From: Nathan TeBlunthuis <nathante@uw.edu>
Date: Fri, 2 Sep 2022 18:34:50 +0000 (-0700)
Subject: update simulation and mle code
X-Git-Url: https://code.communitydata.science/ml_measurement_error_public.git/commitdiff_plain/979dc14b6861ae31f00d56392fd5b8cf69f17333?hp=--cc

update simulation and mle code
---

979dc14b6861ae31f00d56392fd5b8cf69f17333
diff --git a/simulations/02_indep_differential.R b/simulations/02_indep_differential.R
index d4c4397..c6907d3 100644
--- a/simulations/02_indep_differential.R
+++ b/simulations/02_indep_differential.R
@@ -125,7 +125,7 @@ simulate_data <- function(N, m, B0, Bxy, Bzx, Bzy, seed, y_explained_variance=0.
 
 parser <- arg_parser("Simulate data and fit corrected models")
 parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
-aparser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
+parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
 parser <- add_argument(parser, "--seed", default=51, help='seed for the rng')
 parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
 parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.1)
diff --git a/simulations/03_depvar.R b/simulations/03_depvar.R
index 69b4485..a2d88e0 100644
--- a/simulations/03_depvar.R
+++ b/simulations/03_depvar.R
@@ -70,7 +70,7 @@ parser <- add_argument(parser, "--N", default=1000, help="number of observations
 parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
 parser <- add_argument(parser, "--seed", default=17, help='seed for the rng')
 parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
-parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005)
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.1)
 parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.72)
 ## parser <- add_argument(parser, "--x_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
 ## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
diff --git a/simulations/05_irr_indep.R b/simulations/05_irr_indep.R
new file mode 100644
index 0000000..4c3a109
--- /dev/null
+++ b/simulations/05_irr_indep.R
@@ -0,0 +1,113 @@
+### 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("irr_simulation_base.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)
+#### 
+
+simulate_data <- function(N, m, B0=0, Bxy=0.2, Bzy=-0.2, Bzx=0.2, y_explained_variance=0.025, prediction_accuracy=0.73, coder_accuracy=0.9, seed=1){
+    set.seed(seed)
+    z <- rbinom(N, 1, 0.5)
+                                        #    x.var.epsilon <- var(Bzx *z) * ((1-zx_explained_variance)/zx_explained_variance)
+    xprime <- Bzx * z #+ x.var.epsilon
+    x <- rbinom(N,1,plogis(xprime))
+
+    y.var.epsilon <- (var(Bzy * z) + var(Bxy *x) + 2*cov(Bxy*x,Bzy*z)) * ((1-y_explained_variance)/y_explained_variance)
+    y.epsilon <- rnorm(N, sd = sqrt(y.var.epsilon))
+    y <- Bzy * z + Bxy * x + y.epsilon
+
+    df <- data.table(x=x,y=y,z=z)
+
+    if(m < N){
+        df <- df[sample(nrow(df), m), x.obs := x]
+    } else {
+        df <- df[, x.obs := x]
+    }
+
+    df[ (!is.na(x.obs)) ,x.obs.0 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
+    df[ (!is.na(x.obs)) ,x.obs.1 := abs(x.obs - rbinom(.N, 1, 1-coder_accuracy))]
+    
+
+    ## how can you make a model with a specific accuracy?
+    w0 =(1-x)**2 + (-1)**(1-x) * prediction_accuracy
+
+    ## how can you make a model with a specific accuracy, with a continuous latent variable.
+    # now it makes the same amount of mistake to each point, probably
+    # add mean0 noise to the odds.
+    
+    w.noisey.odds = rlogis(N,qlogis(w0))
+    df[,w := plogis(w.noisey.odds)]
+    df[,w_pred:=as.integer(w > 0.5)]
+    (mean(df$x==df$w_pred))
+    return(df)
+}
+
+parser <- arg_parser("Simulate data and fit corrected models")
+parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
+parser <- add_argument(parser, "--seed", default=57, help='seed for the rng')
+parser <- add_argument(parser, "--outfile", help='output file', default='example_1.feather')
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.05)
+# parser <- add_argument(parser, "--zx_explained_variance", help='what proportion of the variance of x can be explained by z?', default=0.3)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.73)
+parser <- add_argument(parser, "--coder_accuracy", help='how accurate is the predictive model?', default=0.8)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~x")
+
+# parser <- add_argument(parser, "--rater_formula", help='formula for the true variable', default="x.obs~x")
+parser <- add_argument(parser, "--truth_formula", help='formula for the true variable', default="x~z")
+parser <- add_argument(parser, "--Bzx", help='Effect of z on x', default=-0.3)
+parser <- add_argument(parser, "--Bzy", help='Effect of z on y', default=-0.3)
+parser <- add_argument(parser, "--Bxy", help='Effect of z on y', default=0.3)
+
+args <- parse_args(parser)
+B0 <- 0
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+Bzx <- args$Bzx
+
+if (args$m < args$N){
+
+    df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, Bzx, seed=args$seed + 500, y_explained_variance = args$y_explained_variance,  prediction_accuracy=args$prediction_accuracy, coder_accuracy=args$coder_accuracy)
+
+    result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy, Bzx=Bzx, 'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'accuracy_imbalance_difference'=args$accuracy_imbalance_difference, 'outcome_formula'=args$outcome_formula, 'truth_formula'=args$truth_formula, 'proxy_formula'=args$proxy_formula,truth_formula=args$truth_formula, 'coder_accuracy'=args$coder_accuracy, error='')
+
+    outline <- run_simulation(df, result, outcome_formula=as.formula(args$outcome_formula), proxy_formula=as.formula(args$proxy_formula), truth_formula=as.formula(args$truth_formula))
+    
+    outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+    if(file.exists(args$outfile)){
+        logdata <- read_feather(args$outfile)
+        logdata <- rbind(logdata,as.data.table(outline),fill=TRUE)
+    } else {
+        logdata <- as.data.table(outline)
+    }
+
+    print(outline)
+    write_feather(logdata, args$outfile)
+    unlock(outfile_lock)
+}
diff --git a/simulations/06_irr_dv.R b/simulations/06_irr_dv.R
new file mode 100644
index 0000000..0dd13b6
--- /dev/null
+++ b/simulations/06_irr_dv.R
@@ -0,0 +1,99 @@
+
+library(argparser)
+library(mecor)
+library(ggplot2)
+library(data.table)
+library(filelock)
+library(arrow)
+library(Amelia)
+library(Zelig)
+library(predictionError)
+options(amelia.parallel="no",
+        amelia.ncpus=1)
+setDTthreads(40)
+
+source("irr_dv_simulation_base.R")
+
+
+## one way to do it is by adding correlation to x.obs and y that isn't in w.
+## in other words, the model is missing an important feature of x.obs that's related to y.
+simulate_data <- function(N, m, B0, Bxy, Bzy, seed, prediction_accuracy=0.73, coder_accuracy=0.8){
+    set.seed(seed)
+
+    # make w and y dependent
+    z <- rbinom(N, 1, 0.5)
+    x <- rbinom(N, 1, 0.5)
+
+    ystar <- Bzy * z + Bxy * x + B0
+    y <- rbinom(N,1,plogis(ystar))
+
+    # glm(y ~ x + z, family="binomial")
+
+    df <- data.table(x=x,y=y,ystar=ystar,z=z)
+
+    if(m < N){
+        df <- df[sample(nrow(df), m), y.obs := y]
+    } else {
+        df <- df[, y.obs := y]
+    }
+    
+    df[ (!is.na(y.obs)) ,y.obs.0 := abs(y.obs - rbinom(.N, 1, 1-coder_accuracy))]
+    df[ (!is.na(y.obs)) ,y.obs.1 := abs(y.obs - rbinom(.N, 1, 1-coder_accuracy))]
+
+    odds.y1 <- qlogis(prediction_accuracy)
+    odds.y0 <- qlogis(prediction_accuracy,lower.tail=F)
+
+    df[y==0,w:=plogis(rlogis(.N,odds.y0))]
+    df[y==1,w:=plogis(rlogis(.N,odds.y1))]
+
+    df[,w_pred := as.integer(w > 0.5)]
+
+    print(mean(df[x==0]$y == df[x==0]$w_pred))
+    print(mean(df[x==1]$y == df[x==1]$w_pred))
+    print(mean(df$w_pred == df$y))
+    return(df)
+}
+
+parser <- arg_parser("Simulate data and fit corrected models")
+parser <- add_argument(parser, "--N", default=1000, help="number of observations of w")
+parser <- add_argument(parser, "--m", default=500, help="m the number of ground truth observations")
+parser <- add_argument(parser, "--seed", default=17, help='seed for the rng')
+parser <- add_argument(parser, "--outfile", help='output file', default='example_2.feather')
+parser <- add_argument(parser, "--y_explained_variance", help='what proportion of the variance of y can be explained?', default=0.005)
+parser <- add_argument(parser, "--prediction_accuracy", help='how accurate is the predictive model?', default=0.72)
+## parser <- add_argument(parser, "--x_bias_y1", help='how is the classifier biased when y = 1?', default=-0.75)
+## parser <- add_argument(parser, "--x_bias_y0", help='how is the classifier biased when y = 0 ?', default=0.75)
+parser <- add_argument(parser, "--Bxy", help='coefficient of x on y', default=0.3)
+parser <- add_argument(parser, "--Bzy", help='coeffficient of z on y', default=-0.3)
+parser <- add_argument(parser, "--outcome_formula", help='formula for the outcome variable', default="y~x+z")
+parser <- add_argument(parser, "--proxy_formula", help='formula for the proxy variable', default="w_pred~y")
+parser <- add_argument(parser, "--coder_accuracy", help='How accurate are the coders?', default=0.8)
+
+args <- parse_args(parser)
+
+B0 <- 0
+Bxy <- args$Bxy
+Bzy <- args$Bzy
+
+
+if(args$m < args$N){
+    df <- simulate_data(args$N, args$m, B0, Bxy, Bzy, args$seed, args$prediction_accuracy, args$coder_accuracy)
+
+#    result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'x_bias_y0'=args$x_bias_y0,'x_bias_y1'=args$x_bias_y1,'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
+    result <- list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bzy'=Bzy, 'seed'=args$seed, 'y_explained_variance'=args$y_explained_variance, 'prediction_accuracy'=args$prediction_accuracy, 'outcome_formula' = args$outcome_formula, 'proxy_formula' = args$proxy_formula)
+
+    outline <- run_simulation_depvar(df, result, outcome_formula = as.formula(args$outcome_formula), proxy_formula = as.formula(args$proxy_formula))
+
+    outfile_lock <- lock(paste0(args$outfile, '_lock'),exclusive=TRUE)
+
+    if(file.exists(args$outfile)){
+        logdata <- read_feather(args$outfile)
+        logdata <- rbind(logdata,as.data.table(outline),fill=TRUE)
+    } else {
+        logdata <- as.data.table(outline)
+    }
+
+    print(outline)
+    write_feather(logdata, args$outfile)
+    unlock(outfile_lock)
+}
diff --git a/simulations/Makefile b/simulations/Makefile
index d278c8c..44910cb 100644
--- a/simulations/Makefile
+++ b/simulations/Makefile
@@ -1,12 +1,12 @@
 
 SHELL=bash
 
-Ns=[1000, 2000, 4000, 8000]
-ms=[100, 200, 400, 800]
-seeds=[$(shell seq -s, 1 100)]
+Ns=[1000, 2000, 4000]
+ms=[200, 400, 800]
+seeds=[$(shell seq -s, 1 250)]
 explained_variances=[0.1]
 
-all:remembr.RDS
+all:remembr.RDS remember_irr.RDS
 
 srun=srun -A comdata -p compute-bigmem --time=6:00:00 --mem 4G -c 1
 
@@ -31,7 +31,7 @@ example_1.feather: example_1_jobs
 #	sbatch --wait --verbose --array=3001-6001 run_simulation.sbatch 0 example_1_jobs
 
 example_2_jobs: 02_indep_differential.R simulation_base.R
-	grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y*z*x"], "truth_formula":["x~z"]}' --outfile example_2_jobs
+	grid_sweep.py --command "Rscript 02_indep_differential.R" --arg_dict '{"N":${Ns},"m":${ms}, "seed":${seeds}, "outfile":["example_2.feather"],"y_explained_variance":${explained_variances},  "Bzy":[-0.3],"Bxy":[0.3],"Bzx":[0.3], "outcome_formula":["y~x+z"], "proxy_formula":["w_pred~y*z*x"]}' --outfile example_2_jobs
 
 example_2.feather: example_2_jobs 
 	rm -f example_2.feather
@@ -59,6 +59,7 @@ example_4.feather: example_4_jobs
 	rm -f example_4.feather	
 	sbatch --wait --verbose --array=1-$(shell cat example_4_jobs | wc -l)  run_simulation.sbatch 0 example_4_jobs
 
+
 remembr.RDS:example_1.feather example_2.feather example_3.feather example_4.feather plot_example.R plot_dv_example.R
 	rm -f remembr.RDS
 	${srun} Rscript plot_example.R --infile example_1.feather --name "plot.df.example.1"
@@ -66,6 +67,32 @@ remembr.RDS:example_1.feather example_2.feather example_3.feather example_4.feat
 	${srun} Rscript plot_dv_example.R --infile example_3.feather --name "plot.df.example.3"
 	${srun} Rscript plot_dv_example.R --infile example_4.feather --name "plot.df.example.4"
 
+
+irr_Ns = ${Ns}
+irr_ms = ${ms}
+irr_seeds=${seeds}
+irr_explained_variances=${explained_variances}
+
+example_5_jobs: 05_irr_indep.R irr_simulation_base.R
+	grid_sweep.py --command "Rscript 05_irr_indep.R" --arg_dict '{"N":${irr_Ns},"m":${irr_ms}, "seed":${irr_seeds}, "outfile":["example_5.feather"], "y_explained_variance":${irr_explained_variances}}' --outfile example_5_jobs
+
+example_5.feather:example_5_jobs
+	rm -f example_5.feather
+	sbatch --wait --verbose --array=1-$(shell cat example_5_jobs | wc -l)  run_simulation.sbatch 0 example_5_jobs
+
+
+example_6_jobs: 06_irr_dv.R irr_dv_simulation_base.R
+	grid_sweep.py --command "Rscript 06_irr_dv.R" --arg_dict '{"N":${irr_Ns},"m":${irr_ms}, "seed":${irr_seeds}, "outfile":["example_6.feather"], "y_explained_variance":${irr_explained_variances}}' --outfile example_6_jobs
+
+example_6.feather:example_6_jobs
+	rm -f example_6.feather
+	sbatch --wait --verbose --array=1-$(shell cat example_6_jobs | wc -l)  run_simulation.sbatch 0 example_6_jobs
+
+remember_irr.RDS: example_5.feather example_6.feather plot_irr_example.R plot_irr_dv_example.R
+	rm -f remember_irr.RDS
+	${srun} Rscript plot_irr_example.R --infile example_5.feather --name "plot.df.example.5"
+	${srun} Rscript plot_irr_dv_example.R --infile example_6.feather --name "plot.df.example.6"
+
 clean:
 	rm *.feather
 	rm -f remembr.RDS
diff --git a/simulations/irr_dv_simulation_base.R b/simulations/irr_dv_simulation_base.R
new file mode 100644
index 0000000..3f63d7a
--- /dev/null
+++ b/simulations/irr_dv_simulation_base.R
@@ -0,0 +1,107 @@
+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_depvar <- function(df, result, outcome_formula = y ~ x + z, rater_formula = y.obs ~ x, proxy_formula = w_pred ~ y){
+
+    accuracy <- df[,mean(w_pred==y)]
+    result <- append(result, list(accuracy=accuracy))
+
+    (model.true <- glm(y ~ x + z, data=df, family=binomial(link='logit')))
+    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 <- glm(y.obs.0 ~ x + z, data = df[!(is.na(y.obs.0))], family=binomial(link='logit'))
+
+    loa0.ci.Bxy <- confint(loa0.feasible)['x',]
+    loa0.ci.Bzy <- confint(loa0.feasible)['z',]
+
+    result <- append(result, list(Bxy.est.loa0.feasible=coef(loa0.feasible)['x'],
+                                  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[,y:=y.obs.0]
+    loa0.mle <- measerr_mle_dv(df.loa0.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+    fisher.info <- solve(loa0.mle$hessian)
+    coef <- loa0.mle$par
+    ci.upper <- coef + sqrt(diag(fisher.info)) * 1.96
+    ci.lower <- coef - sqrt(diag(fisher.info)) * 1.96
+
+    result <- append(result, list(Bxy.est.loa0.mle=coef['x'],
+                                  Bzy.est.loa0.mle=coef['z'],
+                                  Bxy.ci.upper.loa0.mle = ci.upper['x'],
+                                  Bxy.ci.lower.loa0.mle = ci.lower['x'],
+                                  Bzy.ci.upper.loa0.mle = ci.upper['z'],
+                                  Bzy.ci.lower.loa0.mle = ci.upper['z']))
+
+    loco.feasible <- glm(y.obs.0 ~ x + z, data = df[(!is.na(y.obs.0)) & (y.obs.1 == y.obs.0)], family=binomial(link='logit'))
+
+    loco.feasible.ci.Bxy <- confint(loco.feasible)['x',]
+    loco.feasible.ci.Bzy <- confint(loco.feasible)['z',]
+
+    result <- append(result, list(Bxy.est.loco.feasible=coef(loco.feasible)['x'],
+                                  Bzy.est.loco.feasible=coef(loco.feasible)['z'],
+                                  Bxy.ci.upper.loco.feasible = loco.feasible.ci.Bxy[2],
+                                  Bxy.ci.lower.loco.feasible = loco.feasible.ci.Bxy[1],
+                                  Bzy.ci.upper.loco.feasible = loco.feasible.ci.Bzy[2],
+                                  Bzy.ci.lower.loco.feasible = loco.feasible.ci.Bzy[1]))
+
+
+    df.loco.mle <- copy(df)
+    df.loco.mle[,y.obs:=NA]
+    df.loco.mle[(y.obs.0)==(y.obs.1),y.obs:=y.obs.0]
+    df.loco.mle[,y.true:=y]
+    df.loco.mle[,y:=y.obs]
+    print(df.loco.mle[!is.na(y.obs.1),mean(y.true==y,na.rm=TRUE)])
+    loco.mle <- measerr_mle_dv(df.loco.mle, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
+    fisher.info <- solve(loco.mle$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)
+
+}
diff --git a/simulations/irr_simulation_base.R b/simulations/irr_simulation_base.R
new file mode 100644
index 0000000..ebb215b
--- /dev/null
+++ b/simulations/irr_simulation_base.R
@@ -0,0 +1,106 @@
+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)
+
+}
diff --git a/simulations/measerr_methods.R b/simulations/measerr_methods.R
index 6bf8c3f..00f1746 100644
--- a/simulations/measerr_methods.R
+++ b/simulations/measerr_methods.R
@@ -102,17 +102,211 @@ measerr_mle_dv <- function(df, outcome_formula, outcome_family=binomial(link='lo
     return(fit)
 }
 
+## Experimental, and not necessary if errors are independent.
+measerr_irr_mle <- function(df, outcome_formula, outcome_family=gaussian(), rater_formula, proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit')){
+
+    ### in this scenario, the ground truth also has measurement error, but we have repeated measures for it. 
+
+    ## probability of y given observed data.
+    df.obs <- df[!is.na(x.obs.1)]
+    proxy.variable <- all.vars(proxy_formula)[1]
+    df.x.obs.1 <- copy(df.obs)[,x:=1]
+    df.x.obs.0 <- copy(df.obs)[,x:=0]
+    y.obs <- df.obs[,y]
+
+    nll <- function(params){
+        outcome.model.matrix.x.obs.0 <- model.matrix(outcome_formula, df.x.obs.0)
+        outcome.model.matrix.x.obs.1 <- model.matrix(outcome_formula, df.x.obs.1)
+
+        param.idx <- 1
+        n.outcome.model.covars <- dim(outcome.model.matrix.x.obs.0)[2]
+        outcome.params <- params[param.idx:n.outcome.model.covars]
+        param.idx <- param.idx + n.outcome.model.covars
+
+        sigma.y <- params[param.idx]
+        param.idx <- param.idx + 1
+
+        ll.y.x.obs.0 <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix.x.obs.0),sd=sigma.y, log=TRUE)
+        ll.y.x.obs.1 <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix.x.obs.1),sd=sigma.y, log=TRUE)
+
+        ## assume that the two coders are statistically independent conditional on x
+        ll.x.obs.0.x0 <- vector(mode='numeric', length=nrow(df.obs))
+        ll.x.obs.1.x0 <- vector(mode='numeric', length=nrow(df.obs))
+        ll.x.obs.0.x1 <- vector(mode='numeric', length=nrow(df.obs))
+        ll.x.obs.1.x1 <- vector(mode='numeric', length=nrow(df.obs))
+
+        rater.model.matrix.x.obs.0 <- model.matrix(rater_formula, df.x.obs.0)
+        rater.model.matrix.x.obs.1 <- model.matrix(rater_formula, df.x.obs.1)
+
+        n.rater.model.covars <- dim(rater.model.matrix.x.obs.0)[2]
+        rater.0.params <- params[param.idx:(n.rater.model.covars + param.idx - 1)]
+        param.idx <- param.idx + n.rater.model.covars
+
+        rater.1.params <- params[param.idx:(n.rater.model.covars + param.idx - 1)]
+        param.idx <- param.idx + n.rater.model.covars
+        
+        # probability of rater 0 if x is 0 or 1
+        ll.x.obs.0.x0[df.obs$x.obs.0==1] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.0==1,]), log=TRUE)
+        ll.x.obs.0.x0[df.obs$x.obs.0==0] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.0==0,]), log=TRUE, lower.tail=FALSE)
+        ll.x.obs.0.x1[df.obs$x.obs.0==1] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.0==1,]), log=TRUE)
+        ll.x.obs.0.x1[df.obs$x.obs.0==0] <- plogis(rater.0.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.0==0,]), log=TRUE, lower.tail=FALSE)
+
+        # probability of rater 1 if x is 0 or 1
+        ll.x.obs.1.x0[df.obs$x.obs.1==1] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.1==1,]), log=TRUE)
+        ll.x.obs.1.x0[df.obs$x.obs.1==0] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.0[df.obs$x.obs.1==0,]), log=TRUE, lower.tail=FALSE)
+        ll.x.obs.1.x1[df.obs$x.obs.1==1] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.1==1,]), log=TRUE)
+        ll.x.obs.1.x1[df.obs$x.obs.1==0] <- plogis(rater.1.params %*% t(rater.model.matrix.x.obs.1[df.obs$x.obs.1==0,]), log=TRUE, lower.tail=FALSE)
+
+        proxy.model.matrix.x0 <- model.matrix(proxy_formula, df.x.obs.0)
+        proxy.model.matrix.x1 <- model.matrix(proxy_formula, df.x.obs.1)
+
+        n.proxy.model.covars <- dim(proxy.model.matrix.x0)[2]
+        proxy.params <- params[param.idx:(n.proxy.model.covars+param.idx-1)]
+        param.idx <- param.idx + n.proxy.model.covars
+
+        proxy.obs <- with(df.obs, eval(parse(text=proxy.variable)))
+
+        if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
+            ll.w.obs.x0 <- vector(mode='numeric',length=dim(proxy.model.matrix.x0)[1])
+            ll.w.obs.x1 <- vector(mode='numeric',length=dim(proxy.model.matrix.x1)[1])
+
+                                        # proxy_formula likelihood using logistic regression
+            ll.w.obs.x0[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.obs==1,]),log=TRUE)
+            ll.w.obs.x0[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
+
+            ll.w.obs.x1[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.obs==1,]),log=TRUE)
+            ll.w.obs.x1[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
+        }
+
+        ## assume that the probability of x is a logistic regression depending on z
+        truth.model.matrix.obs <- model.matrix(truth_formula, df.obs)
+        n.truth.params <- dim(truth.model.matrix.obs)[2]
+        truth.params <- params[param.idx:(n.truth.params + param.idx - 1)]
+
+        ll.obs.x0 <- plogis(truth.params %*% t(truth.model.matrix.obs), log=TRUE)
+        ll.obs.x1 <- plogis(truth.params %*% t(truth.model.matrix.obs), log=TRUE, lower.tail=FALSE)
+
+        ll.obs <- colLogSumExps(rbind(ll.y.x.obs.0 + ll.x.obs.0.x0 + ll.x.obs.1.x0 + ll.obs.x0 + ll.w.obs.x0,
+                                      ll.y.x.obs.1 + ll.x.obs.0.x1 + ll.x.obs.1.x1 + ll.obs.x1 + ll.w.obs.x1))
+
+        ### NOW FOR THE FUN PART. Likelihood of the unobserved data.
+        ### we have to integrate out x.obs.0, x.obs.1, and x.
+
+
+        ## THE OUTCOME
+        df.unobs <- df[is.na(x.obs)]
+        df.x.unobs.0 <- copy(df.unobs)[,x:=0]
+        df.x.unobs.1 <- copy(df.unobs)[,x:=1]
+        y.unobs <- df.unobs$y
+
+        outcome.model.matrix.x.unobs.0 <- model.matrix(outcome_formula, df.x.unobs.0)
+        outcome.model.matrix.x.unobs.1 <- model.matrix(outcome_formula, df.x.unobs.1)
+
+        ll.y.unobs.x0 <- dnorm(y.unobs, outcome.params %*% t(outcome.model.matrix.x.unobs.0), sd=sigma.y, log=TRUE)
+        ll.y.unobs.x1 <- dnorm(y.unobs, outcome.params %*% t(outcome.model.matrix.x.unobs.1), sd=sigma.y, log=TRUE)
+
+        
+        ## THE UNLABELED DATA
+
+        
+        ## assume that the two coders are statistically independent conditional on x
+        ll.x.unobs.0.x0 <- vector(mode='numeric', length=nrow(df.unobs))
+        ll.x.unobs.1.x0 <- vector(mode='numeric', length=nrow(df.unobs))
+        ll.x.unobs.0.x1 <- vector(mode='numeric', length=nrow(df.unobs))
+        ll.x.unobs.1.x1 <- vector(mode='numeric', length=nrow(df.unobs))
+        
+        df.x.unobs.0[,x.obs := 1]
+        df.x.unobs.1[,x.obs := 1]
+
+        rater.model.matrix.x.unobs.0 <- model.matrix(rater_formula, df.x.unobs.0)
+        rater.model.matrix.x.unobs.1 <- model.matrix(rater_formula, df.x.unobs.1)
+
+         
+        ## # probability of rater 0 if x is 0 or 1
+        ## ll.x.unobs.0.x0 <- colLogSumExps(rbind(plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE),
+        ##                                      plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE, lower.tail=TRUE)))
+
+        ## ll.x.unobs.0.x1 <- colLogSumExps(rbind(plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE),
+        ##                                        plogis(rater.0.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE, lower.tail=TRUE)))
+
+        ## # probability of rater 1 if x is 0 or 1
+        ## ll.x.unobs.1.x0 <- colLogSumExps(rbind(plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE),
+        ##                                      plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.0), log=TRUE, lower.tail=TRUE)))
+
+        ## ll.x.unobs.1.x1 <- colLogSumExps(rbind(plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE),
+        ##                                      plogis(rater.1.params %*% t(rater.model.matrix.x.unobs.1), log=TRUE, lower.tail=TRUE)))
+
+
+        proxy.unobs <- with(df.unobs, eval(parse(text=proxy.variable)))
+        proxy.model.matrix.x0.unobs <- model.matrix(proxy_formula, df.x.unobs.0)
+        proxy.model.matrix.x1.unobs <- model.matrix(proxy_formula, df.x.unobs.1)
+
+        if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
+            ll.w.unobs.x0 <- vector(mode='numeric',length=dim(proxy.model.matrix.x0)[1])
+            ll.w.unobs.x1 <- vector(mode='numeric',length=dim(proxy.model.matrix.x1)[1])
+
+
+                                        # proxy_formula likelihood using logistic regression
+            ll.w.unobs.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0.unobs[proxy.unobs==1,]),log=TRUE)
+            ll.w.unobs.x0[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x0.unobs[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
+
+            ll.w.unobs.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1.unobs[proxy.unobs==1,]),log=TRUE)
+            ll.w.unobs.x1[proxy.unobs==0] <- plogis(proxy.params %*% t(proxy.model.matrix.x1.unobs[proxy.unobs==0,]),log=TRUE, lower.tail=FALSE)
+        }
+
+        truth.model.matrix.unobs <- model.matrix(truth_formula, df.unobs)
+
+        ll.unobs.x0 <- plogis(truth.params %*% t(truth.model.matrix.unobs), log=TRUE)
+        ll.unobs.x1 <- plogis(truth.params %*% t(truth.model.matrix.unobs), log=TRUE, lower.tail=FALSE)
+
+        ll.unobs <- colLogSumExps(rbind(ll.unobs.x0 + ll.w.unobs.x0 + ll.y.unobs.x0,
+                                        ll.unobs.x1 + ll.w.unobs.x1 + ll.y.unobs.x1))
+
+        return(-1 *( sum(ll.obs) + sum(ll.unobs)))
+    }
+
+    outcome.params <- colnames(model.matrix(outcome_formula,df))
+    lower <- rep(-Inf, length(outcome.params))
+
+    if(outcome_family$family=='gaussian'){
+        params <- c(outcome.params, 'sigma_y')
+        lower <- c(lower, 0.00001)
+    } else {
+        params <- outcome.params
+    }
+    
+    rater.0.params <- colnames(model.matrix(rater_formula,df))
+    params <- c(params, paste0('rater_0',rater.0.params))
+    lower <- c(lower, rep(-Inf, length(rater.0.params)))
+
+    rater.1.params <- colnames(model.matrix(rater_formula,df))
+    params <- c(params, paste0('rater_1',rater.1.params))
+    lower <- c(lower, rep(-Inf, length(rater.1.params)))
+
+    proxy.params <- colnames(model.matrix(proxy_formula, df))
+    params <- c(params, paste0('proxy_',proxy.params))
+    lower <- c(lower, rep(-Inf, length(proxy.params)))
+
+    truth.params <- colnames(model.matrix(truth_formula, df))
+    params <- c(params, paste0('truth_', truth.params))
+    lower <- c(lower, rep(-Inf, length(truth.params)))
+    start <- rep(0.1,length(params))
+    names(start) <- params
+    
+    fit <- optim(start, fn = nll, lower=lower, method='L-BFGS-B', hessian=TRUE, control=list(maxit=1e6))
+    return(fit)
+}
+
+
 measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_formula, proxy_family=binomial(link='logit'), truth_formula, truth_family=binomial(link='logit')){
 
     measrr_mle_nll <- function(params){
         df.obs <- model.frame(outcome_formula, df)
-        
         proxy.variable <- all.vars(proxy_formula)[1]
         proxy.model.matrix <- model.matrix(proxy_formula, df)
-
         response.var <- all.vars(outcome_formula)[1]
         y.obs <- with(df.obs,eval(parse(text=response.var)))
-        
+
         outcome.model.matrix <- model.matrix(outcome_formula, df)
 
         param.idx <- 1
@@ -125,7 +319,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
             sigma.y <- params[param.idx]
             param.idx <- param.idx + 1
 
-            #  outcome_formula likelihood using linear regression
+                                        #  outcome_formula likelihood using linear regression
             ll.y.obs <- dnorm(y.obs, outcome.params %*% t(outcome.model.matrix),sd=sigma.y, log=TRUE)
         }
         
@@ -138,7 +332,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
         if( (proxy_family$family=="binomial") & (proxy_family$link=='logit')){
             ll.w.obs <- vector(mode='numeric',length=dim(proxy.model.matrix)[1])
 
-            # proxy_formula likelihood using logistic regression
+                                        # proxy_formula likelihood using logistic regression
             ll.w.obs[proxy.obs==1] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==1,]),log=TRUE)
             ll.w.obs[proxy.obs==0] <- plogis(proxy.params %*% t(proxy.model.matrix[proxy.obs==0,]),log=TRUE, lower.tail=FALSE)
         }
@@ -154,12 +348,12 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
         if( (truth_family$family=="binomial") & (truth_family$link=='logit')){
             ll.x.obs <- vector(mode='numeric',length=dim(truth.model.matrix)[1])
 
-            # truth_formula likelihood using logistic regression
+                                        # truth_formula likelihood using logistic regression
             ll.x.obs[truth.obs==1] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==1,]),log=TRUE)
             ll.x.obs[truth.obs==0] <- plogis(truth.params %*% t(truth.model.matrix[truth.obs==0,]),log=TRUE, lower.tail=FALSE)
         }
         
-        # add the three likelihoods
+                                        # add the three likelihoods
         ll.obs <- sum(ll.y.obs + ll.w.obs + ll.x.obs)
 
         ## likelihood for the predicted data
@@ -177,9 +371,9 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
             outcome.model.matrix.x1 <- model.matrix(outcome_formula, df.unobs.x1)
             if(outcome_family$family=="gaussian"){
 
-                # likelihood of outcome
-            ll.y.x0 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x0), sd=sigma.y, log=TRUE)
-            ll.y.x1 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x1), sd=sigma.y, log=TRUE)
+                                        # likelihood of outcome
+                ll.y.x0 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x0), sd=sigma.y, log=TRUE)
+                ll.y.x1 <- dnorm(outcome.unobs, outcome.params %*% t(outcome.model.matrix.x1), sd=sigma.y, log=TRUE)
             }
 
             if( (proxy_family$family=='binomial') & (proxy_family$link=='logit')){
@@ -190,7 +384,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
                 ll.w.x0 <- vector(mode='numeric', length=dim(df.unobs)[1])
                 ll.w.x1 <- vector(mode='numeric', length=dim(df.unobs)[1])
 
-                # likelihood of proxy
+                                        # likelihood of proxy
                 ll.w.x0[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x0[proxy.unobs==1,]), log=TRUE)
                 ll.w.x1[proxy.unobs==1] <- plogis(proxy.params %*% t(proxy.model.matrix.x1[proxy.unobs==1,]), log=TRUE)
 
@@ -200,7 +394,7 @@ measerr_mle <- function(df, outcome_formula, outcome_family=gaussian(), proxy_fo
 
             if(truth_family$link=='logit'){
                 truth.model.matrix <- model.matrix(truth_formula, df.unobs.x0)
-                # likelihood of truth
+                                        # likelihood of truth
                 ll.x.x1 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE)
                 ll.x.x0 <- plogis(truth.params %*% t(truth.model.matrix), log=TRUE, lower.tail=FALSE)
             }
diff --git a/simulations/plot_dv_example.R b/simulations/plot_dv_example.R
index b4d9d93..4052c38 100644
--- a/simulations/plot_dv_example.R
+++ b/simulations/plot_dv_example.R
@@ -10,8 +10,6 @@ parser <- add_argument(parser, "--infile", default="", help="name of the file to
 parser <- add_argument(parser, "--name", default="", help="The name to safe the data to in the remember file.")
 args <- parse_args(parser)
 
-
-
 summarize.estimator <- function(df, suffix='naive', coefname='x'){
 
     part <- df[,c('N',
diff --git a/simulations/plot_irr_dv_example.R b/simulations/plot_irr_dv_example.R
new file mode 100644
index 0000000..f5e2c41
--- /dev/null
+++ b/simulations/plot_irr_dv_example.R
@@ -0,0 +1,63 @@
+source("RemembR/R/RemembeR.R")
+library(arrow)
+library(data.table)
+library(ggplot2)
+library(filelock)
+library(argparser)
+
+parser <- arg_parser("Simulate data and fit corrected models.")
+parser <- add_argument(parser, "--infile", default="", help="name of the file to read.")
+parser <- add_argument(parser, "--name", default="", help="The name to safe the data to in the remember file.")
+args <- parse_args(parser)
+source("summarize_estimator.R")
+
+build_plot_dataset <- function(df){
+    
+    x.true <-  summarize.estimator(df, 'true','x')
+
+    z.true <-  summarize.estimator(df, 'true','z')
+
+    x.loa0.feasible <- summarize.estimator(df, 'loa0.feasible','x')
+    
+    z.loa0.feasible <- summarize.estimator(df,'loa0.feasible','z')
+
+    x.loa0.mle <- summarize.estimator(df, 'loa0.mle', 'x')
+
+    z.loa0.mle <- summarize.estimator(df, 'loa0.mle', 'z')
+
+    x.loco.feasible <- summarize.estimator(df, 'loco.feasible', 'x')
+
+    z.loco.feasible <- summarize.estimator(df, 'loco.feasible', 'z')
+
+    x.loco.mle <- summarize.estimator(df, 'loco.mle', 'x')
+
+    z.loco.mle <- summarize.estimator(df, 'loco.mle', 'z')
+
+
+    accuracy <- df[,mean(accuracy)]
+    plot.df <- rbindlist(list(x.true,z.true,x.loa0.feasible,z.loa0.feasible,x.loa0.mle,z.loa0.mle,x.loco.feasible, z.loco.feasible, z.loco.mle, x.loco.mle),use.names=T)
+    plot.df[,accuracy := accuracy]
+    plot.df <- plot.df[,":="(sd.est=sqrt(var.est)/N.sims)]
+    return(plot.df)
+}
+
+
+plot.df <- read_feather(args$infile)
+print(unique(plot.df$N))
+
+# df <- df[apply(df,1,function(x) !any(is.na(x)))]
+
+if(!('Bzx' %in% names(plot.df)))
+    plot.df[,Bzx:=NA]
+
+if(!('accuracy_imbalance_difference' %in% names(plot.df)))
+    plot.df[,accuracy_imbalance_difference:=NA]
+
+unique(plot.df[,'accuracy_imbalance_difference'])
+
+#plot.df <- build_plot_dataset(df[accuracy_imbalance_difference==0.1][N==700])
+plot.df <- build_plot_dataset(plot.df)
+
+change.remember.file("remember_irr.RDS",clear=TRUE)
+
+remember(plot.df,args$name)
diff --git a/simulations/plot_irr_example.R b/simulations/plot_irr_example.R
new file mode 100644
index 0000000..bf5e661
--- /dev/null
+++ b/simulations/plot_irr_example.R
@@ -0,0 +1,129 @@
+source("RemembR/R/RemembeR.R")
+library(arrow)
+library(data.table)
+library(ggplot2)
+library(filelock)
+library(argparser)
+
+parser <- arg_parser("Simulate data and fit corrected models.")
+parser <- add_argument(parser, "--infile", default="", help="name of the file to read.")
+parser <- add_argument(parser, "--name", default="", help="The name to safe the data to in the remember file.")
+args <- parse_args(parser)
+source("summarize_estimator.R")
+
+build_plot_dataset <- function(df){
+    
+    x.true <-  summarize.estimator(df, 'true','x')
+
+    z.true <-  summarize.estimator(df, 'true','z')
+
+    x.loa0.feasible <- summarize.estimator(df, 'loa0.feasible','x')
+    
+    z.loa0.feasible <- summarize.estimator(df,'loa0.feasible','z')
+
+    x.loa0.mle <- summarize.estimator(df, 'loa0.mle', 'x')
+
+    z.loa0.mle <- summarize.estimator(df, 'loa0.mle', 'z')
+
+    x.loco.feasible <- summarize.estimator(df, 'loco.feasible', 'x')
+
+    z.loco.feasible <- summarize.estimator(df, 'loco.feasible', 'z')
+
+    x.loco.mle <- summarize.estimator(df, 'loco.mle', 'x')
+
+    z.loco.mle <- summarize.estimator(df, 'loco.mle', 'z')
+
+    ## x.mle <- summarize.estimator(df, 'mle', 'x')
+
+    ## z.mle <- summarize.estimator(df, 'mle', 'z')
+
+    accuracy <- df[,mean(accuracy)]
+    plot.df <- rbindlist(list(x.true,z.true,x.loa0.feasible,z.loa0.feasible,x.loa0.mle,z.loa0.mle,x.loco.feasible, z.loco.feasible, x.loco.mle, z.loco.mle),use.names=T)
+    plot.df[,accuracy := accuracy]
+    plot.df <- plot.df[,":="(sd.est=sqrt(var.est)/N.sims)]
+    return(plot.df)
+}
+
+
+plot.df <- read_feather(args$infile)
+print(unique(plot.df$N))
+
+# df <- df[apply(df,1,function(x) !any(is.na(x)))]
+
+if(!('Bzx' %in% names(plot.df)))
+    plot.df[,Bzx:=NA]
+
+if(!('accuracy_imbalance_difference' %in% names(plot.df)))
+    plot.df[,accuracy_imbalance_difference:=NA]
+
+unique(plot.df[,'accuracy_imbalance_difference'])
+
+#plot.df <- build_plot_dataset(df[accuracy_imbalance_difference==0.1][N==700])
+plot.df <- build_plot_dataset(plot.df)
+change.remember.file("remember_irr.RDS",clear=TRUE)
+remember(plot.df,args$name)
+
+#ggplot(df,aes(x=Bxy.est.mle)) + geom_histogram() + facet_grid(accuracy_imbalance_difference ~ Bzy)
+
+## ## ## df[gmm.ER_pval<0.05]
+
+## plot.df.test <- plot.df[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Bespoke MLE", "Feasible"),ordered=T),
+##                                    N=factor(N),
+##                                    m=factor(m))]
+
+## plot.df.test <- plot.df.test[(variable=='x') & (method!="Multiple imputation (Classifier features unobserved)")]
+## p <- ggplot(plot.df.test, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
+## p <- p + geom_hline(data=plot.df.test, mapping=aes(yintercept=0.1),linetype=2)
+
+## p <- p + geom_pointrange() + facet_grid(N~m,as.table=F,scales='free') + scale_x_discrete(labels=label_wrap_gen(4))
+## print(p)
+
+## plot.df.test <- plot.df[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Bespoke MLE", "Feasible"),ordered=T),
+##                                    N=factor(N),
+##                                    m=factor(m))]
+
+## plot.df.test <- plot.df.test[(variable=='z') & (method!="Multiple imputation (Classifier features unobserved)")]
+## p <- ggplot(plot.df.test, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
+## p <- p + geom_hline(data=plot.df.test, mapping=aes(yintercept=-0.1),linetype=2)
+
+## p <- p + geom_pointrange() + facet_grid(m~N,as.table=F,scales='free') + scale_x_discrete(labels=label_wrap_gen(4))
+## print(p)
+
+
+## x.mle <- df[,.(N,m,Bxy.est.mle,Bxy.ci.lower.mle, Bxy.ci.upper.mle, y_explained_variance, Bzx, Bzy, accuracy_imbalance_difference)]
+## x.mle.plot <- x.mle[,.(mean.est = mean(Bxy.est.mle),
+##                        var.est = var(Bxy.est.mle),
+##                        N.sims = .N,
+##                        variable='z',
+##                        method='Bespoke MLE'
+##                        ),
+##                     by=c("N","m",'y_explained_variance', 'Bzx', 'Bzy','accuracy_imbalance_difference')]
+
+## z.mle <- df[,.(N,m,Bzy.est.mle,Bzy.ci.lower.mle, Bzy.ci.upper.mle, y_explained_variance, Bzx, Bzy, accuracy_imbalance_difference)]
+
+## z.mle.plot <- z.mle[,.(mean.est = mean(Bzy.est.mle),
+##                        var.est = var(Bzy.est.mle),
+##                        N.sims = .N,
+##                        variable='z',
+##                        method='Bespoke MLE'
+##                        ),
+##                     by=c("N","m",'y_explained_variance','Bzx')]
+
+## plot.df <- z.mle.plot
+## plot.df.test <- plot.df[,':='(method=factor(method,levels=c("Naive","Multiple imputation", "Multiple imputation (Classifier features unobserved)","Regression Calibration","2SLS+gmm","Bespoke MLE", "Feasible"),ordered=T),
+##                                    N=factor(N),
+##                                    m=factor(m))]
+
+## plot.df.test <- plot.df.test[(variable=='z') & (m != 1000) & (m!=500) & (method!="Multiple imputation (Classifier features unobserved)")]
+## p <- ggplot(plot.df.test, aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method))
+## p <- p + geom_hline(aes(yintercept=0.2),linetype=2)
+
+## p <- p + geom_pointrange() + facet_grid(m~Bzx, Bzy,as.table=F) + scale_x_discrete(labels=label_wrap_gen(4))
+## print(p)
+
+
+## ## ggplot(plot.df[variable=='x'], aes(y=mean.est, ymax=mean.est + var.est/2, ymin=mean.est-var.est/2, x=method)) + geom_pointrange() + facet_grid(-m~N) + scale_x_discrete(labels=label_wrap_gen(10))
+
+## ## ggplot(plot.df,aes(y=N,x=m,color=p.sign.correct)) + geom_point() + facet_grid(variable ~ method) + scale_color_viridis_c(option='D') + theme_minimal() + xlab("Number of gold standard labels") + ylab("Total sample size") 
+
+## ## ggplot(plot.df,aes(y=N,x=m,color=abs(mean.bias))) + geom_point() + facet_grid(variable ~ method) + scale_color_viridis_c(option='D') + theme_minimal() + xlab("Number of gold standard labels") + ylab("Total sample size") 
diff --git a/simulations/summarize_estimator.R b/simulations/summarize_estimator.R
new file mode 100644
index 0000000..8199c06
--- /dev/null
+++ b/simulations/summarize_estimator.R
@@ -0,0 +1,42 @@
+
+summarize.estimator <- function(df, suffix='naive', coefname='x'){
+
+    part <- df[,c('N',
+                  'm',
+                  'Bxy',
+                  paste0('B',coefname,'y.est.',suffix),
+                  paste0('B',coefname,'y.ci.lower.',suffix),
+                  paste0('B',coefname,'y.ci.upper.',suffix),
+                  'y_explained_variance',
+                  'Bzx',
+                  'Bzy',
+                  'accuracy_imbalance_difference'
+                  ),
+               with=FALSE]
+    
+    true.in.ci <- as.integer((part$Bxy >= part[[paste0('B',coefname,'y.ci.lower.',suffix)]]) & (part$Bxy <= part[[paste0('B',coefname,'y.ci.upper.',suffix)]]))
+    zero.in.ci <- as.integer(0 >= part[[paste0('B',coefname,'y.ci.lower.',suffix)]]) & (0 <= part[[paste0('B',coefname,'y.ci.upper.',suffix)]])
+    bias <- part$Bxy - part[[paste0('B',coefname,'y.est.',suffix)]]
+    sign.correct <- as.integer(sign(part$Bxy) == sign(part[[paste0('B',coefname,'y.est.',suffix)]]))
+
+    part <- part[,':='(true.in.ci = true.in.ci,
+                       zero.in.ci = zero.in.ci,
+                       bias=bias,
+                       sign.correct =sign.correct)]
+
+    part.plot <- part[, .(p.true.in.ci = mean(true.in.ci),
+                          mean.bias = mean(bias),
+                          mean.est = mean(.SD[[paste0('B',coefname,'y.est.',suffix)]]),
+                          var.est = var(.SD[[paste0('B',coefname,'y.est.',suffix)]]),
+                          est.upper.95 = quantile(.SD[[paste0('B',coefname,'y.est.',suffix)]],0.95,na.rm=T),
+                          est.lower.95 = quantile(.SD[[paste0('B',coefname,'y.est.',suffix)]],0.05,na.rm=T),
+                          N.sims = .N,
+                          p.sign.correct = mean(as.integer(sign.correct & (! zero.in.ci))),
+                          variable=coefname,
+                          method=suffix
+                          ),
+                      by=c("N","m",'y_explained_variance','Bzx', 'Bzy', 'accuracy_imbalance_difference')
+                      ]
+    
+    return(part.plot)
+}