299 lines
12 KiB
R
299 lines
12 KiB
R
library(predictionError)
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library(mecor)
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options(amelia.parallel="no",
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amelia.ncpus=1)
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library(Amelia)
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library(Zelig)
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library(stats4)
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## This uses the pseudolikelihood approach from Carroll page 349.
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## assumes MAR
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## assumes differential error, but that only depends on Y
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## inefficient, because pseudolikelihood
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logistic.correction.pseudo <- function(df){
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p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
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p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
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nll <- function(B0, Bxy, Bgy){
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probs <- (1 - p0.est) + (p1.est + p0.est - 1)*plogis(B0 + Bxy * df$x + Bgy * df$g)
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part1 = sum(log(probs[df$w_pred == 1]))
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part2 = sum(log(1-probs[df$w_pred == 0]))
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return(-1*(part1 + part2))
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}
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mlefit <- stats4::mle(minuslogl = nll, start = list(B0=0, Bxy=0.0, Bgy=0.0))
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return(mlefit)
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}
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## This uses the likelihood approach from Carroll page 353.
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## assumes that we have a good measurement error model
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logistic.correction.liklihood <- function(df){
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## liklihood for observed responses
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nll <- function(B0, Bxy, Bgy, gamma0, gamma_y, gamma_g){
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df.obs <- df[!is.na(y.obs)]
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p.y.obs <- plogis(B0 + Bxy * df.obs$x + Bgy*df.obs$g)
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p.y.obs[df.obs$y==0] <- 1-p.y.obs[df.obs$y==0]
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p.s.obs <- plogis(gamma0 + gamma_y * df.obs$y + gamma_g*df.obs$g)
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p.s.obs[df.obs$w_pred==0] <- 1 - p.s.obs[df.obs$w_pred==0]
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p.obs <- p.s.obs * p.y.obs
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df.unobs <- df[is.na(y.obs)]
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p.unobs.1 <- plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g)*plogis(gamma0 + gamma_y + gamma_g*df.unobs$g)
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p.unobs.0 <- (1-plogis(B0 + Bxy * df.unobs$x + Bgy*df.unobs$g))*plogis(gamma0 + gamma_g*df.unobs$g)
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p.unobs <- p.unobs.1 + p.unobs.0
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p.unobs[df.unobs$w_pred==0] <- 1 - p.unobs[df.unobs$w_pred==0]
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p <- c(p.obs, p.unobs)
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return(-1*(sum(log(p))))
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}
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mlefit <- stats4::mle(minuslogl = nll, start = list(B0=1, Bxy=0,Bgy=0, gamma0=5, gamma_y=0, gamma_g=0))
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return(mlefit)
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}
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logistic <- function(x) {1/(1+exp(-1*x))}
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run_simulation_depvar <- function(df, result){
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accuracy <- df[,mean(w_pred==y)]
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result <- append(result, list(accuracy=accuracy))
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(model.true <- glm(y ~ x + g, data=df,family=binomial(link='logit')))
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true.ci.Bxy <- confint(model.true)['x',]
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true.ci.Bgy <- confint(model.true)['g',]
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result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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Bgy.est.true=coef(model.true)['g'],
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Bxy.ci.upper.true = true.ci.Bxy[2],
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Bxy.ci.lower.true = true.ci.Bxy[1],
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Bgy.ci.upper.true = true.ci.Bgy[2],
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Bgy.ci.lower.true = true.ci.Bgy[1]))
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(model.feasible <- glm(y.obs~x+g,data=df,family=binomial(link='logit')))
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feasible.ci.Bxy <- confint(model.feasible)['x',]
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result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
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Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
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Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
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feasible.ci.Bgy <- confint(model.feasible)['g',]
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result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
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Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
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Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
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(model.naive <- glm(w_pred~x+g, data=df, family=binomial(link='logit')))
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naive.ci.Bxy <- confint(model.naive)['x',]
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naive.ci.Bgy <- confint(model.naive)['g',]
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result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
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Bgy.est.naive=coef(model.naive)['g'],
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Bxy.ci.upper.naive = naive.ci.Bxy[2],
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Bxy.ci.lower.naive = naive.ci.Bxy[1],
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Bgy.ci.upper.naive = naive.ci.Bgy[2],
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Bgy.ci.lower.naive = naive.ci.Bgy[1]))
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(model.naive.cont <- lm(w~x+g, data=df))
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naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
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naivecont.ci.Bgy <- confint(model.naive.cont)['g',]
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## my implementatoin of liklihood based correction
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mod.caroll.lik <- logistic.correction.liklihood(df)
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coef <- coef(mod.caroll.lik)
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ci <- confint(mod.caroll.lik)
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result <- append(result,
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list(Bxy.est.mle = coef['Bxy'],
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Bxy.ci.upper.mle = ci['Bxy','97.5 %'],
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Bxy.ci.lower.mle = ci['Bxy','2.5 %'],
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Bgy.est.mle = coef['Bgy'],
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Bgy.ci.upper.mle = ci['Bgy','97.5 %'],
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Bgy.ci.lower.mle = ci['Bgy','2.5 %']))
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## my implementatoin of liklihood based correction
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mod.caroll.pseudo <- logistic.correction.pseudo(df)
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coef <- coef(mod.caroll.pseudo)
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ci <- confint(mod.caroll.pseudo)
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result <- append(result,
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list(Bxy.est.pseudo = coef['Bxy'],
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Bxy.ci.upper.pseudo = ci['Bxy','97.5 %'],
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Bxy.ci.lower.pseudo = ci['Bxy','2.5 %'],
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Bgy.est.pseudo = coef['Bgy'],
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Bgy.ci.upper.pseudo = ci['Bgy','97.5 %'],
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Bgy.ci.lower.pseudo = ci['Bgy','2.5 %']))
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# amelia says use normal distribution for binary variables.
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amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w_pred'))
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mod.amelia.k <- zelig(y.obs~x+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
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(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
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est.x.mi <- coefse['x','Estimate']
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est.x.se <- coefse['x','Std.Error']
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result <- append(result,
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list(Bxy.est.amelia.full = est.x.mi,
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Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
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Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
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))
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est.g.mi <- coefse['g','Estimate']
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est.g.se <- coefse['g','Std.Error']
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result <- append(result,
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list(Bgy.est.amelia.full = est.g.mi,
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Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
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Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
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))
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return(result)
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}
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run_simulation <- function(df, result){
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accuracy <- df[,mean(w_pred==x)]
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result <- append(result, list(accuracy=accuracy))
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(model.true <- lm(y ~ x + g, data=df))
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true.ci.Bxy <- confint(model.true)['x',]
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true.ci.Bgy <- confint(model.true)['g',]
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result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
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Bgy.est.true=coef(model.true)['g'],
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Bxy.ci.upper.true = true.ci.Bxy[2],
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Bxy.ci.lower.true = true.ci.Bxy[1],
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Bgy.ci.upper.true = true.ci.Bgy[2],
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Bgy.ci.lower.true = true.ci.Bgy[1]))
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(model.feasible <- lm(y~x.obs+g,data=df))
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feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
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result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
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Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
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Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
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feasible.ci.Bgy <- confint(model.feasible)['g',]
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result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
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Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
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Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
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(model.naive <- lm(y~w+g, data=df))
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naive.ci.Bxy <- confint(model.naive)['w',]
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naive.ci.Bgy <- confint(model.naive)['g',]
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result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
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Bgy.est.naive=coef(model.naive)['g'],
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Bxy.ci.upper.naive = naive.ci.Bxy[2],
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Bxy.ci.lower.naive = naive.ci.Bxy[1],
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Bgy.ci.upper.naive = naive.ci.Bgy[2],
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Bgy.ci.lower.naive = naive.ci.Bgy[1]))
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amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'))
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mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
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(coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
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est.x.mi <- coefse['x.obs','Estimate']
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est.x.se <- coefse['x.obs','Std.Error']
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result <- append(result,
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list(Bxy.est.amelia.full = est.x.mi,
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Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
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Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
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))
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est.g.mi <- coefse['g','Estimate']
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est.g.se <- coefse['g','Std.Error']
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result <- append(result,
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list(Bgy.est.amelia.full = est.g.mi,
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Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
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Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
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))
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## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
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## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
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## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
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## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
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## est.x.mi <- coefse['x.obs','Estimate']
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## est.x.se <- coefse['x.obs','Std.Error']
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## result <- append(result,
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## list(Bxy.est.amelia.nok = est.x.mi,
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## Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
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## Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
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## ))
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## est.g.mi <- coefse['g','Estimate']
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## est.g.se <- coefse['g','Std.Error']
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## result <- append(result,
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## list(Bgy.est.amelia.nok = est.g.mi,
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## Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
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## Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
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## ))
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N <- nrow(df)
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m <- nrow(df[!is.na(x.obs)])
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p <- v <- train <- rep(0,N)
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M <- m
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p[(M+1):(N)] <- 1
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v[1:(M)] <- 1
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df <- df[order(x.obs)]
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y <- df[,y]
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x <- df[,x.obs]
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g <- df[,g]
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w <- df[,w]
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# gmm gets pretty close
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(gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=TRUE))
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result <- append(result,
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list(Bxy.est.gmm = gmm.res$beta[1,1],
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Bxy.ci.upper.gmm = gmm.res$confint[1,2],
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Bxy.ci.lower.gmm = gmm.res$confint[1,1],
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gmm.ER_pval = gmm.res$ER_pval
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))
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result <- append(result,
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list(Bgy.est.gmm = gmm.res$beta[2,1],
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Bgy.ci.upper.gmm = gmm.res$confint[2,2],
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Bgy.ci.lower.gmm = gmm.res$confint[2,1]))
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mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
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(mod.calibrated.mle)
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(mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
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result <- append(result, list(
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Bxy.est.mecor = mecor.ci['Estimate'],
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Bxy.upper.mecor = mecor.ci['UCI'],
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Bxy.lower.mecor = mecor.ci['LCI'])
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)
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(mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
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result <- append(result, list(
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Bgy.est.mecor = mecor.ci['Estimate'],
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Bgy.upper.mecor = mecor.ci['UCI'],
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Bgy.lower.mecor = mecor.ci['LCI'])
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)
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## clean up memory
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## rm(list=c("df","y","x","g","w","v","train","p","amelia.out.k","amelia.out.nok", "mod.calibrated.mle","gmm.res","mod.amelia.k","mod.amelia.nok", "model.true","model.naive","model.feasible"))
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## gc()
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return(result)
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}
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