Visualizing, Summarizing, and Comparing Odds Ratio Structures

Rooij, Mark de; Anderson, Carolyn J.

doi:10.1027/1614-2241.3.4.139

Cited by 8 publications

(11 citation statements)

References 23 publications

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“…Odds ratios (OR) were calculated as OR = [( a / b )/( c / d )] for each session as the likelihood that a given posture–vocalization dyad would co‐occur. The OR is a descriptive measure of effect size for categorical variables and a primary measure of association in 2 × 2 frequency tables (Andrade, ; De Rooij & Anderson, ). ORs greater than 1 indicated that contingencies were more likely to occur than not, ORs less than 1 indicate that contingencies were unlikely to occur, and p values indicate whether these likelihoods were significant.…”

Section: Resultsmentioning

confidence: 99%

The Trajectory of Concurrent Motor and Vocal Behaviors Over the Transition to Crawling in Infancy

Berger

Cunsolo

Ali

et al. 2017

Infancy

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To document the trajectory of motor and vocal behaviors in real and developmental time, researchers observed infants at each of 4 biweekly naturalistic play sessions over the transition to crawling. An exhaustive and mutually exclusive coding scheme documented every vocalization and posture. Odds ratios of the likelihood of a given posture-vocalization dyad revealed that vocalization and crawling were significantly unlikely to co-occur at the session marking the onset of crawling. Infants’ allocation of attention over the transition to crawling prompted behavioral trade-offs. During mastery of a novel skill, infants had difficulty allocating attention to multiple tasks, but with experience a decrease in attentional load for the new skill allowed performance of simultaneous behaviors in other domains to occur.

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Section: Resultsmentioning

confidence: 99%

The Trajectory of Concurrent Motor and Vocal Behaviors Over the Transition to Crawling in Infancy

Berger

Cunsolo

Ali

et al. 2017

Infancy

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“…The odds ratio (OR) is one of the main measures of association in 2 × 2 contingency tables. The OR is also commonly used to describe the relationship between the row and column variables in I × J two‐way contingency tables, see for example Altham (), Goodman (, ), Greenacre (), De Rooij & Anderson () and de Rooij & Heiser (). In this case the total number of ORs to compute is [ I ( I − 1)]/2 × [ J ( J − 1)]/2 although this number can be reduced using the basic set of ORs, as defined by De Rooij & Anderson ().…”

Section: Introductionmentioning

confidence: 99%

“…The OR is also commonly used to describe the relationship between the row and column variables in I × J two‐way contingency tables, see for example Altham (), Goodman (, ), Greenacre (), De Rooij & Anderson () and de Rooij & Heiser (). In this case the total number of ORs to compute is [ I ( I − 1)]/2 × [ J ( J − 1)]/2 although this number can be reduced using the basic set of ORs, as defined by De Rooij & Anderson (). Irrespective of the results of De Rooij & Anderson (), in this paper we consider the complete set of ORs, because, as we will show, the matrix containing all of the ORs is linked in an important way with the original two‐way contingency table of dimension I × J .…”

Section: Introductionmentioning

confidence: 99%

“…In this case the total number of ORs to compute is [ I ( I − 1)]/2 × [ J ( J − 1)]/2 although this number can be reduced using the basic set of ORs, as defined by De Rooij & Anderson (). Irrespective of the results of De Rooij & Anderson (), in this paper we consider the complete set of ORs, because, as we will show, the matrix containing all of the ORs is linked in an important way with the original two‐way contingency table of dimension I × J .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Measures of Association and Visualization of Log Odds Ratio Structure for a Two Way Contingency Table

Sarnacchiaro

D’Ambra

Camminatiello

2015

Aus NZ J of Statistics

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The odds ratio (OR) is a measure of association used for analysing an I × J contingencytable. The total number of ORs to check grows with I and J . Several statistical methodshave been developed for summarising them. These methods begin from two differentstarting points, the I × J contingency table and the two-way table composed by the ORs.In this paper we focus our attention on the relationship between these methods and pointout that, for an exhaustive analysis of association through log ORs, it is necessary toconsider all the outcomes of these methods. We also introduce some new methodologicaland graphical features. In order to illustrate previously used methodologies, we consider adata table of the cross-classiﬁcation of the colour of eyes and hair of 5387 children fromScotland. We point out how, through the log OR analysis, it is possible to extract usefulinformation about the association between variables

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“…(Erosheva 2005) employed a geometric approach to compare the potential value of using the Grade of Membership, latent class, and Rasch models in representing population heterogeneity for 2 J tables. Similarly, (Heiser 2004, De Rooij and Anderson 2007, De Rooij and Heiser 2005 have given geometric characterisations linked to odds ratios and related models for I × J tables, (Greenacre and Hastie 1987) focus on the geometric interpretation of correspondence analysis for contingency tables, (Carlini and Rapallo 2005) described some of the links to (Fienberg and Gilbert 1970) as well as the geometric structure of statistical models for case-control studies, and (Flach 2003) linked the geometry to Receiver Operating Characteristic space.…”

Section: Introductionmentioning

confidence: 99%

Algebraic geometry of 2×2 contingency tables

Slavković¹,

Fienberg

2009

Algebraic and Geometric Methods in Statistics

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Contingency tables represent the joint distribution of categorical variables. In this chapter we use modern algebraic geometry to update the geometric representation of 2 × 2 contingency tables first explored in (Fienberg 1968) and (Fienberg and Gilbert 1970). Then we use this geometry for a series of new ends including various characterizations of the joint distribution in terms of combinations of margins, conditionals, and odds ratios. We also consider incomplete characterisations of the joint distribution and the link to latent class models and to the phenomenon known as Simpson's paradox. Many of the ideas explored here generalise rather naturally to I × J and higher-way tables. We end with a brief discussion of generalisations and open problems. For contingency tables, beginning with (Fienberg 1968) and (Fienberg and Gilbert 1970), several authors have exploited the geometric representation of contingency table models, in terms of quantities such as margins and odds ratios, both for the proof of statistical results and to gain deeper understanding of models used for contingency table representation. For example, see (Fienberg 1970) for the convergence of iterative proportional fitting procedure, (Diaconis 1977) for the geometric representation of exchangeability, and (Kenett 1983) for uses in exploratory data analysis. More recently, (Nelsen 1995, Nelsen 2006 in a discussion of copulas for binary variables points out that two faces of the tetrahedron form the Fréchet upper bound, the other two the lower bound, and the surface of independence is the independence copula.There has also been considerable recent interest in geometric descriptions of contingency tables models and analytical tools, from highly varying perspectives.

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Visualizing, Summarizing, and Comparing Odds Ratio Structures

Cited by 8 publications

References 23 publications

The Trajectory of Concurrent Motor and Vocal Behaviors Over the Transition to Crawling in Infancy

The Trajectory of Concurrent Motor and Vocal Behaviors Over the Transition to Crawling in Infancy

Measures of Association and Visualization of Log Odds Ratio Structure for a Two Way Contingency Table

Algebraic geometry of 2×2 contingency tables

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