n <- 10000000 p <- 10 x <- matrix(rnorm(n*p),ncol = p) # n行p列的随机矩阵x，其中每个元素都服从标准正态分布 beta <- matrix(c(1:p),ncol = 1) # p行1列的系数矩阵beta，其中第i个元素为i z <- x %*% beta # x与beta的矩阵乘积 condprob <- pnorm(z) # 计算二项式分布的概率参数condprob，即每个观测值y为1的概率 y <- matrix(rbinom(n,size = 1,prob = condprob),ncol = 1) # n行1列的随机矩阵y，其中每个元素都服从二项式分布 prob.fit <- glm.fit(x,y,family = binomial(link = "probit"))$coefficients # probit建模 logit.fit <- glm.fit(x,y,family = binomial(link = "logit"))$coefficients # logit建模 linear.fit <- glm.fit(x,y,family = gaussian(link = "identity"))$coefficients # 线性回归建模 coef.mat <- cbind(prob.fit,logit.fit,linear.fit) # 将三个模型的系数矩阵按列合并为一个p行3列的矩阵coef.mat print(coef.mat) prop.mat <- cbind(prob.fit/logit.fit,prob.fit/linear.fit,logit.fit/linear.fit) # 计算三个模型系数之间的比例，并将它们按列合并为一个p行3列的矩阵prop.mat print(prop.mat)

这是一段使用R语言进行二项式回归、logistic回归和线性回归的代码。其中，n为样本量，p为自变量个数，x是从标准正态分布中随机生成的样本数据，beta是一个1到p的向量，z是x和beta的点积，condprob是z的累积分布函数值，y是从二项分布中生成的响应变量。

接下来，使用三种不同的link函数，分别对y和x进行回归拟合，并输出各个系数的值。最后，将三个模型的系数进行比较得到prop.mat。

如果您想使用其他语言或库进行回归分析，可以将代码中的glm函数替换为对应语言或库中的线性回归、逻辑回归或概率模型函数。

相关问题

用r语言写程序：Simulate a dataset containing continuous traits with given h^2. Split itinto training and testing datasets with proportion 4 ∶ 1.set.seed(20132014)n <- 5000p <- 1000h <- c(0.2, 0.8)[1]# simulate genotype (not exactly)x_r <- matrix(rnorm(n * p), ncol = p)xmean <- matrix(rep(colMeans(x_r), n), ncol=p, byrow = TRUE)xsd <- matrix(rep(apply(x_r, 2, sd), n), ncol=p, byrow = TRUE)x <- (x_r - xmean)/xsdPlease perform the marginal model.## [1] 526 776 50 557 801 345 298 559 178 214 • Show the locations of significant SNPs.• Replicate above figure, and highlight the significant coefficents in red.

Sure, here's some R code to perform the marginal model and plot the locations of significant SNPs:

# set seed for reproducibility
set.seed(20132014)

# simulate data
n <- 5000
p <- 1000
h <- c(0.2, 0.8)[1]

# simulate genotype (not exactly)
x_r <- matrix(rnorm(n * p), ncol = p)
xmean <- matrix(rep(colMeans(x_r), n), ncol=p, byrow=TRUE)
xsd <- matrix(rep(apply(x_r, 2, sd), n), ncol=p, byrow=TRUE)
x <- (x_r - xmean)/xsd

# simulate continuous trait
y <- sqrt(h) * x[,1] + sqrt(1 - h) * rnorm(n)

# split data into training and testing sets
train_idx <- sample(1:n, size=round(0.8*n), replace=FALSE)
x_train <- x[train_idx,]
y_train <- y[train_idx]
x_test <- x[-train_idx,]
y_test <- y[-train_idx]

# perform marginal model
library(glmnet)
fit <- glmnet(x_train, y_train, family="gaussian")
cv_fit <- cv.glmnet(x_train, y_train, family="gaussian")
lambda_min <- cv_fit$lambda.min
coef <- coef(fit, s=lambda_min)

# plot locations of significant SNPs
library(ggplot2)
library(dplyr)
library(tidyr)
library(ggrepel)

# get SNP names
snp_names <- paste0("SNP", 1:p)

# create data frame of SNP locations and coefficients
snp_df <- data.frame(snp_names, coef[-1])
snp_df <- snp_df %>% gather(key="snp", value="coef", -snp_names)
snp_df$significant <- snp_df$coef != 0

# plot SNP locations
ggplot(snp_df, aes(x=snp, y=1, color=significant)) +
  geom_point(size=3) +
  scale_color_manual(values=c("gray","red")) +
  theme(axis.text.x = element_blank(),
        axis.ticks.x = element_blank()) +
  labs(x="SNP", y="")

This will produce a plot of SNP locations with significant coefficients highlighted in red. You can adjust the `lambda_min` value to control the level of sparsity in the model and the number of significant SNPs identified.

1 Simulate a dataset containing continuous traits with given ℎ 2 . Split it into training and testing datasets with proportion 4 ∶ 1. set.seed(20132014) n <- 5000 p <- 1000 h <- c(0.2, 0.8)[1] # simulate genotype (not exactly) x_r <- matrix(rnorm(n * p), ncol = p) xmean <- matrix(rep(colMeans(x_r), n), ncol=p, byrow = TRUE) xsd <- matrix(rep(apply(x_r, 2, sd), n), ncol=p, byrow = TRUE) x <- (x_r - xmean)/xsd # ... 2 Please perform the marginal model. ## [1] 526 776 50 557 801 345 298 559 178 214 1 2 −0.025 0.000 0.025 0.050 0 250 500 750 1000 snp u • Show the locations of significant SNPs. • Replicate above figure, and highlight the significant coefficents in red

For the first question, I understand that you want me to simulate a dataset with continuous traits and split it into training and testing datasets with a given heritability (h2) and some specific code. Here is the modified code to simulate the dataset and split it into training and testing datasets:

set.seed(20132014)
n <- 5000
p <- 1000
h2 <- 0.2

# simulate genotype (not exactly)
x_r <- matrix(rnorm(n * p), ncol = p)
xmean <- matrix(rep(colMeans(x_r), n), ncol=p, byrow = TRUE)
xsd <- matrix(rep(apply(x_r, 2, sd), n), ncol=p, byrow = TRUE)
x <- (x_r - xmean)/xsd

# simulate phenotype
g <- colSums(x) * sqrt(2 * h2 / p) # genetic effect
e <- rnorm(n) * sqrt(1 - h2) # environmental effect
y <- g + e # phenotype

# split into training and testing datasets
train_idx <- sample(1:n, size = n * 0.8, replace = FALSE)
x_train <- x[train_idx, ]
y_train <- y[train_idx]
x_test <- x[-train_idx, ]
y_test <- y[-train_idx]

This code simulates a dataset with n = 5000 individuals and p = 1000 SNPs. The heritability is set to 0.2. The code first simulates the genotype matrix x, and then uses it to simulate the phenotype y. The genetic effect is proportional to the sum of each SNP's effect, and the environmental effect is simulated from a normal distribution. Finally, the code splits the dataset into training (80%) and testing (20%) datasets.

For the second question, I understand that you want me to perform a marginal model and then show the locations of significant SNPs and replicate a figure highlighting significant coefficients in red. Here is the code to perform the marginal model and visualize the results:

library(glmnet)
set.seed(1234)

# fit marginal model
cvfit <- cv.glmnet(x_train, y_train, alpha = 0)
lam <- cvfit$lambda.min
fit <- glmnet(x_train, y_train, alpha = 0, lambda = lam)

# identify significant SNPs
coef <- coef(fit)
nz_idx <- which(coef != 0)
nz_snps <- nz_idx - 1

# visualize results
par(mar = c(5, 4, 4, 8) + 0.1)
plot(coef, xvar = "lambda", label = TRUE, main = "Marginal Model")
abline(v = lam, lty = 2)
significant_snps <- which(abs(coef) > 0.1)
points(coef[significant_snps], col = "red", pch = 19, cex = 1.2)

This code fits a marginal model using the glmnet package and identifies significant SNPs based on a threshold of 0.1. The code then visualizes the results using the plot function and highlights the significant SNPs in red. The abline function adds a vertical line at the optimal lambda value selected by cross-validation.