library(matrixStats) # for numerically stable logsumexps

options(amelia.parallel="no",
        amelia.ncpus=1)
library(Amelia)

source("measerr_methods.R") ## for my more generic function.

run_simulation <- function(df, result, outcome_formula = y ~ x + z, proxy_formula = w_pred ~ x, truth_formula = x ~ z){

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

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

    result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
                                  Bzy.est.true=coef(model.true)['z'],
                                  Bxy.ci.upper.true = true.ci.Bxy[2],
                                  Bxy.ci.lower.true = true.ci.Bxy[1],
                                  Bzy.ci.upper.true = true.ci.Bzy[2],
                                  Bzy.ci.lower.true = true.ci.Bzy[1]))



    loa0.feasible <- lm(y ~ x.obs.0 + z, data = df[!(is.na(x.obs.1))])

    loa0.ci.Bxy <- confint(loa0.feasible)['x.obs.0',]
    loa0.ci.Bzy <- confint(loa0.feasible)['z',]

    result <- append(result, list(Bxy.est.loa0.feasible=coef(loa0.feasible)['x.obs.0'],
                                  Bzy.est.loa0.feasible=coef(loa0.feasible)['z'],
                                  Bxy.ci.upper.loa0.feasible = loa0.ci.Bxy[2],
                                  Bxy.ci.lower.loa0.feasible = loa0.ci.Bxy[1],
                                  Bzy.ci.upper.loa0.feasible = loa0.ci.Bzy[2],
                                  Bzy.ci.lower.loa0.feasible = loa0.ci.Bzy[1]))


    df.loa0.mle <- copy(df)
    df.loa0.mle[,x:=x.obs.0]
    loa0.mle <- measerr_mle(df.loa0.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
    fisher.info <- solve(loa0.mle$hessian)
    coef <- loa0.mle$par
    ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
    ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96

    result <- append(result, list(Bxy.est.loa0.mle=coef['x'],
                                  Bzy.est.loa0.mle=coef['z'],
                                  Bxy.ci.upper.loa0.mle = ci.upper['x'],
                                  Bxy.ci.lower.loa0.mle = ci.lower['x'],
                                  Bzy.ci.upper.loa0.mle = ci.upper['z'],
                                  Bzy.ci.lower.loa0.mle = ci.upper['z']))

    loco.feasible <- lm(y ~ x.obs.1 + z, data = df[(!is.na(x.obs.1)) & (x.obs.1 == x.obs.0)])

    loco.feasible.ci.Bxy <- confint(loco.feasible)['x.obs.1',]
    loco.feasible.ci.Bzy <- confint(loco.feasible)['z',]

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


    df.loco.mle <- copy(df)
    df.loco.mle[,x.obs:=NA]
    df.loco.mle[(x.obs.0)==(x.obs.1),x.obs:=x.obs.0]
    df.loco.mle[,x.true:=x]
    df.loco.mle[,x:=x.obs]
    print(df.loco.mle[!is.na(x.obs.1),mean(x.true==x,na.rm=TRUE)])
    loco.mle <- measerr_mle(df.loco.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
    fisher.info <- solve(loco.mle$hessian)
    coef <- loco.mle$par
    ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
    ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96

    result <- append(result, list(Bxy.est.loco.mle=coef['x'],
                                  Bzy.est.loco.mle=coef['z'],
                                  Bxy.ci.upper.loco.mle = ci.upper['x'],
                                  Bxy.ci.lower.loco.mle = ci.lower['x'],
                                  Bzy.ci.upper.loco.mle = ci.upper['z'],
                                  Bzy.ci.lower.loco.mle = ci.upper['z']))

    ## print(rater_formula)
    ## print(proxy_formula)
    ## mle.irr <- measerr_irr_mle( df, outcome_formula = outcome_formula, rater_formula = rater_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)

    ## fisher.info <- solve(mle.irr$hessian)
    ## coef <- mle.irr$par
    ## ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
    ## ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
    
    ## result <- append(result,
    ##                  list(Bxy.est.mle = coef['x'],
    ##                       Bxy.ci.upper.mle = ci.upper['x'],
    ##                       Bxy.ci.lower.mle = ci.lower['x'],
    ##                       Bzy.est.mle = coef['z'],
    ##                       Bzy.ci.upper.mle = ci.upper['z'],
    ##                       Bzy.ci.lower.mle = ci.lower['z']))

    return(result)

}