library(matrixStats) # for numerically stable logsumexps options(amelia.parallel="no", amelia.ncpus=1) library(Amelia) source("measerr_methods.R") source("pl_methods.R") run_simulation <- function(df, result, outcome_formula = y ~ x + z, proxy_formula = w_pred ~ x, coder_formulas=list(x.obs.1~x, x.obs.0~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])) print("fitting loa0 model") 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])) (model.naive <- lm(y~w_pred+z, data=df)) naive.ci.Bxy <- confint(model.naive)['w_pred',] naive.ci.Bzy <- confint(model.naive)['z',] result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'], Bzy.est.naive=coef(model.naive)['z'], Bxy.ci.upper.naive = naive.ci.Bxy[2], Bxy.ci.lower.naive = naive.ci.Bxy[1], Bzy.ci.upper.naive = naive.ci.Bzy[2], Bzy.ci.lower.naive = naive.ci.Bzy[1])) print("fitting loco model") 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.accuracy <- df.loco.mle[(!is.na(x.obs.1)) & (x.obs.1 == x.obs.0),mean(x.obs.1 == x.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(loco.accuracy=loco.accuracy, 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.lower['z'])) df.double.proxy.mle <- copy(df) df.double.proxy.mle[,x.obs:=NA] print("fitting double proxy model") double.proxy.mle <- measerr_irr_mle(df.double.proxy.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula, coder_formulas=coder_formulas[1], truth_formula=truth_formula) fisher.info <- solve(double.proxy.mle$hessian) coef <- double.proxy.mle$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.double.proxy=coef['x'], Bzy.est.double.proxy=coef['z'], Bxy.ci.upper.double.proxy = ci.upper['x'], Bxy.ci.lower.double.proxy = ci.lower['x'], Bzy.ci.upper.double.proxy = ci.upper['z'], Bzy.ci.lower.double.proxy = ci.lower['z'])) df.triple.proxy.mle <- copy(df) df.triple.proxy.mle[,x.obs:=NA] print("fitting triple proxy model") triple.proxy.mle <- measerr_irr_mle(df.triple.proxy.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula, coder_formulas=coder_formulas, truth_formula=truth_formula) fisher.info <- solve(triple.proxy.mle$hessian) coef <- triple.proxy.mle$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.triple.proxy=coef['x'], Bzy.est.triple.proxy=coef['z'], Bxy.ci.upper.triple.proxy = ci.upper['x'], Bxy.ci.lower.triple.proxy = ci.lower['x'], Bzy.ci.upper.triple.proxy = ci.upper['z'], Bzy.ci.lower.triple.proxy = ci.lower['z'])) tryCatch({ amelia.out.k <- amelia(df.loco.mle, m=200, p2s=0, idvars=c('x.true','w','x.obs.1','x.obs.0','x')) mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE) (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE)) est.x.mi <- coefse['x.obs','Estimate'] est.x.se <- coefse['x.obs','Std.Error'] result <- append(result, list(Bxy.est.amelia.full = est.x.mi, Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se, Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se )) est.z.mi <- coefse['z','Estimate'] est.z.se <- coefse['z','Std.Error'] result <- append(result, list(Bzy.est.amelia.full = est.z.mi, Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se, Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se )) }, error = function(e){ message("An error occurred:\n",e) result$error <-paste0(result$error,'\n', e) } ) tryCatch({ mod.zhang.lik <- zhang.mle.iv(df.loco.mle) coef <- coef(mod.zhang.lik) ci <- confint(mod.zhang.lik,method='quad') result <- append(result, list(Bxy.est.zhang = coef['Bxy'], Bxy.ci.upper.zhang = ci['Bxy','97.5 %'], Bxy.ci.lower.zhang = ci['Bxy','2.5 %'], Bzy.est.zhang = coef['Bzy'], Bzy.ci.upper.zhang = ci['Bzy','97.5 %'], Bzy.ci.lower.zhang = ci['Bzy','2.5 %'])) }, error = function(e){ message("An error occurred:\n",e) result$error <- paste0(result$error,'\n', e) }) df <- df.loco.mle N <- nrow(df) m <- nrow(df[!is.na(x.obs)]) p <- v <- train <- rep(0,N) M <- m p[(M+1):(N)] <- 1 v[1:(M)] <- 1 df <- df[order(x.obs)] y <- df[,y] x <- df[,x.obs] z <- df[,z] w <- df[,w_pred] # gmm gets pretty close (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE)) result <- append(result, list(Bxy.est.gmm = gmm.res$beta[1,1], Bxy.ci.upper.gmm = gmm.res$confint[1,2], Bxy.ci.lower.gmm = gmm.res$confint[1,1], gmm.ER_pval = gmm.res$ER_pval )) result <- append(result, list(Bzy.est.gmm = gmm.res$beta[2,1], Bzy.ci.upper.gmm = gmm.res$confint[2,2], Bzy.ci.lower.gmm = gmm.res$confint[2,1])) return(result) }