模拟相关变量限制观察到的和定义的相关系数之间的偏差

Question

    dev_allowance <- 0.15 #Deviation in r allowed
    within_limit <- FALSE #Initiate
    count <- 0            #Loop count
    nvar <- 10            #number of variables to simulate
    nobs = 50             #number of observations to simulate
    #define correlation matrix
    M = matrix(c(1., .0, .0, .0, .0, .0, .0, .0, .0, .0,
                 .0, 1., .0, .0, .0, .0, .0, .0, .0, .0,
                 .0, .0, 1., .8, .0, .0, .0, .0, .0, .0,
                 .0, .0, .8, 1., .0, .0, .0, .0, .0, .0,
                 .0, .0, .0, .0, 1., .2, .0, .0, .0, .0,
                 .0, .0, .0, .0, .2, 1., .0, .0, .0, .0,
                 .0, .0, .0, .0, .0, .0, 1., .8, .0, .0,
                 .0, .0, .0, .0, .0, .0, .8, 1., .0, .0,
                 .0, .0, .0, .0, .0, .0, .0, .0, 1., .2,
                 .0, .0, .0, .0, .0, .0, .0, .0, .2, 1.), nrow=nvar, ncol=nvar)
    L = chol(M)           # Cholesky decomposition

    #Loop while not within limit
    while (!within_limit) {
      # Generate random variables
        r = t(L) %*% matrix(rnorm(nvars*nobs), nrow=nvars, ncol=nobs)
        r = t(r)
      # Check if within limit
        within_limit <- all(abs(cor(r) - M) < dev_allowance)
      # Count loop
        count <- count + 1
    }

    cat(paste0("run count: ", count))

我正在尝试模拟大约 10 个具有定义相关性的随机正态变量。同时，我希望模拟变量的相关性在以定义的相关性为中心的某个范围内。

但是运行时间长得令人无法接受，如果不是无限的话。

现在，我想做 nobs=50 和 nobs=200。虽然我计划设置 dev_allowance=0.05，但我现在的情况是，当 dev_allowance 小于大约 1 分钟时，可能需要一分多钟。 nobs=50 的 0.16 和大约。 nobs=200 为 0.08。不敢尝试更小的dev_allowance...

如果我要坚持目前的参数方案，是否有解决方法？

Answer 1

好吧...打到一半我想到了这个问题：

    sim_nvar <- matrix(rnorm(nobs), ncol=nobs)
    for (i in 2:nvar) {
      within_limit <- FALSE
      while (!within_limit) {
        #Generate random variables
          sim_var <- t(L)[i, 1:i] %*% rbind(sim_nvar, matrix(rnorm(nobs), ncol=nobs))
          sim_var <- t(rbind(sim_nvar, sim_var))
        #Check if within limit
          within_limit <- all(abs(cor(sim_var) - M[1:i, 1:i]) < dev_allowance)
      }
      sim_nvar <- t(sim_var)
    }
    sim_nvar <- t(sim_nvar)

    all(abs(cor(sim_nvar) - M) < dev_allowance)
    [1] TRUE

我觉得还可以。但是如果我这样分开模拟会有什么缺陷吗？或者这是最好的方法吗？

模拟相关变量限制观察到的和定义的相关系数之间的偏差

Simulate correlated variables limiting deviations between observed and defined correlation coefficients

r

simulation

correlation

normal-distribution