Logratio approach to statistical analysis of 2×2 compositional tables

Fačevicová, Kamila; Hron, Karel; Todorov, Valentin; Guo, Dong; Templ, Matthias

doi:10.1080/02664763.2013.856871

Cited by 12 publications

(13 citation statements)

References 10 publications

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“…Balances can be easily interpreted in the general case of D ‐part compositional data (Egozcue & Pawlowsky‐Glahn, ; Fišerová & Hron, ). This is also true for 2 × 2 compositional tables (see Fačevicová, , for details). Compositional tables require another approach to provided interpretation.…”

Section: Compositional Tables and The Aitchison Geometrymentioning

confidence: 65%

“…However, this does not hold when standard methods are applied for statistical analysis of compositional tables. The reason is that contrary to standard multivariate observations (and the corresponding statistical methods) that rely on the Euclidean geometry in real space, compositional tables are characterized by their specific geometric nature, represented by the Aitchison geometry on the simplex (Pawlowsky‐Glahn & Egozcue, ; Egozcue et al , ; Fačevicová et al ., ).…”

Section: Introductionmentioning

confidence: 97%

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Compositional Tables Analysis in Coordinates

Fačevicová¹,

Hron²,

Todorov

et al. 2016

Scandinavian J Statistics

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Compositional tables -a continuous counterpart to the contingency tables -carry relative information about relationships between row and column factors; thus, for their analysis, only ratios between cells of a table are informative. Consequently, the standard Euclidean geometry should be replaced by the Aitchison geometry on the simplex that enables decomposition of the table into its independent and interactive parts. The aim of the paper is to find interpretable coordinate representation for independent and interaction tables (in sense of balances and odds ratios of cells, respectively), where further statistical processing of compositional tables can be performed.Theoretical results are applied to real-world problems from a health survey and in macroeconomics.

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Section: Compositional Tables and The Aitchison Geometrymentioning

confidence: 65%

Section: Introductionmentioning

confidence: 97%

Compositional Tables Analysis in Coordinates

Fačevicová¹,

Hron²,

Todorov

et al. 2016

Scandinavian J Statistics

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“…Following Fačevicová et al (2014a), it is possible to assign also another system of orthonormal coordinates to a 2 × 2 compositional table. Specificaly, we get…”

Section: Implications For 2 X 2 Compositional Tablesmentioning

confidence: 99%

“…In practice, 2 × 2 compositional (and also contingency) tables represent a prominent special case that requires a special treatment (Fačevicová et al 2014a;Agresti 2002). From Equations (3), (4) and (5) it is easy to see that for coordinate representation of the compositional table…”

Section: Implications For 2 X 2 Compositional Tablesmentioning

confidence: 99%

“…multivariate observations carrying relative information (Aitchison 1986;Pawlowsky-Glahn and Buccianti 2011), it is also suitable for more complex data structures, where not the absolute values but rather ratios are of primary interest. One of them are compositional tables (Egozcue, Díaz-Barrero, and Pawlowsky-Glahn 2008;Egozcue, Pawlowsky-Glahn, Templ, and Hron 2014;Fačevicová, Hron, Todorov, Guo, and Templ 2014a;Fačevicová, Hron, Todorov, and Templ 2014b), a continuous counterpart to well-known contingency tables (Agresti 2002). Besides the difference in the nature of data, (cells of the contingency table are discrete counts, while parts of the compositional tables are continuous values), the main difference between is that, on the one hand, a contingency table collects results from n independent observations, while, on the other hand, a compositional table itself represents one observation.…”

Section: Introductionmentioning

confidence: 99%

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Covariance Structure of Compositional Tables

Fačevicová¹,

Hron²

2015

AJS

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Recent experience with interpretation of orthonormal coordinates in compositional data shows clearly a necessity of their better understanding in terms of logratios that form the primary source of information within the logratio methodology. This is even more crucial in the special case of compositional tables, where both balances and coordinates with odds ratio interpretation are involved. The aim of the paper is to provide a decomposition of covariance structure of orthonormal coordinates in compositional tables in terms of logratio variances, which could serve this purpose. For their better interpretability, the formulas are also accompanied with appropriate comments and graphical illustrations, and implications for the prominent case of 2 × 2 compositional tables are discussed.

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Measurement, selection, and visualization of association rules: A compositional data perspective

Vives‐Mestres

Kenett

Thió‐Henestrosa

et al. 2021

Quality & Reliability Eng

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Association rule mining is a powerful data analytic technique used for extracting information from transaction databases with a collection of itemsets. The aim is to indicate what item goes with what item (ie, an association rule) in a set of collected transactions. It is extensively used in text analytics of text records or social media. Here we use Compositional Data analysis (CoDa) techniques to generate new visualizations and insights from association rule mining. These CoDa methods show the relationship between itemsets, their strength, and direction of dependency. Moreover, after expressing each association rule as a contingency table, we discuss two statistical tests to guide identification of the relevant rules by analyzing the relative importance of the elements of the table. As an example, we use these visualizations and statistical tests for investigating the association of negative mood emotions to various types of headache/migraine events. Data for those analysis comes from N1‐HeadacheTM, a digital platform where individual users record attacks and symptoms as well as their daily exposure to a list of potential factors.

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Logratio approach to statistical analysis of 2×2 compositional tables

Cited by 12 publications

References 10 publications

Compositional Tables Analysis in Coordinates

Compositional Tables Analysis in Coordinates

Covariance Structure of Compositional Tables

Measurement, selection, and visualization of association rules: A compositional data perspective

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