我进行一个小型仿真，以在不同样本量下测试Little的MCAR检验1。我可以研究线性回归中的异方差。我能够找到一些使用Little's MCAR检验的小样本研究人员的例子，因此我进行了仿真。

library(BaylorEdPsych)
library(simglm)
library(ggplot2)
library(dplyr)
library(mice)
fixed <- ~1 + age + income
fixed_param <- c(2, 0.3, 1.3)
cov_param <- list(dist_fun = c('rnorm', 'rnorm'),
                  var_type = c("single", "single"),
                  opts = list(list(mean = 0, sd = 4),
                              list(mean = 0, sd = 3)))

ggplot(little.mcar.p, aes(x = n, y = p)) + geom_boxplot() +
  geom_crossbar(aes(ymin = q025, y = q05, ymax = q075), data = summarise(
    group_by(little.mcar.p, n), q025 = quantile(p, .025, na.rm = TRUE),
    q05 = quantile(p, .05, na.rm = TRUE), q075 = quantile(p, .075, na.rm = TRUE)
  )) +
  geom_hline(yintercept = .05) +
  scale_y_continuous(breaks = seq(0, 1, .05), limits = c(0, 1)) +
  labs(x = "Sample size", y = "p-value",
       title = "Little's MCAR test for data that are MCAR",
       subtitle = "2000 replications",
       caption = paste(paste("For the narrow boxes, going from top to bottom, lines",
                             "represent 7.5th, 5th and 2.5th percentiles of p-values."),
                       "Test maintains nominal error rate across wide range of sample sizes.",
                       sep = "\n"))

回归接近完美（没有多重共线性）。