r - 模拟数据以固定r2进行逻辑回归

我想为逻辑回归模拟数据，在此可以事先指定其解释的方差。看看下面的代码。我模拟了四个独立变量，并指定每个logit系数的大小应为log(2)= 0.69。效果很好，解释的方差(我报告Cox＆Snell的r2)为0.34。

但是，我需要以某种方式指定回归系数，以便从回归中得出预先指定的r2。因此，如果我想产生一个r2，例如精确地为0.1。如何指定系数？我对此有点挣扎。

# Create independent variables
sigma.1 <- matrix(c(1,0.25,0.25,0.25,
                0.25,1,0.25,0.25,
                0.25,0.25,1,0.25,
                0.25,0.25,0.25,1),nrow=4,ncol=4)
mu.1 <- rep(0,4)
n.obs <- 500000

library(MASS)
sample1 <- as.data.frame(mvrnorm(n = n.obs, mu.1, sigma.1, empirical=FALSE))

# Create latent continuous response variable
sample1$ystar <- 0 + log(2)*sample1$V1 + log(2)*sample1$V2 + log(2)*sample1$V3 + log(2)*sample1$V4

# Construct binary response variable
sample1$prob <- exp(sample1$ystar) / (1 + exp(sample1$ystar))
sample1$y <- rbinom(n.obs,size=1,prob=sample1$prob)

# Logistic regression
logreg <- glm(y ~ V1 + V2 + V3 + V4, data=sample1, family=binomial)
summary(logreg)

输出为:

Call:
glm(formula = y ~ V1 + V2 + V3 + V4, family = binomial, data = sample1)

Deviance Residuals:
    Min       1Q   Median       3Q      Max
-3.7536  -0.7795  -0.0755   0.7813   3.3382

Coefficients:
             Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.002098   0.003544  -0.592    0.554
V1           0.691034   0.004089 169.014   <2e-16 ***
V2           0.694052   0.004088 169.776   <2e-16 ***
V3           0.693222   0.004079 169.940   <2e-16 ***
V4           0.699091   0.004081 171.310   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 693146  on 499999  degrees of freedom
Residual deviance: 482506  on 499995  degrees of freedom
AIC: 482516

Number of Fisher Scoring iterations: 5

Cox和Snell的r2给出:

library(pscl)
pR2(logreg)["r2ML"]

> pR2(logreg)["r2ML"]
 r2ML
0.3436523

最佳答案

如果将随机误差项添加到ystat.r的ystar变量中，然后对其进行处理，则可以将标准差调整成星期，直到其符合您的规范。

sample1$ystar.r <- sample1$ystar+rnorm(n.obs, 0, 3.8)  # tried a few values
sample1$prob <- exp(sample1$ystar.r) / (1 + exp(sample1$ystar.r))
sample1$y <- rbinom(n.obs,size=1,prob=sample1$prob)
logreg <- glm(y ~ V1 + V2 + V3 + V4, data=sample1, family=binomial)
summary(logreg)  # the estimates "shrink"
pR2(logreg)["r2ML"]
#-------
     r2ML
0.1014792

关于r - 模拟数据以固定r2进行逻辑回归，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/49300320/