R语言在不同样本量下的Little‘s MCAR检验

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"))

ggplot(little.mcar.p.mar, aes(x = n, y = p)) + geom_boxplot() +geom_crossbar(aes(ymin = q925, y = q95, ymax = q975), data = summarise(group_by(little.mcar.p.mar, n), q925 = quantile(p, .925, na.rm = TRUE),q95 = quantile(p, .95, na.rm = TRUE), q975 = quantile(p, .975, na.rm = TRUE)), linetype = 2) +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 MAR",subtitle = "2000 replications",caption = paste(paste("For the dashed boxes, going from top to bottom, lines","represent 97.5th, 95th and 92.5th percentiles of p-values."),"Test only maintains nominal error rate around sample size of 120.",sep = "\n"))

回归接近完美（没有多重共线性）。

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