用R模拟高维多元正态数据
用R模拟高维多元正态数据
提问于 2022-09-29 16:44:54
我试图用n= 100和p= 400在R中模拟高维多元正态数据(两组不同的变量具有一定的相关性)。以下是我的代码：
## load library MASS
library(MASS)
## sample size set to n = 100
sample_size <- 100
## I try to simulate two different groups of variables for each with 200 variables
sample_meanvector <- c(runif(200,0,1), runif(200,6,8))
## covariance matrix, some variables set to be correlated
sample_covariance_matrix <- matrix(NA, nrow = 400, ncol = 400)
diag(sample_covariance_matrix) <- 1
set.seed(666)
sample_covariance_matrix[lower.tri(sample_covariance_matrix)] <- runif(79800, 0.00001, 0.2)
sample_covariance_matrix[lower.tri(sample_covariance_matrix)][sample(1:79800, 10000)] <- runif(10000, 0.6, 0.9)
## make the matrix symmetric
sample_covariance_matrix[upper.tri(sample_covariance_matrix)]<-t(sample_covariance_matrix)[upper.tri(sample_covariance_matrix)]
## create multivariate normal distribution
sample_distribution <- mvrnorm(n = sample_size,
mu = sample_meanvector,
Sigma = sample_covariance_matrix)但是，每次运行这个mvrnorm函数时，我都会得到以下错误：
mu范数中的
误差(n= sample_size，mu= sample_meanvector，Sigma = sample_covariance_matrix)：'Sigma‘不是正定的
我有两个问题：
- 为什么会有这个错误？
- 如何编辑我的代码来模拟高维多变量正常数据？
非常感谢！
回答 3
Stack Overflow用户
回答已采纳
发布于 2022-09-29 21:20:01
下面是一种可以生成高度相关矩阵的方法：
library(MASS)
library(Matrix)
sample_size <- 100
sample_meanvector <- c(runif(200,0,1), runif(200,6,8))
sample_covariance_matrix <- matrix(NA, nrow = 400, ncol = 400)
diag(sample_covariance_matrix) <- 1
set.seed(666)
mat_Sim <- matrix(data = NA, nrow = 400, ncol = 400)
U <- runif(n = 400) * 0.5
for(i in 1 : 400)
{
if(i <= 350)
{
U_Star <- pmin(U + 0.25 * runif(n = 400), 0.99999)
}else
{
U_Star <- pmin(pmax(U + sample(c(-1, 1), size = 400, replace = TRUE) * runif(n = 400), 0.00001), 0.99999)
}
mat_Sim[, i] <- qnorm(U_Star)
}
cor_Mat <- cor(mat_Sim)
sample_covariance_matrix <- cor_Mat * 200
## create multivariate normal distribution
sample_distribution <- mvrnorm(n = sample_size,
mu = sample_meanvector,
Sigma = sample_covariance_matrix)
image(cor_Mat)7/8矩阵的相关系数在0.6 ~ 0.8之间，1/8矩阵的相关系数在0~ 0.3之间。
Stack Overflow用户
发布于 2022-09-29 20:57:46
您可以考虑以下代码：
library(MASS)
library(Matrix)
sample_size <- 100
sample_meanvector <- c(runif(200,0,1), runif(200,6,8))
sample_covariance_matrix <- matrix(NA, nrow = 400, ncol = 400)
diag(sample_covariance_matrix) <- 1
set.seed(666)
sample_covariance_matrix[lower.tri(sample_covariance_matrix)] <- runif(79800, 0.00001, 0.2)
sample_covariance_matrix[lower.tri(sample_covariance_matrix)][sample(1:79800, 10000)] <- runif(10000, 0.6, 0.9)
sample_covariance_matrix[upper.tri(sample_covariance_matrix)]<-t(sample_covariance_matrix)[upper.tri(sample_covariance_matrix)]
sample_covariance_matrix_Near_PD <- nearPD(sample_covariance_matrix)$mat
## create multivariate normal distribution
sample_distribution <- mvrnorm(n = sample_size,
mu = sample_meanvector,
Sigma = sample_covariance_matrix_Near_PD)Stack Overflow用户
发布于 2022-09-30 14:21:51
在我的问题中，我把高相关性和低相关性放在同一个协方差矩阵中。在此基础上，利用“查找正定矩阵”函数破坏了高相关性。然而，当我分别模拟这两个部分时，高相关性不会受到太大的影响。以下是我的最新代码：
# load library MASS
library(MASS)
sample_size <- 100
##### Saperate high and low correlation part ####
### High correlation ###
sample_mean_high <- c(runif(50, -1 , 1))
sample_cov_high <- matrix(0, nrow = 50, ncol = 50)
diag(sample_cov_high) <- 1
sample_cov_high[lower.tri(sample_cov_high)] <- runif(1225, 0.6, 0.9)
sample_cov_high[upper.tri(sample_cov_high)] <- t(sample_cov_high[lower.tri(sample_cov_high)])
sample_cov_high <- sfsmisc::posdefify(sample_cov_high)
# create multivariate normal distribution
sample_dist_high <- mvrnorm(n = sample_size, mu = sample_mean_high, Sigma = sample_cov_high)
### Low correlation ###
sample_mean_low <- c(runif(350, -1 , 1))
sample_cov_low <- matrix(0, nrow = 350, ncol = 350)
diag(sample_cov_low) <- 1
sample_cov_low[lower.tri(sample_cov_low)] <- runif(61075, -0.5, 0.5)
sample_cov_low[upper.tri(sample_cov_low)] <- t(sample_cov_low[lower.tri(sample_cov_low)])
sample_cov_low <- sfsmisc::posdefify(sample_cov_low)
# create multivariate normal distribution
sample_dist_low <- mvrnorm(n = sample_size, mu = sample_mean_low, Sigma = sample_cov_low)
### Check correlation ###
cor_high <- cor(sample_dist_high)
hist(cor_high[lower.tri(cor_high)])
cor_low <- cor(sample_dist_low)
hist(cor_low[lower.tri(cor_low)])
cor_between <- cor(sample_dist_high, sample_dist_low)
hist(cor_between[lower.tri(cor_between)])然后我得到了我所期望的相关性。
页面原文内容由Stack Overflow提供。腾讯云小微IT领域专用引擎提供翻译支持
原文链接：
https://stackoverflow.com/questions/73899053
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