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Networks Based on Regression Models and Prediction Methods

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Abstract

Prediction methods (e.g., linear and nonlinear regression models) can be used to construct a network among a set of vectors x 1, , x n . The construction follows three steps. First, the prediction method is used to predict y = x j on the basis of x = x i . Second, a measure of predictive accuracy or statistical significance (e.g., a likelihood ratio test p value) is calculated. Third, the measure is transformed into an adjacency measure A ij between the two vectors. Although general prediction and machine learning methods can be used, we focus on regression models for measuring nonlinear relationships (e.g., polynomial and spline regression models). Spline regression models are attractive since they provide a statistical framework for robustly capturing general nonlinear relationships. Generalized linear models allow one to model the relationship between binary variables, count data, and categorical variables. Multivariate regression models allow one to define a pairwise adjacency measure between variables, which conditions on additional covariates, which describe sample properties (e.g., batch effects). The partial correlation coefficient can be interpreted as a pairwise correlation measure which adjusts for other variables. Partial correlation networks can be used to define networks that encode direct relationships between variables.

Keywords

  • Regression Model
  • Model Matrix
  • Partial Correlation
  • Data Frame
  • Likelihood Ratio Statistic

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 13.1

References

  • Chen L, Zheng S (2009) Studying alternative splicing regulatory networks through partial correlation analysis. Genome Biol 10(1):R3

    PubMed  CrossRef  Google Scholar 

  • Faraway JJ (2002) Practical regression and anova using R. R pdf file at http://cranr-projectorg/doc/contrib/Faraway-PRApdf

  • Krainik A, Duffau H, PelegriniIssac S, Lehericy J, Benali H (2006) Partial correlation for functional brain interactivity investigation in functional MRI. NeuroImage 32:228–237

    PubMed  CrossRef  Google Scholar 

  • Magwene P, Kim J (2004) Estimating genomic coexpression networks using first-order conditional independence. Genome Biol 5(12):R100

    PubMed  CrossRef  Google Scholar 

  • Opgen-Rhein R, Strimmer K (2007) From correlation to causation networks: A simple approximate learning algorithm and its application to high-dimensional plant gene expression data. BMC Syst Biol 1:37

    PubMed  CrossRef  Google Scholar 

  • Schaefer J, Strimmer K (2005) An empirical Bayes approach to inferring large-scale gene association networks. Bioinformatics 21(6):754–764

    CrossRef  CAS  Google Scholar 

  • Whittaker J (1990) Graphical models in applied multivariate statistics. Wiley, Chichester

    Google Scholar 

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Correspondence to Steve Horvath .

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Horvath, S. (2011). Networks Based on Regression Models and Prediction Methods. In: Weighted Network Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8819-5_13

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