vignette.Rmd 4.37 KB
 Armin Rauschenberger committed Mar 08, 2019 1 ---  Armin Rauschenberger committed Aug 08, 2019 2 title: Multivariate Elastic Net Regression  Armin Rauschenberger committed Mar 08, 2019 3 4 5 6 7 8 9 10 11 12 13 output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{vignette} %\VignetteEncoding{UTF-8} %\VignetteEngine{knitr::rmarkdown} editor_options: chunk_output_type: console --- {r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE)  Armin Rauschenberger committed Aug 07, 2019 14 set.seed(1)  Armin Rauschenberger committed Mar 08, 2019 15 16 17 18  ## Installation  Armin Rauschenberger committed Jul 31, 2019 19 Install the current release from [CRAN](https://CRAN.R-project.org/package=joinet):  Armin Rauschenberger committed Mar 08, 2019 20 21  {r,eval=FALSE}  Armin Rauschenberger committed Jul 31, 2019 22 install.packages("joinet")  Armin Rauschenberger committed Mar 08, 2019 23 24   Armin Rauschenberger committed Aug 07, 2019 25 Or install the latest development version from [GitHub](https://github.com/rauschenberger/joinet):  Armin Rauschenberger committed Mar 08, 2019 26 27 28  {r,eval=FALSE} #install.packages("devtools")  Armin Rauschenberger committed Jul 31, 2019 29 devtools::install_github("rauschenberger/joinet")  Armin Rauschenberger committed Mar 08, 2019 30   Armin Rauschenberger committed Mar 18, 2019 31   Armin Rauschenberger committed Aug 07, 2019 32 33 34 35 36 37 38 39 40 ## Initialisation Load and attach the package: {r} library(joinet)  And access the [documentation](https://rauschenberger.github.io/joinet/):  Armin Rauschenberger committed Jul 31, 2019 41 42 43 44  {r,eval=FALSE} ?joinet help(joinet)  Armin Rauschenberger committed Aug 07, 2019 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 browseVignettes("joinet")  ## Simulation For n samples, we simulate p inputs (features, covariates) and q outputs (outcomes, responses). We assume high-dimensional inputs (p$\gg$n) and low-dimensional outputs (q$\ll$n). {r} n <- 100 q <- 2 p <- 500  We simulate the p inputs from a multivariate normal distribution. For the mean, we use the p-dimensional vector mu, where all elements equal zero. For the covariance, we use the p$\times$p matrix Sigma, where the entry in row$i$and column$j$equals rho$^{|i-j|}\$. The parameter rho determines the strength of the correlation among the inputs, with small rho leading weak correlations, and large rho leading to strong correlations (0 < rho < 1). The input matrix X has n rows and p columns. {r} mu <- rep(0,times=p) rho <- 0.90 Sigma <- rho^abs(col(diag(p))-row(diag(p))) X <- MASS::mvrnorm(n=n,mu=mu,Sigma=Sigma)  Armin Rauschenberger committed Jul 31, 2019 65 66   Armin Rauschenberger committed Aug 07, 2019 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 We simulate the input-output effects from independent Bernoulli distributions. The parameter pi determines the number of effects, with small pi leading to few effects, and large pi leading to many effects (0 < pi < 1). The scalar alpha represents the intercept, and the p-dimensional vector beta represents the slopes. {r} pi <- 0.01 alpha <- 0 beta <- rbinom(n=p,size=1,prob=pi)  From the intercept alpha, the slopes beta and the inputs X, we calculate the linear predictor, the n-dimensional vector eta. Rescale the linear predictor to make the effects weaker or stronger. Set the argument family to "gaussian", "binomial", or "poisson" to define the distribution. The n times p matrix Y represents the outputs. We assume the outcomes are *positively* correlated. {r,results="hide"} eta <- alpha + X %*% beta eta <- 1.5*scale(eta) family <- "gaussian" if(family=="gaussian"){ mean <- eta Y <- replicate(n=q,expr=rnorm(n=n,mean=mean)) } if(family=="binomial"){ prob <- 1/(1+exp(-eta)) Y <- replicate(n=q,expr=rbinom(n=n,size=1,prob=prob)) } if(family=="poisson"){ lambda <- exp(eta) Y <- replicate(n=q,expr=rpois(n=n,lambda=lambda)) } cor(Y)  ## Application The function joinet fits univariate and multivariate regression. Set the argument alpha.base to 0 (ridge) or 1 (lasso). {r} object <- joinet(Y=Y,X=X,family=family)  Standard methods are available. The function predict returns the predicted values from the univariate (base) and multivariate (meta) models. The function coef returns the estimated intercepts (alpha) and slopes (beta) from the multivariate model (input-output effects). And the function weights returns the weights from stacking (output-output effects). {r,eval=FALSE} predict(object,newx=X) coef(object) weights(object)  The function cv.joinet compares the predictive performance of univariate (base) and multivariate (meta) regression by nested cross-validation. The argument type.measure determines the loss function. {r} cv.joinet(Y=Y,X=X,family=family)  ## Reference  Armin Rauschenberger committed Aug 08, 2019 126 Armin Rauschenberger and Enrico Glaab (2019). "joinet: predicting correlated outcomes jointly to improve clinical prognosis". *Manuscript in preparation.*  Armin Rauschenberger committed Jul 31, 2019 127