Measuring multivariate association and beyond

Josse, Julie; Holmes, Susan

doi:10.1214/16-ss116

Cited by 76 publications

(69 citation statements)

References 88 publications

(135 reference statements)

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“…In canonical correlation analysis [CCA; 19], the first k pairs of Xand Ycanonical variates are given by X * M and Y * L, where X * and Y * are column-standardized versions of X and Y, M is the p × k loading matrix for X * , and L is the q × k loading matrix for Y * . The matrices M and L are obtained by maximizing the RV coefficient RV (X * M, Y * L) [4]. Our work on the contribution plot suggests an alternative criterion function to maximize, namely RV (X * M, Y * L|α m ), where α m is the power that minimizes the p-value of the test based on the generalized RV coefficient RV (X * , Y * |α) in equation (9).…”

Section: Discussionmentioning

confidence: 99%

“…In this section, we define the RV coefficient and its population counterpart, the multivariate correlation coefficient ρ V , following [4]. Our intended use of the RV coefficient is to investigate correlations between matrices of genetic marker genotypes and brain phenotypes, and our descriptions will be in those terms, though the methods apply in any multivariate setting.…”

Section: The Contribution Plotmentioning

confidence: 99%

“…To measure the association between multivariate datasets, many different correlation coefficients have been introduced. One of the most popular is the RV coefficient, which measures the linear association between two datasets by estimating the population vector correlation coefficient ρ V [4]. When both datasets consist of a single variable, RV is the squared Pearson-correlation coefficient and ρ V is the squared population-correlation coefficient.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer’s Disease

Choi

Beg

et al. 2019

Hum Hered

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Alzheimer's disease (AD) is a chronic neurodegenerative disease that causes memory loss and decline in cognitive abilities. AD is the sixth leading cause of death in the United States, affecting an estimated 5 million Americans. To assess the association between multiple genetic variants and multiple measurements of structural changes in the brain a recent study of AD used a multivariate measure of linear dependence, the RV coefficient. The authors decomposed the RV coefficient into contributions from individual variants and displayed these contributions graphically. We investigate the properties of such a "contribution plot" in terms of an underlying linear model, and discuss estimation of the components of the plot when the correlation signal may be sparse. The contribution plot is applied to simulated data and to genomic and brain imaging data from the Alzheimer's Disease Neuroimaging Initiative.

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Section: Discussionmentioning

confidence: 99%

Section: The Contribution Plotmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer’s Disease

Choi

Beg

et al. 2019

Hum Hered

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“…120 A Mantel's test can be used to test the hypothesis that geographic distance predicts similarity in the composition of bacterial communities across sites. 121 This model assumes that the relationship between the geographic distance and community dissimilarity is linear and that small or large values in one matrix correspond to similarly sized values in the other. 122 For this reason, the Mantel test can assess the extent to which dispersal, birth, death, and other contagious biotic processes induce spatial autocorrelation in the data (eg, communities are more similar when they are geographic neighbors, with incremental gains in community dissimilarity occurring with increasing geographic separation).…”

Section: Dispersalmentioning

confidence: 99%

Microbial biogeography and ecology of the mouth and implications for periodontal diseases

Proctor

Shelef

González

et al. 2019

Periodontology 2000

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In humans, the composition of microbial communities differs among body sites and between habitats within a single site. Patterns of variation in the distribution of organisms across time and space are referred to as “biogeography.” The human oral cavity is a critical observatory for exploring microbial biogeography because it is spatially structured, easily accessible, and its microbiota has been linked to the promotion of both health and disease. The biogeographic features of microbial communities residing in spatially distinct, but ecologically similar, environments on the human body, including the subgingival crevice, have not yet been adequately explored. The purpose of this paper is twofold. First, we seek to provide the dental community with a primer on biogeographic theory, highlighting its relevance to the study of the human oral cavity. We summarize what is known about the biogeographic variation of dental caries and periodontitis and postulate that disease occurrence reflects spatial patterning in the composition and structure of oral microbial communities. Second, we present a number of methods that investigators can use to test specific hypotheses using biogeographic theory. To anchor our discussion, we apply each method to a case study and examine the spatial variation of the human subgingival microbiota in 2 individuals. Our case study suggests that the composition of subgingival communities may conform to an anterior‐to‐posterior gradient within the oral cavity. The gradient appears to be structured by both deterministic and nondeterministic processes, although additional work is needed to confirm these findings. A better understanding of biogeographic patterns and processes will lead to improved efficacy of dental interventions targeting the oral microbiota.

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“…A Mantel's test can be used to test the hypothesis that geographic distance predicts similarity in the composition of bacterial communities across sites 121 . This model assumes that the relationship between the geographic distance and community dissimilarity is linear and that small or large values in one matrix correspond to similarly sized values in the other 122 .…”

Section: Case Study -Applying the Neutral Model To The Subgingival MImentioning

confidence: 99%

Microbial biogeography and ecology of the mouth and implications for periodontal diseases

Proctor

Shelef

González

et al. 2019

Preprint

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Human-associated microbial communities differ in composition among body sites and between habitats within a site. Patterns of variation in the distribution of organisms across time and space is referred to as 'biogeography'. The human oral cavity is a critical observatory for exploring microbial biogeography because it is spatially structured, easily accessible, and its microbiota has been linked to the promotion of both health and disease. The biogeographic features of microbial communities residing in spatially distinct but ecologically similar environments on the human body, including the subgingival crevice, have not yet been adequately explored. The purpose of this paper is twofold. First, we seek to provide the dental community with a primer on biogeographic theory, highlighting its relevance to the study of the human oral cavity. For this reason, we summarize what is known about the biogeographic variation of dental caries and periodontitis and postulate as to how this may be driven by spatial patterning in oral microbial community composition and structure. Second, we present a number of methods that investigators can use to test specific hypotheses using biogeographic theory.To anchor our discussion, we apply each method to a case study and examine the spatial variation of the human subgingival microbiota of 2 individuals. Our case study suggests that subgingival communities in the aggregate may conform to an anterior-to-posterior gradient in community composition. The gradient appears to be structured both by deterministic and nondeterministic processes, though additional work is needed to test and confirm specific hypotheses. A better understanding of biogeographic patterns and processes will advance our understanding of ways to optimize the efficacy of dental interventions targeting the oral microbiota.

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Measuring multivariate association and beyond

Cited by 76 publications

References 88 publications

The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer’s Disease

The Contribution Plot: Decomposition and Graphical Display of the RV Coefficient, with Application to Genetic and Brain Imaging Biomarkers of Alzheimer’s Disease

Microbial biogeography and ecology of the mouth and implications for periodontal diseases

Microbial biogeography and ecology of the mouth and implications for periodontal diseases

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