### EXAMPLE 1: demonstrates how measurement error can lead to a type sign error in a covariate
### What kind of data invalidates fong + tyler?
### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
### Even when you include the proxy variable in the regression.
### But with some ground truth and multiple imputation, you can fix it.

library(argparser)
library(mecor)
library(ggplot2)
library(data.table)
library(filelock)
library(arrow)
library(Amelia)
library(Zelig)
library(predictionError)
options(amelia.parallel="no",
        amelia.ncpus=1)
setDTthreads(40)

source("simulation_base.R")

## SETUP:
### we want to estimate x -> y; x is MAR
### we have x -> k; k -> w; x -> w is used to predict x via the model w.
### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
### The labels x are binary, but the model provides a continuous predictor

### simulation:
#### how much power do we get from the model in the first place? (sweeping N and m)
#### 

## one way to do it is by adding correlation to x.obs and y that isn't in w.
## in other words, the model is missing an important feature of x.obs that's related to y.
simulate_data <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed, xy.explained.variance=0.01, u.explained.variance=0.1){
    set.seed(seed)

    ## the true value of x

    g <- rbinom(N, 1, 0.5)

    # make w and y dependent
    u <- rnorm(N,0,)

    xprime <- Bgx * g + rnorm(N,0,1) 

    k <- Bkx*xprime + rnorm(N,0,1.5) + 1.1*Bkx*u

    x <- as.integer(logistic(scale(xprime)) > 0.5)

    y <-  Bxy * x  + Bgy * g + B0 + u + rnorm(N, 0, 1)

    df <- data.table(x=x,k=k,y=y,g=g)

    w.model <- glm(x ~ k,df, family=binomial(link='logit')) 

    if( m < N){
        df <- df[sample(nrow(df), m), x.obs := x]
    } else {
        df <- df[, x.obs := x]
    }

    df[, x.obs := x.obs]

    w <- predict(w.model, df) + rnorm(N, 0, 1)
    ## y = B0 + B1x + e

    df[,':='(w=w, w_pred = as.integer(w>0.5),u=u)]
    return(df)
}

schennach <- function(df){

    fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
    df[,xstar_pred := predict(fwx, df)]
    gxt <- lm(y ~ xstar_pred+g, df)

}


parser <- arg_parser("Simulate data and fit corrected models")
parser <- add_argument(parser, "--N", default=5000, help="number of observations of w")
parser <- add_argument(parser, "--m", default=200, help="m the number of ground truth observations")
parser <- add_argument(parser, "--seed", default=432, help='seed for the rng')
parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
args <- parse_args(parser)

B0 <- 0
Bxy <- 0.2
Bgy <- 0
Bkx <- 2
Bgx <- 0


outline <- run_simulation(simulate_data(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
                         ,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))

outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
if(file.exists(args$outfile)){
    logdata <- read_feather(args$outfile)
    logdata <- rbind(logdata,as.data.table(outline))
} else {
    logdata <- as.data.table(outline)
}

print(outline)
write_feather(logdata, args$outfile)
unlock(outfile_lock)