Dataset Information

Measuring multivariate association and beyond.

ABSTRACT: Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients are being used by different research communities. Scientists use these coefficients to test whether two random vectors are linked. Once it has been ascertained that there is such association through testing, then a next step, often ignored, is to explore and uncover the association's underlying patterns. This article provides a survey of various measures of dependence between random vectors and tests of independence and emphasizes the connections and differences between the various approaches. After providing definitions of the coefficients and associated tests, we present the recent improvements that enhance their statistical properties and ease of interpretation. We summarize multi-table approaches and provide scenarii where the indices can provide useful summaries of heterogeneous multi-block data. We illustrate these different strategies on several examples of real data and suggest directions for future research.

SUBMITTER: Josse J

PROVIDER: S-EPMC5658146 | biostudies-literature | 2016

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Measuring multivariate association and beyond.

Josse Julie J Holmes Susan S

Statistics surveys 20161117

Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients are being used by different research communities. Scientists use these coefficients to test whether two random vectors are linked. Once it has been ascertained that there is such association through testing, then a next step, often ignored, is to explo ...[more]

PMID: 29081877

Similar Datasets

Project description:PurposeMeaningful changes in picture naming responses may be obscured when measuring accuracy instead of quality. A statistic that incorporates information about the severity and nature of impairments may be more sensitive to the effects of treatment.MethodWe analyzed data from repeated administrations of a naming test to 72 participants with stroke aphasia in a clinical trial for anomia therapy. Participants were divided into two groups for analysis to demonstrate replicability. We assessed reliability among response type scores from five raters. We then derived four summary statistics of naming ability and their changes over time for each participant: (a) the standard accuracy measure, (b) an accuracy measure adjusted for item difficulty, (c) an accuracy measure adjusted for item difficulty for specific response types, and (d) a distance measure adjusted for item difficulty for specific response types. While accuracy measures address the likelihood of a correct response, the distance measure reflects that different response types range in their similarity to the target. Model fit was assessed. The frequency of significant improvements and the average magnitude of improvements for each summary statistic were compared between treatment groups and a control group. Effect sizes for each model-based statistic were compared with the effect size for the standard accuracy measure.ResultsInterrater and intrarater reliability were near perfect, on average, though compromised somewhat by phonological-level errors. The effects of treatment were more evident, in terms of both frequency and magnitude, when using the distance measure versus the other accuracy statistics.ConclusionsConsideration of item difficulty and response types revealed additional effects of treatment on naming scores beyond those observed for the standard accuracy measure. The results support theories that assume naming ability is decomposable into subabilities rather than being monolithic, suggesting new opportunities for measuring treatment outcomes.Supplemental materialhttps://doi.org/10.23641/asha.17019515.

Project description:With the advent of modern imaging and measurement technology, complex phenotypes are increasingly represented by large numbers of measurements, which may not bear biological meaning one by one. For such multivariate phenotypes, studying the pairwise associations between all measurements and all alleles is highly inefficient and prevents insight into the genetic pattern underlying the observed phenotypes. We present a new method for identifying patterns of allelic variation (genetic latent variables) that are maximally associated-in terms of effect size-with patterns of phenotypic variation (phenotypic latent variables). This multivariate genotype-phenotype mapping (MGP) separates phenotypic features under strong genetic control from less genetically determined features and thus permits an analysis of the multivariate structure of genotype-phenotype association, including its dimensionality and the clustering of genetic and phenotypic variables within this association. Different variants of MGP maximize different measures of genotype-phenotype association: genetic effect, genetic variance, or heritability. In an application to a mouse sample, scored for 353 SNPs and 11 phenotypic traits, the first dimension of genetic and phenotypic latent variables accounted for >70% of genetic variation present in all 11 measurements; 43% of variation in this phenotypic pattern was explained by the corresponding genetic latent variable. The first three dimensions together sufficed to account for almost 90% of genetic variation in the measurements and for all the interpretable genotype-phenotype association. Each dimension can be tested as a whole against the hypothesis of no association, thereby reducing the number of statistical tests from 7766 to 3-the maximal number of meaningful independent tests. Important alleles can be selected based on their effect size (additive or nonadditive effect on the phenotypic latent variable). This low dimensionality of the genotype-phenotype map has important consequences for gene identification and may shed light on the evolvability of organisms.

Dataset Information

Measuring multivariate association and beyond.

Publications

Measuring multivariate association and beyond.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets