+    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]))
+