Partial canonical correlations

Rao, B. Raja

doi:10.1007/bf03028532

Cited by 38 publications

(13 citation statements)

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“…Separate CCAs, each with a single explanatory variable (also called constraint), were used to test gross effects. The net effect of each particular variable after partitioning out the effect shared with the other explanatory variables (also called conditionals) was tested with a partial CCA (pCCA), proposed by Rao [33], with a single explanatory variable (i.e., constraint) and the other 5 variables used as covariates (i.e., conditionals). The significance of constraints was tested using permutation based ANOVA (N = 999 permutations).…”

Section: Discussionmentioning

confidence: 99%

Disentangling the Effects of Tillage Timing and Weather on Weed Community Assembly

et al. 2017

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Abstract:The effect of tillage timing on weed community assembly was assessed at four locations in the Northeastern United States by tilling the soil every two weeks from April to September and quantifying the emerged weed community six weeks after each tillage event. Variance partitioning analysis was used to test the relative importance of tillage timing and weather on weed community assembly (106 weed species). At a regional scale, site (75.5% of the explained inertia)-and to a lesser extent, timing-of tillage (18.3%), along with weather (18.1%), shaped weed communities. At a local scale, the timing of tillage explained approximately 50% of the weed community variability. The effect of tillage timing, after partitioning out the effect of weather variables, remained significant at all locations. Weather conditions, mainly growing degree days, but also precipitation occurring before tillage, were important factors and could improve our ability to predict the impact of tillage timing on weed community assemblages. Our findings illustrate the role of disturbance timing on weed communities, and can be used to improve the timing of weed control practices and to maximize their efficacy.

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Section: Discussionmentioning

confidence: 99%

Disentangling the Effects of Tillage Timing and Weather on Weed Community Assembly

et al. 2017

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“…Thus, in the previous notation: Rao (1969) and Lee (1978). However, the asymptotic properties ofρ 12 under the null hypothesis are difficult to determine analytically, due to the partialization step, temporal autocorrelation (since the variables are time series) of BOLD signal, and possibly non-Gaussian probability distribution.…”

Section: Partialization In Canonical Correlation Analysismentioning

confidence: 98%

“…In its original proposal, CCA does not consider the partialization by a third set of time series. The partialization of CCA was described by Rao (1969) and is explained in more detail in Appendix A. The asymptotic properties of the partial canonical correlation coefficient ρ, necessary for using statistical tests, are difficult to obtain analytically.…”

Section: Canonical Correlation Analysis and Granger Causalitymentioning

confidence: 99%

“…When analyzing the relationships between two sets of time series, partialization is a crucial step to remove the influences from autocorrelation in the target series set and also cross-correlations from other possible sets. In the framework of partial canonical correlation analysis (PCCA) introduced by Rao (1969), suppose that, when combined, the three matrices of variables, Y i t , Y j t − 1 and X(X = Y t − 1 \{Y j t − 1 }, which denotes all time series in Y t − 1 except Y j t − 1 ) have the following partitioned estimated variance-covariance matrix:…”

Section: Partialization In Canonical Correlation Analysismentioning

confidence: 99%

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Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for fMRI data analysis

et al. 2010

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The identification, modeling, and analysis of interactions between nodes of neural systems in the human brain have become the aim of interest of many studies in neuroscience. The complex neural network structure and its correlations with brain functions have played a role in all areas of neuroscience, including the comprehension of cognitive and emotional processing. Indeed, understanding how information is stored, retrieved, processed, and transmitted is one of the ultimate challenges in brain research. In this context, in functional neuroimaging, connectivity analysis is a major tool for the exploration and characterization of the information flow between specialized brain regions. In most functional magnetic resonance imaging (fMRI) studies, connectivity analysis is carried out by first selecting regions of interest (ROI) and then calculating an average BOLD time series (across the voxels in each cluster). Some studies have shown that the average may not be a good choice and have suggested, as an alternative, the use of principal component analysis (PCA) to extract the principal eigen-time series from the ROI(s). In this paper, we introduce a novel approach called cluster Granger analysis (CGA) to study connectivity between ROIs. The main aim of this method was to employ multiple eigen-time series in each ROI to avoid temporal information loss during identification of Granger causality. Such information loss is inherent in averaging (e.g., to yield a single "representative" time series per ROI). This, in turn, may lead to a lack of power in detecting connections. The proposed approach is based on multivariate statistical analysis and integrates PCA and partial canonical correlation in a framework of Granger causality for clusters (sets) of time series. We also describe an algorithm for statistical significance testing based on bootstrapping. By using Monte Carlo simulations, we show that the proposed approach outperforms conventional Granger causality analysis (i.e., using representative time series extracted by signal averaging or first principal components estimation from ROIs). The usefulness of the CGA approach in real fMRI data is illustrated in an experiment using human faces expressing emotions. With this data set, the proposed approach suggested the presence of significantly more connections between the ROIs than were detected using a single representative time series in each ROI.

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“…Partial canonical correlation analysis (Rao 1969) Cont Cont Bipartial canonical correlation analysis (Timm and Carlson 1976) Cat* Cat* Partial correspondence analysis (Yanai 1986) Cat* Cat* Bipartial correspondence analysis New constrained co-inertia analysis: COA(P ⊥ HX XP T ZX/QX , P ⊥ HY YP T ZY/QY ) QX,QY…”

Section: Cont Contmentioning

confidence: 99%

Generalized constrained co-inertia analysis

Amenta

2008

ADAC

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In this paper a method for generalized constrained co-inertia analysis is proposed. This approach is based on a suitable decomposition of each set of variables which incorporates external information on both rows and columns of data matrices. These external information are incorporated in the analysis in order to improve the interpretability of the phenomenon under investigation. Once both matrices are decomposed according to the external information, we propose to apply the co-inertia analysis to any pair of obtainable submatrices in order to study relationships between them. A variety of existing and new extensions of COA are then realized. According to the nature of the data, this approach subsumes also several generalized constrained methods proposed in literature. An example is given to illustrate the proposed method.

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Partial canonical correlations

Cited by 38 publications

References 0 publications

Disentangling the Effects of Tillage Timing and Weather on Weed Community Assembly

Disentangling the Effects of Tillage Timing and Weather on Weed Community Assembly

Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for fMRI data analysis

Generalized constrained co-inertia analysis

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