the six grading criteria, with the peer groupings exhibiting distinct patterns.

A new mixed integer programming approach for inverse correspondence analysis

Correspondence analysis (CA) is a dimension reduction technique for categorical data in a two-way contingency table. The low-dimensional CA solution optimally depicts the relationship between the categorical variables. We consider the inverse correspondence analysis (ICA) problem, where we use the low-dimensional representation in order to retrieve the original data table. We propose a mixed integer programming formulation for the ICA problem based on transition formulas, which link the row and column coordinates in a CA solution. We show that our formulation has better theoretical characteristics than the existing formulation in the literature and is able to model a generalised ICA problem, which requires less input. In addition, we introduce an iterative method, which uses the fit of individual points in the low-dimensional CA solution. By incorporating statistical information on the quality of CA solutions into our methodology, we are able to retrieve the original data for larger ICA instances.

Face-to-Face, Online or Hybrid, Which Model is Preferred by University Students And Why?

Teaching model preferences of current university students and the factors explaining them indicate educators and decision makers how to design future higher education system. The literatüre indicates the importance of teaching, social and cognitive presence, gender and experience for sustainability of online environments. Therefore, this study aims to examine to what degree university students' experiences and opinions affect their teaching model preferences (face-to-face, online, hybrid). 5504 university students participated to the study and the data were collected by an online questionnaire. gender, opinions about the complexity of the learning management system, the sufficiency of digital materials, knowing how to solve problems during online learning, course participation preferences, online teaching methods (synchronous, asynchronous, both) preferences and teaching, social and cognitive presence levels are the factors of the study. Two-way contingency table analyses using Pearson \chi^2 and multinomial logistic regression model (MLR) were applied to determine the factors affecting the teaching model preferences. The results indicated that 71.2 prefered online supported methods (online, hybrid) while only 25.8% preferred wholly face to face methods. Interestingly, more than half of the females preferred face-to-face and hybrid, while more than half of the males preferred online education. the teaching preferences of the students are dependent of the determined variables and Community of Inquiry elements that addressed in this study.

Adherence to Federal Dietary Recommendations for Total Fruit Consumption and the Intake of Underconsumed Nutrients: Findings from the National Health and Nutrition Examination Survey, 2015 to 2018

BackgroundA persistent gap exists between U.S. consumers’ actual fruit consumption and Federal dietary recommendations for fruit. Individuals who most deviate from recommendations may be at a greater risk of underconsuming some nutrients. ObjectiveWe investigated how widely total fruit consumption varies across adult consumers and whether those who most deviate from recommendations also consume less vitamins A and C, calcium, magnesium, and potassium. The 2020 Dietary Guidelines Advisory Committee has identified each of these nutrients as being underconsumed by the U.S. population in general. MethodsData used were from the NHANES, 2015 to 2016 and 2017 to 2018 cycles. For 9832 adults (age >18), we compared their total fruit consumption to recommendations for their age and sex. We also calculated 2015 Healthy Eating Index (HEI-2015) scores. Component scores for Total Fruit and Whole Fruit were subtracted from the total HEI-2015 scores to measure adherence with dietary recommendations outside the fruit group. Two-way and 3-way contingency tables were then used to measure the association between adherence to fruit recommendations and the intake of underconsumed nutrients before and after controlling for adherence to other food group recommendations, respectively. ResultsAbout two-thirds of adults eat less than half the recommended amount of fruit on any given day. Those who routinely unconsume fruit may be at a greater risk of underconsuming potassium and vitamin C. Calcium, magnesium, and vitamin A consumption do not show a consistent relationship with fruit intake relative to recommendations after controlling for diet quality outside the fruit group. ConclusionsThere is much variation across the U.S. population in fruit consumption relative to recommendations. The present study suggests that individuals who deviate the most are at a particularly increased risk of underconsuming vitamin C and potassium.

Measure of departure from marginal point-symmetry for multi-way contingency tables

To analyze two-way contingency tables with ordered categories, Iki and Tomizawa (2018) proposed a measure to distinguish two kinds of marginal asymmetry for the midpoint. However, that measure cannot necessarily judge all of the marginal asymmetries. We improve the measure and give a new measure for multi-way contingency tables. We also derive an approximate confidence interval for the measure.

Dimensionality reduction approach for many-objective epistasis analysis.

In epistasis analysis, single-nucleotide polymorphism-single-nucleotide polymorphism interactions (SSIs) among genes may, alongside other environmental factors, influence the risk of multifactorial diseases. To identify SSI between cases and controls (i.e. binary traits), the score for model quality is affected by different objective functions (i.e. measurements) because of potential disease model preferences and disease complexities. Our previous study proposed a multiobjective approach-based multifactor dimensionality reduction (MOMDR), with the results indicating that two objective functions could enhance SSI identification with weak marginal effects. However, SSI identification using MOMDR remains a challenge because the optimal measure combination of objective functions has yet to be investigated. This study extended MOMDR to the many-objective version (i.e. many-objective MDR, MaODR) by integrating various disease probability measures based on a two-way contingency table to improve the identification of SSI between cases and controls. We introduced an objective function selection approach to determine the optimal measure combination in MaODR among 10 well-known measures. In total, 6 disease models with and 40 disease models without marginal effects were used to evaluate the general algorithms, namely those based on multifactor dimensionality reduction, MOMDR and MaODR. Our results revealed that the MaODR-based three objective function model, correct classification rate, likelihood ratio and normalized mutual information (MaODR-CLN) exhibited the higher 6.47% detection success rates (Accuracy) than MOMDR and higher 17.23% detection success rates than MDR through the application of an objective function selection approach. In a Wellcome Trust Case Control Consortium, MaODR-CLN successfully identified the significant SSIs (P < 0.001) associated with coronary artery disease. We performed a systematic analysis to identify the optimal measure combination in MaODR among 10 objective functions. Our combination detected SSIs-based binary traits with weak marginal effects and thus reduced spurious variables in the score model. MOAI is freely available at https://sites.google.com/view/maodr/home.

Extension of generalized proportional reduction in variation measure for two-way contingency tables

Extension of generalized proportional reduction in variation measure for two-way contingency tables

Simultaneous estimation of Poisson means in two-way contingency tables under normalized squared error loss

Simultaneous estimation of Poisson means in two-way contingency tables under normalized squared error loss

Robust Correspondence Analysis

AbstractCorrespondence analysis is a method for the visual display of information from two-way contingency tables. We introduce a robust form of correspondence analysis based on minimum covariance determinant estimation. This leads to the systematic deletion of outlying rows of the table and to plots of greatly increased informativeness. Our examples are trade flows of clothes and consumer evaluations of the perceived properties of cars. The robust method requires that a specified proportion of the data be used in fitting. To accommodate this requirement we provide an algorithm that uses a subset of complete rows and one row partially, both sets of rows being chosen robustly. We prove the convergence of this algorithm.

The impact of understanding tourists’ preferences on optimizing tourism outcome in Lebanese rural destinations

The Lebanese economy primarily relies on the service sector, and tourism is one of the most important economic service sectors in Lebanon, for it constitutes 20% of Lebanon’s national income. One particularly interesting aspect of tourism is rural tourism, which could represent a significant economic opportunity for Lebanon, especially after the outbreak of COVID-19 pandemic and amongst the Lebanese economic crisis. This article focuses on nine main factors that are believed to have an influence on the decision-making process of tourists visiting rural destination in Lebanon. These factors include tourist attraction, tourist transportation, accommodation, tourist entertainment, natural environment, hospitality environment, tourist information, marketing and safety and security. The aim of this study is to analyze the perception of Lebanese tourism stakeholders towards the mentioned nine factors that could affect the decisions of tourists, thereby aiding those stakeholders to create appropriate tourism strategies that match the needs of tourists more accurately. The main research question addressed is stated as follows: “What are the factors that have the most impact on the decision-making process of tourists visiting rural tourism destinations in Lebanon?” Tourism stakeholders targeted in this article include tourists visiting Lebanon, tour operators, the Lebanese government and local authorities such as municipalities, local residents of tourism destinations, the private sector, NGOs and others. As for the research methodology, a quantitative research approach based on a self-designed survey was applied. Primary data was collected from several rural Lebanese villages randomly selecting 354 respondents of varied profiles. These respondents were also interviewed face-to-face. Data obtained were analyzed using the SPSS 20.0; The Chi Square test (two-way contingency table) and a correlation analysis were used to analyze data and check the validity of the proposed hypotheses. Results of the study revealed that (i) transportation facilities, (ii) the natural environment, and (iii) the safety and security of a tourism destination were the most impactful factors that affected decisions of tourists. It is recommended that tourism stakeholders carefully study their target market in order to meet the corresponding tourism demands. Nevertheless, stakeholders such as the government should cooperate with other stakeholders and enroll them in tourism planning in order to optimize tourism capacity and achieve sustainable tourism development in the future. A future perspective of the subject could highlight foreign currency exchange rate and COVID-19 vaccination as additional factors that could have a remarkable impact on the decision-making process of tourists considering Lebanese rural tourism destinations.

Weighted cumulative correspondence analysis based on a particular cumulative power divergence family

AbstractThe Pearson’s $$X^2$$ X 2 statistic and the likelihood ratio statistic $$G^2$$ G 2 are most frequently used for testing independence or homogeneity, in two-way contingency table. These indexes are members of a continuous family of Power Divergence (PD) statistics, but they perform badly in studying the association between ordinal categorical variables. Taguchi’s and Nair’s statistics have been introduced in the literature as simple alternatives to Pearson’s index for contingency tables with ordered categorical variables. It’s possible to show, using a parameter, how to link Taguchi’s and Nair’s statistics obtaining a new class called Weighted Cumulative Chi-Squared (WCCS-type tests). Therefore, the main aim of this paper is to introduce a new divergence family based on cumulative frequencies called Weighted Cumulative Power Divergence. Moreover, an extension of Cumulative Correspondence Analysis based on WCCS and further properties are shown.

Social Networking as Leisure: An Attempt to Conceptualize Liquid Leisure

Our research was intended to find out whether social networking is recognized and experienced as leisure or should be considered liquid leisure because its borders are fluid. This aim was connected to the broader question of whether there are still clear borders between work, leisure, and other life aspects. The research was designed as a cross-sectional ex-post-facto study. The survey examined data collected through a structured questionnaire completed and returned by 3451 respondents aged 15+ selected from the general population of the Czech Republic. The statistical significance of hypotheses was tested using χ2 statistics for two-way (C × R) and three-way (C × R × L) contingency tables. Only 752 (21.79%) respondents reported not having or using an online social network account. Even though there is no reason why social networking should not be considered leisure, there was a considerable discrepancy between those who considered social media a leisure activity (8.2%) and those who did not (78.21%). Therefore, this kind of leisure activity is conceptualized in this paper as a specific liquid leisure.

Two-mode clustering through profiles of regions and sectors

This paper is concerned with simultaneously regrouping regions and sectors when analyzing the relative sectorial specialization of regions and the relative regional concentration of sectors. An automatic two-mode clustering algorithm is proposed with a view toward a concept of overall localization, corresponding to a discrepancy between an actual two-way contingency table (regions \(\times \) sectors) and an hypothetical table reflecting independence between regions and sectors. This procedure identifies similar regions (respectively sectors) according to the relative sectorial (respectively regional) structure. This algorithm significantly reduces the size of the original table and obtain an optimal collapsed table with low level of information loss vis-à-vis the degree of overall localization. The properties and results of the algorithm are discussed through two applications, namely Argentina and Brazil.

DEPARTURE FROM QUASI-UNIFORM ASSOCIATION MODEL IN ORDERED SQUARE CONTINGENCY TABLES

The Uniform Association (UA) and Quasi-Uniform Association (QUA) models are used for analysis of two-way square contingency tables with ordered categories. When the QUA model does not fit the data, one wants to measure the degree of departure from the quasi-uniform association model. The degree of the departure from the model is calculated by usingthe power divergence statistics. In this study, as an alternative to measures in the literature, a measure to estimate the degree of departure from the QUA model is suggested. This suggested measure allows us to compare the several R×R tables in terms of the departure from the model. The measures are compared by the simulation study and discussed by three unaided distance vision data.

Diversity, Equity and Inclusion in an Age-Friendly Health System

The Age-Friendly Health Systems (AFHS) initiative uses a 4Ms framework to encourage patient-centered care for older adults. Many health systems have implemented the core elements of AFHS – What Matters, Mentation (Cognition and Depression), Medications, and Mobility – with the goal to uniformly apply these elements to all patients 65 years and older. However, equity in AFHS delivery has not yet been examined. Five diversity, equity, and inclusion (DEI) factors, including gender, race, ethnicity, preferred language and MyChart activation, were cross-sectionally analyzed against the 4Ms framework for patients seen (in person or virtual visit) in an academic internal medicine clinic between April 2020 and April 2021 (N= 3370) using two-way contingency tables. Preferred language, gender, and MyChart activation yielded significant pairings with the 4M metrics. For the AFHS What Matters metric, females were 1.10 times more likely than males and English-speaking patients were 1.67 times more likely than non-English speaking patients to receive advance care planning (p <0.01). Females and patients with MyChart activation were about 2.0 times more likely to have a high-risk medication on their medication list compared to males and patients without MyChart activation (p <0.01). MyChart activation was also significantly associated with cognitive screening. Patients with MyChart activation were 1.09 times more likely than patients without MyChart activation to get cognitive screening (p <0.001). This study, the first to incorporate demographic data, into AFHS quality measures, suggest a need to develop best practices for equitable Age-Friendly care at the clinical team and the institutional policy level.