check_dist_conv.R

#devtools::install_github("debruine/faux")
library(faux)

# compare the correlations between simulated normally distributed data and the likert-scale version
check_likert <- function(n = 100, r = 0.5, 
                         prob = c(.05, .1, .2, .3, .2, .1, .05)) {
  df <- faux::rnorm_multi(n, 2, 0, 1, r) %>%
    dplyr::mutate(
      L1 = norm2likert(X1, prob, 0, 1),
      L2 = norm2likert(X2, prob, 0, 1)
    )
  list(norm = cor(df$X1, df$X2), 
       likert = cor(df$L1, df$L2))
}

# compare the correlations between simulated normally distributed data and the truncated version
check_trunc <- function(n = 100, mu = 0, sd = 1, r = 0.5,
                        min = -Inf, max = Inf) {
  df <- faux::rnorm_multi(n, 2, mu, sd, r) %>%
    dplyr::mutate(
      T1 = norm2trunc(X1, min, max, mu, sd),
      T2 = norm2trunc(X2, min, max, mu, sd)
    )
  list(norm = cor(df$X1, df$X2), 
       trunc = cor(df$T1, df$T2))
}

# symmetric normal-ish likert distribution
x <- purrr::map_df(1:1000, ~check_likert())
plot(x$norm, x$likert)
cor(x$norm, x$likert)

# symmetric low-n likert
x <- purrr::map_df(1:1000, ~check_likert(prob = c(.1, .2, .4, .2, .1)))
plot(x$norm, x$likert)
cor(x$norm, x$likert)

# asymmetric likert
x <- purrr::map_df(1:1000, ~check_likert(prob = c(.05, .1, .15, .2, .2, .25, .05)))
plot(x$norm, x$likert)
cor(x$norm, x$likert)

# asymmetric low-n likert
x <- purrr::map_df(1:1000, ~check_likert(prob = c(.1, .2, .3, .4)))
plot(x$norm, x$likert)
cor(x$norm, x$likert)

# truncated to 1 SD
x <- purrr::map_df(1:1000, ~check_trunc())
plot(x$norm, x$trunc)
cor(x$norm, x$trunc)

# truncated to N(3.5, 2) to 1-7
x <- purrr::map_df(1:1000, ~check_trunc(100, 3.5, 2, 0.5, 1, 7))
plot(x$norm, x$trunc)
cor(x$norm, x$trunc)