cumulative_distribution_plots.r

generate_logit_cdf <- function(mu, s, 
                               sigma_y=0.1, 
                               x=seq(-5,20,0.1)) {
  x_ms <- (x-mu)/s
  y    <- 0.5 + 0.5 * tanh(x_ms)  
  y    <- abs(y + rnorm(length(x), 0, sigma_y))
  ix   <- which(y>=1.0)
  if(length(ix)>=1) { 
    y[ix] <- 1.0
  }
  return(y)
}

set.seed(424242)
x      <- seq(-5,20,0.025) # 1001 observation
mu_vec <- c(1,2,3,5,7,8)   # 6 variables
s_vec  <- c(2,2,4,3,4,2)
# Syntetic variables
observations_df<- mapply(generate_logit_cdf, 
                              mu_vec, 
                              s_vec, 
                              MoreArgs = list(x=x))
# Give them names
colnames(observations_df) <- c("Var1", "Var2", "Var3", "Var4", "Var5", "Var6")

> head(observations_df) 
           Var1        Var2       Var3       Var4       Var5       Var6
[1,] 0.04646783 0.178231019 0.07197742 0.11099645 0.06384057 0.02629486
[2,] 0.09946289 0.081685028 0.18240798 0.06993340 0.10113648 0.04727540
[3,] 0.07871231 0.029549890 0.08254837 0.09690864 0.08558282 0.16012873
[4,] 0.01986314 0.060743272 0.18354161 0.17263607 0.04554137 0.03000444
[5,] 0.04518787 0.029594108 0.02928619 0.04532478 0.02640770 0.09849672
[6,] 0.22511967 0.007850177 0.08122381 0.13976551 0.05582895 0.04619664

> head(df_all)
  x observation          y
1 1        Var1 0.04646783
2 2        Var1 0.09946289
3 3        Var1 0.07871231
4 4        Var1 0.01986314
5 5        Var1 0.04518787
6 6        Var1 0.22511967

library(ggplot2)
library(reshape2)
df_all <- reshape2:::melt(observations_df)
colnames(df_all) <- c("x", "observation", "y")
df_all$observation <- as.factor(df_all$observation)
ggplot(df_all, aes(x=x, y=y, colour=observation)) + geom_point(size=3)  + scale_color_brewer(palette = "Reds") + geom_smooth(aes(group=observation),method="glm", family=quasibinomial(), formula="y~x", se = FALSE, size=1.5)

#cumulative plot:
#https://cloud.githubusercontent.com/assets/3885659/12447432/6f1b296c-bf70-11e5-82d8-cb105beafc17.png

#useful links:
#fitting models - https://www.zoology.ubc.ca/~schluter/R/fit-model/
#http://www.r-bloggers.com/s-shaped-data-smoothing-with-quasibinomial-distribution/