### EXAMPLE 2_b: demonstrates how measurement error can lead to a type sign error in a covariate
### This is the same as example 2, only instead of x->k we have k->x.
### 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)

source("simulation_base_mecor.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)
#### 
logistic <- function(x) {1/(1+exp(-1*x))}

simulate_latent_cocause <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
    set.seed(seed)

    ## the true value of x

    g <- rbinom(N, 1, 0.5)
    xprime <- Bgx * g + rnorm(N,0,1)

    k <- Bkx*xprime + rnorm(N,0,3)

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

    y <-  Bxy * x  + Bgy * g + rnorm(N, 0, 1) + B0
    df <- data.table(x=x,k=k,y=y,g=g)

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

    w.model <- glm(x ~ k,df, family=binomial(link='logit'))
    w <- predict(w.model,data.frame(k=k)) + rnorm(N,0,1)
    ## y = B0 + B1x + e

    df[,':='(w=w, w_pred = as.integer(w>0.5))]
    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=100, help="number of observations of w")
parser <- add_argument(parser, "--m", default=20, help="m the number of ground truth observations")
parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng')
parser <- add_argument(parser, "--outfile", help='output file', default='example_2_B.feather')
args <- parse_args(parser)

B0 <- 0
Bxy <- 0.2

Bkx <- 0.5

rows <- list()

B0 <- 0
Bxy <- 0.4
Bgy <- 0.25
Bkx <- 3.2
Bgx <- -0.5

outline <- run_simulation(simulate_latent_cocause(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$outfile, '_lock'))
if(file.exists(args$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)

## Ns <- c(1e6, 5e4, 1000)
## ms <- c(100, 250, 500, 1000)
## seeds <- 1:500

## rowssets <- list()
## library(doParallel)
## options(mc.cores = parallel::detectCores())
## cl <- makeCluster(20)
## registerDoParallel(cl)

## ## library(future)

## ## plan(multiprocess,workers=40,gc=TRUE)

## for(N in Ns){
##     print(N)
##     for(m in ms){
##         if(N>m){
##             new.rows <- foreach(iter=seeds, .combine=rbind, .packages = c('mecor','Amelia','Zelig','predictionError','data.table'),
##                                 .export = c("run_simulation","simulate_latent_cocause","logistic","N","m","B0","Bxy","Bgy","Bkx","Bgx")) %dopar%
                
##                 {run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, iter)
##                                ,list('N'=N,'m'=m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=iter))}
##             rowsets <- append(rowssets, list(data.table(new.rows)))
##        }

##     }
##                 ## rows <- append(rows, list(future({run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)
## }
                ##                                                 ,list(N=N,m=m,B0=B0,Bxy=Bxy,Bgy=Bgy, Bkx=Bkx, Bgx=Bgx, seed=seed))w},
                ##                                  packages=c('mecor','Amelia','Zelig','predictionError'),
                ##                                  seed=TRUE)))


## df <- rbindlist(rowsets)

## write_feather(df,"example_2B_simulation.feather")

## run_simulation <-  function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
##     result <- list()
##     df <- simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)

##     result <- append(result, list(N=N,
##                                   m=m,
##                                   B0=B0,
##                                   Bxy=Bxy,
##                                   Bgy=Bgy,
##                                   Bkx=Bkx,
##                                   seed=seed))

##     (accuracy <- df[,.(mean(w_pred==x))])
##     result <- append(result, list(accuracy=accuracy))

##     (model.true <- lm(y ~ x + g, data=df))
##     true.ci.Bxy <- confint(model.true)['x',]
##     true.ci.Bgy <- confint(model.true)['g',]

##     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
##                                   Bgy.est.true=coef(model.true)['g'],
##                                   Bxy.ci.upper.true = true.ci.Bxy[2],
##                                   Bxy.ci.lower.true = true.ci.Bxy[1],
##                                   Bgy.ci.upper.true = true.ci.Bgy[2],
##                                   Bgy.ci.lower.true = true.ci.Bgy[1]))
                                  
##     (model.feasible <- lm(y~x.obs+g,data=df))

##     feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
##     result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
##                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
##                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))

##     feasible.ci.Bgy <- confint(model.feasible)['g',]
##     result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
##                                   Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
##                                   Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))

##     (model.naive <- lm(y~w+g, data=df))
    
##     naive.ci.Bxy <- confint(model.naive)['w',]
##     naive.ci.Bgy <- confint(model.naive)['g',]

##     result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
##                                   Bgy.est.naive=coef(model.naive)['g'],
##                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
##                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
##                                   Bgy.ci.upper.naive = naive.ci.Bgy[2],
##                                   Bgy.ci.lower.naive = naive.ci.Bgy[1]))
                                  

##     ## multiple imputation when k is observed
##     ## amelia does great at this one.
##     amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=c("x.obs","g"),lgstc=c('w'))
##     mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
##     (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))

##     est.x.mi <- coefse['x.obs','Estimate']
##     est.x.se <- coefse['x.obs','Std.Error']
##     result <- append(result,
##                      list(Bxy.est.amelia.full = est.x.mi,
##                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
##                           Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
##                           ))

##     est.g.mi <- coefse['g','Estimate']
##     est.g.se <- coefse['g','Std.Error']

##     result <- append(result,
##                      list(Bgy.est.amelia.full = est.g.mi,
##                           Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
##                           Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
##                           ))

##     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
##     amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","k"), noms=c("x.obs",'g'),lgstc = c("w"))
##     mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
##     (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))

##     est.x.mi <- coefse['x.obs','Estimate']
##     est.x.se <- coefse['x.obs','Std.Error']
##     result <- append(result,
##                      list(Bxy.est.amelia.nok = est.x.mi,
##                           Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
##                           Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
##                           ))

##     est.g.mi <- coefse['g','Estimate']
##     est.g.se <- coefse['g','Std.Error']

##     result <- append(result,
##                      list(Bgy.est.amelia.nok = est.g.mi,
##                           Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
##                           Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
##                           ))

##     p <- v <- train <- rep(0,N)
##     M <- m
##     p[(M+1):(N)] <- 1
##     v[1:(M)] <- 1
##     df <- df[order(x.obs)]
##     y <- df[,y]
##     x <- df[,x.obs]
##     g <- df[,g]
##     w <- df[,w]
##     # gmm gets pretty close
##     (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=FALSE))

##     result <- append(result,
##                      list(Bxy.est.gmm = gmm.res$beta[1,1],
##                           Bxy.ci.upper.gmm = gmm.res$confint[1,2],
##                           Bxy.ci.lower.gmm = gmm.res$confint[1,1]))

##     result <- append(result,
##                      list(Bgy.est.gmm = gmm.res$beta[2,1],
##                           Bgy.ci.upper.gmm = gmm.res$confint[2,2],
##                           Bgy.ci.lower.gmm = gmm.res$confint[2,1]))


##     mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
##     (mod.calibrated.mle)
##     (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
##     result <- append(result, list(
##                                  Bxy.est.mecor = mecor.ci['Estimate'],
##                                  Bxy.upper.mecor = mecor.ci['UCI'],
##                                  Bxy.lower.mecor = mecor.ci['LCI'])
##                      )

##     (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])

##     result <- append(result, list(
##                                  Bxy.est.mecor = mecor.ci['Estimate'],
##                                  Bxy.upper.mecor = mecor.ci['UCI'],
##                                  Bxy.lower.mecor = mecor.ci['LCI'])
##                      )


##     return(result)
## }