1 ### EXAMPLE 2_b: demonstrates how measurement error can lead to a type sign error in a covariate
2 ### This is the same as example 2, only instead of x->k we have k->x.
3 ### Even when you have a good predictor, if it's biased against a covariate you can get the wrong sign.
4 ### Even when you include the proxy variable in the regression.
5 ### But with some ground truth and multiple imputation, you can fix it.
15 library(predictionError)
16 options(amelia.parallel="no",
19 source("simulation_base_mecor.R")
22 ### we want to estimate x -> y; x is MAR
23 ### we have x -> k; k -> w; x -> w is used to predict x via the model w.
24 ### A realistic scenario is that we have an NLP model predicting something like "racial harassment" in social media comments
25 ### The labels x are binary, but the model provides a continuous predictor
28 #### how much power do we get from the model in the first place? (sweeping N and m)
30 logistic <- function(x) {1/(1+exp(-1*x))}
32 simulate_latent_cocause <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
35 ## the true value of x
37 g <- rbinom(N, 1, 0.5)
38 xprime <- Bgx * g + rnorm(N,0,1)
40 k <- Bkx*xprime + rnorm(N,0,3)
42 x <- as.integer(logistic(scale(xprime)) > 0.5)
44 y <- Bxy * x + Bgy * g + rnorm(N, 0, 1) + B0
45 df <- data.table(x=x,k=k,y=y,g=g)
48 df <- df[sample(nrow(df), m), x.obs := x]
50 df <- df[, x.obs := x]
53 w.model <- glm(x ~ k,df, family=binomial(link='logit'))
54 w <- predict(w.model,data.frame(k=k)) + rnorm(N,0,1)
57 df[,':='(w=w, w_pred = as.integer(w>0.5))]
61 schennach <- function(df){
63 fwx <- glm(x.obs~w, df, family=binomial(link='logit'))
64 df[,xstar_pred := predict(fwx, df)]
65 gxt <- lm(y ~ xstar_pred+g, df)
69 parser <- arg_parser("Simulate data and fit corrected models")
70 parser <- add_argument(parser, "--N", default=100, help="number of observations of w")
71 parser <- add_argument(parser, "--m", default=20, help="m the number of ground truth observations")
72 parser <- add_argument(parser, "--seed", default=4321, help='seed for the rng')
73 parser <- add_argument(parser, "--outfile", help='output file', default='example_2_B.feather')
74 args <- parse_args(parser)
89 outline <- run_simulation(simulate_latent_cocause(args$N, args$m, B0, Bxy, Bgy, Bkx, Bgx, args$seed)
90 ,list('N'=args$N,'m'=args$m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=args$seed))
92 outfile_lock <- lock(paste0(args$outfile, '_lock'))
93 if(file.exists(args$outfile)){
94 logdata <- read_feather(args$outfile)
95 logdata <- rbind(logdata,as.data.table(outline))
97 logdata <- as.data.table(outline)
101 write_feather(logdata, args$outfile)
104 ## Ns <- c(1e6, 5e4, 1000)
105 ## ms <- c(100, 250, 500, 1000)
108 ## rowssets <- list()
109 ## library(doParallel)
110 ## options(mc.cores = parallel::detectCores())
111 ## cl <- makeCluster(20)
112 ## registerDoParallel(cl)
114 ## ## library(future)
116 ## ## plan(multiprocess,workers=40,gc=TRUE)
122 ## new.rows <- foreach(iter=seeds, .combine=rbind, .packages = c('mecor','Amelia','Zelig','predictionError','data.table'),
123 ## .export = c("run_simulation","simulate_latent_cocause","logistic","N","m","B0","Bxy","Bgy","Bkx","Bgx")) %dopar%
125 ## {run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, iter)
126 ## ,list('N'=N,'m'=m,'B0'=B0,'Bxy'=Bxy,'Bgy'=Bgy, 'Bkx'=Bkx, 'Bgx'=Bgx, 'seed'=iter))}
127 ## rowsets <- append(rowssets, list(data.table(new.rows)))
131 ## ## rows <- append(rows, list(future({run_simulation(simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)
133 ## ,list(N=N,m=m,B0=B0,Bxy=Bxy,Bgy=Bgy, Bkx=Bkx, Bgx=Bgx, seed=seed))w},
134 ## packages=c('mecor','Amelia','Zelig','predictionError'),
138 ## df <- rbindlist(rowsets)
140 ## write_feather(df,"example_2B_simulation.feather")
142 ## run_simulation <- function(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed){
144 ## df <- simulate_latent_cocause(N, m, B0, Bxy, Bgy, Bkx, Bgx, seed)
146 ## result <- append(result, list(N=N,
154 ## (accuracy <- df[,.(mean(w_pred==x))])
155 ## result <- append(result, list(accuracy=accuracy))
157 ## (model.true <- lm(y ~ x + g, data=df))
158 ## true.ci.Bxy <- confint(model.true)['x',]
159 ## true.ci.Bgy <- confint(model.true)['g',]
161 ## result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
162 ## Bgy.est.true=coef(model.true)['g'],
163 ## Bxy.ci.upper.true = true.ci.Bxy[2],
164 ## Bxy.ci.lower.true = true.ci.Bxy[1],
165 ## Bgy.ci.upper.true = true.ci.Bgy[2],
166 ## Bgy.ci.lower.true = true.ci.Bgy[1]))
168 ## (model.feasible <- lm(y~x.obs+g,data=df))
170 ## feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
171 ## result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
172 ## Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
173 ## Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
175 ## feasible.ci.Bgy <- confint(model.feasible)['g',]
176 ## result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
177 ## Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
178 ## Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
180 ## (model.naive <- lm(y~w+g, data=df))
182 ## naive.ci.Bxy <- confint(model.naive)['w',]
183 ## naive.ci.Bgy <- confint(model.naive)['g',]
185 ## result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
186 ## Bgy.est.naive=coef(model.naive)['g'],
187 ## Bxy.ci.upper.naive = naive.ci.Bxy[2],
188 ## Bxy.ci.lower.naive = naive.ci.Bxy[1],
189 ## Bgy.ci.upper.naive = naive.ci.Bgy[2],
190 ## Bgy.ci.lower.naive = naive.ci.Bgy[1]))
193 ## ## multiple imputation when k is observed
194 ## ## amelia does great at this one.
195 ## amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=c("x.obs","g"),lgstc=c('w'))
196 ## mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
197 ## (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
199 ## est.x.mi <- coefse['x.obs','Estimate']
200 ## est.x.se <- coefse['x.obs','Std.Error']
201 ## result <- append(result,
202 ## list(Bxy.est.amelia.full = est.x.mi,
203 ## Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
204 ## Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
207 ## est.g.mi <- coefse['g','Estimate']
208 ## est.g.se <- coefse['g','Std.Error']
210 ## result <- append(result,
211 ## list(Bgy.est.amelia.full = est.g.mi,
212 ## Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
213 ## Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
216 ## ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
217 ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","k"), noms=c("x.obs",'g'),lgstc = c("w"))
218 ## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
219 ## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
221 ## est.x.mi <- coefse['x.obs','Estimate']
222 ## est.x.se <- coefse['x.obs','Std.Error']
223 ## result <- append(result,
224 ## list(Bxy.est.amelia.nok = est.x.mi,
225 ## Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
226 ## Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
229 ## est.g.mi <- coefse['g','Estimate']
230 ## est.g.se <- coefse['g','Std.Error']
232 ## result <- append(result,
233 ## list(Bgy.est.amelia.nok = est.g.mi,
234 ## Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
235 ## Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
238 ## p <- v <- train <- rep(0,N)
242 ## df <- df[order(x.obs)]
247 ## # gmm gets pretty close
248 ## (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=FALSE))
250 ## result <- append(result,
251 ## list(Bxy.est.gmm = gmm.res$beta[1,1],
252 ## Bxy.ci.upper.gmm = gmm.res$confint[1,2],
253 ## Bxy.ci.lower.gmm = gmm.res$confint[1,1]))
255 ## result <- append(result,
256 ## list(Bgy.est.gmm = gmm.res$beta[2,1],
257 ## Bgy.ci.upper.gmm = gmm.res$confint[2,2],
258 ## Bgy.ci.lower.gmm = gmm.res$confint[2,1]))
261 ## mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
262 ## (mod.calibrated.mle)
263 ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
264 ## result <- append(result, list(
265 ## Bxy.est.mecor = mecor.ci['Estimate'],
266 ## Bxy.upper.mecor = mecor.ci['UCI'],
267 ## Bxy.lower.mecor = mecor.ci['LCI'])
270 ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
272 ## result <- append(result, list(
273 ## Bxy.est.mecor = mecor.ci['Estimate'],
274 ## Bxy.upper.mecor = mecor.ci['UCI'],
275 ## Bxy.lower.mecor = mecor.ci['LCI'])