simulations/simulation_base.R

   1 library(predictionError)
   2 library(mecor)
   3 options(amelia.parallel="no",
   4         amelia.ncpus=1)
   5 library(Amelia)
   6 library(Zelig)
   7 library(bbmle)
   8 library(matrixStats) # for numerically stable logsumexps
   9
  10 source("pl_methods.R")
  11 source("measerr_methods.R") ## for my more generic function.
  12
  13 ## This uses the pseudolikelihood approach from Carroll page 349.
  14 ## assumes MAR
  15 ## assumes differential error, but that only depends on Y
  16 ## inefficient, because pseudolikelihood
  17
  18 ## This uses the pseudo-likelihood approach from Carroll page 346.
  19 my.pseudo.mle <- function(df){
  20     p1.est <- mean(df[w_pred==1]$y.obs==1,na.rm=T)
  21     p0.est <- mean(df[w_pred==0]$y.obs==0,na.rm=T)
  22
  23     nll <- function(B0, Bxy, Bzy){
  24
  25         pw <- vector(mode='numeric',length=nrow(df))
  26         dfw1 <- df[w_pred==1]
  27         dfw0 <- df[w_pred==0]
  28         pw[df$w_pred==1] <- plogis(B0 + Bxy * dfw1$x + Bzy * dfw1$z, log=T)
  29         pw[df$w_pred==0] <- plogis(B0 + Bxy * dfw0$x + Bzy * dfw0$z, lower.tail=FALSE, log=T)
  30
  31         probs <- colLogSumExps(rbind(log(1 - p0.est), log(p1.est + p0.est - 1) + pw))
  32         return(-1*sum(probs))
  33     }
  34
  35     mlefit <- mle2(minuslogl = nll, start = list(B0=0.0, Bxy=0.0, Bzy=0.0), control=list(maxit=1e6),method='L-BFGS-B')
  36     return(mlefit)
  37
  38 }
  39
  40
  41 ## This uses the likelihood approach from Carroll page 353.
  42 ## assumes that we have a good measurement error model
  43 my.mle <- function(df){
  44
  45     ## liklihood for observed responses
  46     nll <- function(B0, Bxy, Bzy, gamma0, gamma_y, gamma_z, gamma_yz){
  47         df.obs <- df[!is.na(y.obs)]
  48         yobs0 <- df.obs$y==0
  49         yobs1 <- df.obs$y==1
  50         p.y.obs <- vector(mode='numeric', length=nrow(df.obs))
  51
  52         p.y.obs[yobs1] <- plogis(B0 + Bxy * df.obs[yobs1]$x + Bzy*df.obs[yobs1]$z,log=T)
  53         p.y.obs[yobs0] <- plogis(B0 + Bxy * df.obs[yobs0]$x + Bzy*df.obs[yobs0]$z,lower.tail=FALSE,log=T)
  54
  55         wobs0 <- df.obs$w_pred==0
  56         wobs1 <- df.obs$w_pred==1
  57         p.w.obs <- vector(mode='numeric', length=nrow(df.obs))
  58
  59         p.w.obs[wobs1] <- plogis(gamma0 + gamma_y * df.obs[wobs1]$y + gamma_z*df.obs[wobs1]$z + df.obs[wobs1]$z*df.obs[wobs1]$y* gamma_yz, log=T)
  60         p.w.obs[wobs0] <- plogis(gamma0 + gamma_y * df.obs[wobs0]$y + gamma_z*df.obs[wobs0]$z + df.obs[wobs0]$z*df.obs[wobs0]$y* gamma_yz, lower.tail=FALSE, log=T)
  61
  62         p.obs <- p.w.obs + p.y.obs
  63
  64         df.unobs <- df[is.na(y.obs)]
  65
  66         p.unobs.0 <- vector(mode='numeric',length=nrow(df.unobs))
  67         p.unobs.1 <- vector(mode='numeric',length=nrow(df.unobs))
  68
  69         wunobs.0 <- df.unobs$w_pred == 0
  70         wunobs.1 <- df.unobs$w_pred == 1
  71
  72         p.unobs.0[wunobs.1] <- plogis(B0 + Bxy * df.unobs[wunobs.1]$x + Bzy*df.unobs[wunobs.1]$z, log=T) + plogis(gamma0 + gamma_y + gamma_z*df.unobs[wunobs.1]$z + df.unobs[wunobs.1]$z*gamma_yz, log=T)
  73
  74         p.unobs.0[wunobs.0] <- plogis(B0 + Bxy * df.unobs[wunobs.0]$x + Bzy*df.unobs[wunobs.0]$z, log=T) + plogis(gamma0 + gamma_y + gamma_z*df.unobs[wunobs.0]$z + df.unobs[wunobs.0]$z*gamma_yz, lower.tail=FALSE, log=T)
  75
  76         p.unobs.1[wunobs.1] <- plogis(B0 + Bxy * df.unobs[wunobs.1]$x + Bzy*df.unobs[wunobs.1]$z, log=T, lower.tail=FALSE) + plogis(gamma0 + gamma_z*df.unobs[wunobs.1]$z, log=T)
  77
  78         p.unobs.1[wunobs.0] <- plogis(B0 + Bxy * df.unobs[wunobs.0]$x + Bzy*df.unobs[wunobs.0]$z, log=T, lower.tail=FALSE) + plogis(gamma0 + gamma_z*df.unobs[wunobs.0]$z, lower.tail=FALSE, log=T)
  79
  80         p.unobs <- colLogSumExps(rbind(p.unobs.1, p.unobs.0))
  81
  82         p <- c(p.obs, p.unobs)
  83
  84         return(-1*(sum(p)))
  85     }
  86
  87     mlefit <- mle2(minuslogl = nll, start = list(B0=0, Bxy=0,Bzy=0, gamma0=0, gamma_y=0, gamma_z=0, gamma_yz=0), control=list(maxit=1e6),method='L-BFGS-B')
  88
  89     return(mlefit)
  90 }
  91
  92 run_simulation_depvar <- function(df, result, outcome_formula=y~x+z, proxy_formula=w_pred~y){
  93
  94     (accuracy <- df[,mean(w_pred==y)])
  95     result <- append(result, list(accuracy=accuracy))
  96     (error.cor.z <- cor(df$z, df$y - df$w_pred))
  97     (error.cor.x <- cor(df$x, df$y - df$w_pred))
  98     (error.cor.y <- cor(df$y, df$y - df$w_pred))
  99     result <- append(result, list(error.cor.x = error.cor.x,
 100                                   error.cor.z = error.cor.z,
 101                                   error.cor.y = error.cor.y))
 102
 103     model.null <- glm(y~1, data=df,family=binomial(link='logit'))
 104     (model.true <- glm(y ~ x + z, data=df,family=binomial(link='logit')))
 105     (lik.ratio <- exp(logLik(model.true) - logLik(model.null)))
 106
 107     true.ci.Bxy <- confint(model.true)['x',]
 108     true.ci.Bzy <- confint(model.true)['z',]
 109
 110     result <- append(result, list(cor.xz=cor(df$x,df$z)))
 111     result <- append(result, list(lik.ratio=lik.ratio))
 112
 113     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
 114                                   Bzy.est.true=coef(model.true)['z'],
 115                                   Bxy.ci.upper.true = true.ci.Bxy[2],
 116                                   Bxy.ci.lower.true = true.ci.Bxy[1],
 117                                   Bzy.ci.upper.true = true.ci.Bzy[2],
 118                                   Bzy.ci.lower.true = true.ci.Bzy[1]))
 119
 120     (model.feasible <- glm(y.obs~x+z,data=df,family=binomial(link='logit')))
 121
 122     feasible.ci.Bxy <- confint(model.feasible)['x',]
 123     result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x'],
 124                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
 125                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
 126
 127     feasible.ci.Bzy <- confint(model.feasible)['z',]
 128     result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
 129                                   Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
 130                                   Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
 131
 132     (model.naive <- glm(w_pred~x+z, data=df, family=binomial(link='logit')))
 133
 134     naive.ci.Bxy <- confint(model.naive)['x',]
 135     naive.ci.Bzy <- confint(model.naive)['z',]
 136
 137     result <- append(result, list(Bxy.est.naive=coef(model.naive)['x'],
 138                                   Bzy.est.naive=coef(model.naive)['z'],
 139                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
 140                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
 141                                   Bzy.ci.upper.naive = naive.ci.Bzy[2],
 142                                   Bzy.ci.lower.naive = naive.ci.Bzy[1]))
 143
 144
 145     (model.naive.cont <- lm(w~x+z, data=df))
 146     naivecont.ci.Bxy <- confint(model.naive.cont)['x',]
 147     naivecont.ci.Bzy <- confint(model.naive.cont)['z',]
 148
 149     ## my implementation of liklihood based correction
 150
 151     temp.df <- copy(df)
 152     temp.df[,y:=y.obs]
 153     mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
 154     fischer.info <- solve(mod.caroll.lik$hessian)
 155     coef <- mod.caroll.lik$par
 156     ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
 157     ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 158     result <- append(result,
 159                      list(Bxy.est.mle = coef['x'],
 160                           Bxy.ci.upper.mle = ci.upper['x'],
 161                           Bxy.ci.lower.mle = ci.lower['x'],
 162                           Bzy.est.mle = coef['z'],
 163                           Bzy.ci.upper.mle = ci.upper['z'],
 164                           Bzy.ci.lower.mle = ci.lower['z']))
 165
 166
 167     ## my implementatoin of liklihood based correction
 168     mod.zhang <- zhang.mle.dv(df)
 169     coef <- coef(mod.zhang)
 170     ci <- confint(mod.zhang,method='quad')
 171
 172     result <- append(result,
 173                      list(Bxy.est.zhang = coef['Bxy'],
 174                           Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
 175                           Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
 176                           Bzy.est.zhang = coef['Bzy'],
 177                           Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
 178                           Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
 179
 180
 181
 182     # amelia says use normal distribution for binary variables.
 183     amelia_result <- list(Bxy.est.amelia.full = NA,
 184                           Bxy.ci.upper.amelia.full = NA,
 185                           Bxy.ci.lower.amelia.full = NA,
 186                           Bzy.est.amelia.full = NA,
 187                           Bzy.ci.upper.amelia.full = NA,
 188                           Bzy.ci.lower.amelia.full = NA
 189                           )
 190
 191     tryCatch({
 192         amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'))
 193         mod.amelia.k <- zelig(y.obs~x+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
 194         (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
 195         est.x.mi <- coefse['x','Estimate']
 196         est.x.se <- coefse['x','Std.Error']
 197
 198         est.z.mi <- coefse['z','Estimate']
 199         est.z.se <- coefse['z','Std.Error']
 200         amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
 201                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
 202                           Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
 203                           Bzy.est.amelia.full = est.z.mi,
 204                           Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
 205                           Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
 206                           )
 207     },
 208     error = function(e){
 209     result[['error']] <- e}
 210     )
 211     result <- append(result,amelia_result)
 212
 213     return(result)
 214
 215 }
 216
 217
 218 ## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle
 219 run_simulation <-  function(df, result, outcome_formula=y~x+z, proxy_formula=NULL, truth_formula=NULL){
 220
 221     accuracy <- df[,mean(w_pred==x)]
 222     accuracy.y0 <- df[y<=0,mean(w_pred==x)]
 223     accuracy.y1 <- df[y>=0,mean(w_pred==x)]
 224     cor.y.xi <- cor(df$x - df$w_pred, df$y)
 225
 226     fnr <- df[w_pred==0,mean(w_pred!=x)]
 227     fnr.y0 <- df[(w_pred==0) & (y<=0),mean(w_pred!=x)]
 228     fnr.y1 <- df[(w_pred==0) & (y>=0),mean(w_pred!=x)]
 229
 230     fpr <- df[w_pred==1,mean(w_pred!=x)]
 231     fpr.y0 <- df[(w_pred==1) & (y<=0),mean(w_pred!=x)]
 232     fpr.y1 <- df[(w_pred==1) & (y>=0),mean(w_pred!=x)]
 233     cor.resid.w_pred <- cor(resid(lm(y~x+z,df)),df$w_pred)
 234
 235     result <- append(result, list(accuracy=accuracy,
 236                                   accuracy.y0=accuracy.y0,
 237                                   accuracy.y1=accuracy.y1,
 238                                   cor.y.xi=cor.y.xi,
 239                                   fnr=fnr,
 240                                   fnr.y0=fnr.y0,
 241                                   fnr.y1=fnr.y1,
 242                                   fpr=fpr,
 243                                   fpr.y0=fpr.y0,
 244                                   fpr.y1=fpr.y1,
 245                                   cor.resid.w_pred=cor.resid.w_pred
 246                                   ))
 247
 248     result <- append(result, list(cor.xz=cor(df$x,df$z)))
 249     (model.true <- lm(y ~ x + z, data=df))
 250     true.ci.Bxy <- confint(model.true)['x',]
 251     true.ci.Bzy <- confint(model.true)['z',]
 252
 253     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
 254                                   Bzy.est.true=coef(model.true)['z'],
 255                                   Bxy.ci.upper.true = true.ci.Bxy[2],
 256                                   Bxy.ci.lower.true = true.ci.Bxy[1],
 257                                   Bzy.ci.upper.true = true.ci.Bzy[2],
 258                                   Bzy.ci.lower.true = true.ci.Bzy[1]))
 259
 260     (model.feasible <- lm(y~x.obs+z,data=df))
 261
 262     feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
 263     result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
 264                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
 265                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
 266
 267     feasible.ci.Bzy <- confint(model.feasible)['z',]
 268     result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
 269                                   Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
 270                                   Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
 271
 272     (model.naive <- lm(y~w_pred+z, data=df))
 273
 274     naive.ci.Bxy <- confint(model.naive)['w_pred',]
 275     naive.ci.Bzy <- confint(model.naive)['z',]
 276
 277     result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'],
 278                                   Bzy.est.naive=coef(model.naive)['z'],
 279                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
 280                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
 281                                   Bzy.ci.upper.naive = naive.ci.Bzy[2],
 282                                   Bzy.ci.lower.naive = naive.ci.Bzy[1]))
 283
 284     amelia_result <- list(
 285         Bxy.est.amelia.full = NULL,
 286         Bxy.ci.upper.amelia.full = NULL,
 287         Bxy.ci.lower.amelia.full = NULL,
 288         Bzy.est.amelia.full = NULL,
 289         Bzy.ci.upper.amelia.full = NULL,
 290         Bzy.ci.lower.amelia.full = NULL
 291         )
 292
 293     tryCatch({
 294         amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
 295         mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
 296         (coefse <- combine_coef_se(mod.amelia.k))
 297
 298         est.x.mi <- coefse['x.obs','Estimate']
 299         est.x.se <- coefse['x.obs','Std.Error']
 300         est.z.mi <- coefse['z','Estimate']
 301         est.z.se <- coefse['z','Std.Error']
 302
 303         amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
 304                               Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
 305                               Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
 306                               Bzy.est.amelia.full = est.z.mi,
 307                               Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
 308                               Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
 309                               )
 310
 311     },
 312
 313     error = function(e){
 314         result[['error']] <- e}
 315     )
 316
 317
 318     result <- append(result, amelia_result)
 319
 320
 321    mle_result <- list(Bxy.est.mle = NULL,
 322                       Bxy.ci.upper.mle = NULL,
 323                       Bxy.ci.lower.mle = NULL,
 324                       Bzy.est.mle = NULL,
 325                       Bzy.ci.upper.mle = NULL,
 326                       Bzy.ci.lower.mle = NULL)
 327
 328     tryCatch({
 329         temp.df <- copy(df)
 330         temp.df <- temp.df[,x:=x.obs]
 331         mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula)
 332         fischer.info <- solve(mod.caroll.lik$hessian)
 333         coef <- mod.caroll.lik$par
 334         ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
 335         ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 336         mle_result <- list(Bxy.est.mle = coef['x'],
 337                            Bxy.ci.upper.mle = ci.upper['x'],
 338                            Bxy.ci.lower.mle = ci.lower['x'],
 339                            Bzy.est.mle = coef['z'],
 340                            Bzy.ci.upper.mle = ci.upper['z'],
 341                            Bzy.ci.lower.mle = ci.lower['z'])
 342     },
 343
 344     error=function(e) {result[['error']] <- as.character(e)
 345     })
 346
 347
 348     result <- append(result, mle_result)
 349
 350     mod.zhang.lik <- zhang.mle.iv(df)
 351     coef <- coef(mod.zhang.lik)
 352     ci <- confint(mod.zhang.lik,method='quad')
 353     result <- append(result,
 354                      list(Bxy.est.zhang = coef['Bxy'],
 355                           Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
 356                           Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
 357                           Bzy.est.zhang = coef['Bzy'],
 358                           Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
 359                           Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
 360
 361     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
 362     ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
 363     ## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
 364     ## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
 365
 366     ## est.x.mi <- coefse['x.obs','Estimate']
 367     ## est.x.se <- coefse['x.obs','Std.Error']
 368     ## result <- append(result,
 369     ##                  list(Bxy.est.amelia.nok = est.x.mi,
 370     ##                       Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
 371     ##                       Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
 372     ##                       ))
 373
 374     ## est.g.mi <- coefse['g','Estimate']
 375     ## est.g.se <- coefse['g','Std.Error']
 376
 377     ## result <- append(result,
 378     ##                  list(Bgy.est.amelia.nok = est.g.mi,
 379     ##                       Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
 380     ##                       Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
 381     ##                       ))
 382
 383     N <- nrow(df)
 384     m <- nrow(df[!is.na(x.obs)])
 385     p <- v <- train <- rep(0,N)
 386     M <- m
 387     p[(M+1):(N)] <- 1
 388     v[1:(M)] <- 1
 389     df <- df[order(x.obs)]
 390     y <- df[,y]
 391     x <- df[,x.obs]
 392     z <- df[,z]
 393     w <- df[,w_pred]
 394     # gmm gets pretty close
 395     (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))
 396
 397     result <- append(result,
 398                      list(Bxy.est.gmm = gmm.res$beta[1,1],
 399                           Bxy.ci.upper.gmm = gmm.res$confint[1,2],
 400                           Bxy.ci.lower.gmm = gmm.res$confint[1,1],
 401                           gmm.ER_pval = gmm.res$ER_pval
 402                           ))
 403
 404     result <- append(result,
 405                      list(Bzy.est.gmm = gmm.res$beta[2,1],
 406                           Bzy.ci.upper.gmm = gmm.res$confint[2,2],
 407                           Bzy.ci.lower.gmm = gmm.res$confint[2,1]))
 408
 409
 410     ## tryCatch({
 411     ## mod.calibrated.mle <- mecor(y ~ MeasError(w_pred, reference = x.obs) + z, df, B=400, method='efficient')
 412     ## (mod.calibrated.mle)
 413     ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
 414     ## result <- append(result, list(
 415     ##                              Bxy.est.mecor = mecor.ci['Estimate'],
 416     ##                              Bxy.ci.upper.mecor = mecor.ci['UCI'],
 417     ##                              Bxy.ci.lower.mecor = mecor.ci['LCI'])
 418     ##                  )
 419
 420     ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['z',])
 421
 422     ## result <- append(result, list(
 423     ##                              Bzy.est.mecor = mecor.ci['Estimate'],
 424     ##                              Bzy.ci.upper.mecor = mecor.ci['UCI'],
 425     ##                              Bzy.ci.lower.mecor = mecor.ci['LCI'])
 426     ##                  )
 427     ## },
 428     ## error = function(e){
 429     ##     message("An error occurred:\n",e)
 430     ##     result$error <- paste0(result$error, '\n', e)
 431     ## }
 432     ## )
 433 ##    clean up memory
 434 ##    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"))
 435
 436 ##    gc()
 437     return(result)
 438 }