knitr::opts_chunk$set(eval = FALSE)

Simulation constants

pkgs <- list("rmsutilityr", "glmnet", "doParallel", "foreach", "pROC", "stepwiser")
lapply(pkgs, library, character.only = TRUE)
registerDoParallel(cores = 4)
file <- get_dated_filename("dk_sim.csv")
file

Number of simulations

sims <- 10
sims

Stepwise algorithm

## Can be any subset of c("backward", "forward", "both")
directions <- "forward"
directions

Coefficients

betas <- c(1, 2, 3, -1, -2, -3)
#betas <- 2
betas

Sample sizes

#n_values <- c(30, 60, 90, 300, 600, 900, 3000, 6000, 9000)
n_values <- c(30, 60, 90)
n_values

from \(\rho_{X_{i}X_{j}}\)

rho_values <- c(0, sqrt(0.4), sqrt(0.8))
#rho_values <- c(0, sqrt(0.1), sqrt(0.2), sqrt(0.4))
rho_values

Candidate predictor variables

predictors <- c(12, 18, 24, 50, 100)
predictors <- c(12, 18, 24)
predictors

\(\alpha\)

MFWER <- 0.15

alpha_values <- c(0.5, 0.15, 1 - (1 - MFWER)^(1 / predictors), 0.05)
alpha_values

#sim_object <- dk_sim(file = file, directions = directions, betas, n_values, alpha_values, rho_values, predictors, sims = sims, rnorm, 0, 0.2)

weight <- 1
nlambda = 100
sim_object <- dk_and_net_sim(file = file, directions = directions, betas, 
                             n_values, alpha_values, rho_values, predictors, 
                             weight = weight, nlambda = nlambda,
                             sims = sims, rnorm, 0, 0.2)

1. Plot effect of number of observations by number of predictors on number of noise variables
2. Plot effect of number of observations by number of predictors on number of actual variables

library("reshape2")
library("ggplot2")
#backward_sim_object <- sim_object
#save(backward_sim_object, file = "../data/backward_sim_object.RData")
sim_wide_df <- sim_object_to_df(sim_object)
sim_wide_median_df <-
  sim_wide_df[ , !names(sim_wide_df) %in%
                 c("family", "link", "sims", "noise_min_step", 
                   "noise_1st_step", "noise_3rd_step", "noise_max_step",
                   "authentic_min_step", "authentic_1st_step", 
                   "authentic_3rd_step", "authentic_max_step", 
                   "noise_min_lasso", "noise_1st_lasso", "noise_3rd_lasso",
                   "noise_max_lasso", "authentic_min_lasso", 
                   "authentic_1st_lasso", "authentic_3rd_lasso", 
                   "authentic_max_lasso", "noise_min_ridge", 
                   "noise_1st_ridge", "noise_3rd_ridge", "noise_max_ridge",
                   "authentic_min_ridge", "authentic_1st_ridge", 
                   "authentic_3rd_ridge", "authentic_max_ridge",
                   "noise_min_net", "noise_1st_net", "noise_3rd_net", "noise_max_net",
                   "authentic_min_net", "authentic_1st_net", 
                   "authentic_3rd_net", "authentic_max_net")]
# sim_long_median_df <- melt(sim_wide_df, id.vars = c("alpha", "n", "rho", "p"),
#                     measure.vars = c("authentic_median", "noise_median"),
#                     variable.name = "predictor_type",
#                     value.name = "count", factorsAsStrings = FALSE)
# sim_long_df_a5_rho0 <- sim_long_median_df[sim_long_median_df$alpha == 0.5 &
#                                            sim_long_median_df$rho == 0, ]
# sim_long_df_a5_rho0_noise <- 
#   sim_long_df_a5_rho0[sim_long_df_a5_rho0$predictor_type == "noise_median", ]
# sim_long_df_a5_rho0_authentic <- 
#   sim_long_df_a5_rho0[sim_long_df_a5_rho0$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a5_rho0_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a5_rho0_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# 
# sim_long_df_a15_rho0 <- sim_long_median_df[sim_long_median_df$alpha == 0.15 &
#                                            sim_long_median_df$rho == 0, ]
# sim_long_df_a15_rho0_noise <- 
#   sim_long_df_a15_rho0[sim_long_df_a15_rho0$predictor_type == "noise_median", ]
# sim_long_df_a15_rho0_authentic <- 
#   sim_long_df_a15_rho0[sim_long_df_a15_rho0$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a15_rho0_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a15_rho0_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# table(sim_long_median_df$alpha)
# table(sim_long_median_df$rho)
# 
# sim_long_df_a0016_rho0 <- sim_long_median_df[sim_long_median_df$alpha < 0.0017 &
#                                            sim_long_median_df$rho == 0, ]
# sim_long_df_a0016_rho0_noise <- 
#   sim_long_df_a0016_rho0[sim_long_df_a0016_rho0$predictor_type == "noise_median", ]
# sim_long_df_a0016_rho0_authentic <- 
#   sim_long_df_a0016_rho0[sim_long_df_a0016_rho0$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a0016_rho0_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a0016_rho0_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ####### rho = 0.316
# sim_long_df_a5_rho3 <- sim_long_median_df[sim_long_median_df$alpha == 0.5 &
#                                            sim_long_median_df$rho > 0.3 &
#                                             sim_long_median_df$rho < 0.4, ]
# sim_long_df_a5_rho3_noise <- 
#   sim_long_df_a5_rho3[sim_long_df_a5_rho3$predictor_type == "noise_median", ]
# sim_long_df_a5_rho3_authentic <- 
#   sim_long_df_a5_rho3[sim_long_df_a5_rho3$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a5_rho3_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a5_rho3_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# 
# sim_long_df_a15_rho3 <- sim_long_median_df[sim_long_median_df$alpha == 0.15 &
#                                            sim_long_median_df$rho == 0, ]
# sim_long_df_a15_rho3_noise <- 
#   sim_long_df_a15_rho3[sim_long_df_a15_rho3$predictor_type == "noise_median", ]
# sim_long_df_a15_rho3_authentic <- 
#   sim_long_df_a15_rho3[sim_long_df_a15_rho3$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a15_rho3_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a15_rho3_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# table(sim_long_median_df$alpha)
# table(sim_long_median_df$rho)
# 
# sim_long_df_a0016_rho3 <- sim_long_median_df[sim_long_median_df$alpha < 0.0017 &
#                                            sim_long_median_df$rho == 0, ]
# sim_long_df_a0016_rho3_noise <- 
#   sim_long_df_a0016_rho3[sim_long_df_a0016_rho3$predictor_type == "noise_median", ]
# sim_long_df_a0016_rho3_authentic <- 
#   sim_long_df_a0016_rho3[sim_long_df_a0016_rho3$predictor_type == "authentic_median", ]
# 
# ggplot(data=sim_long_df_a0016_rho3_noise,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()
# ggplot(data=sim_long_df_a0016_rho3_authentic,
#        aes(x=p, y=count, colour=n)) +
#        geom_line()