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, confint_method='quad'){
  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
 154     mod.caroll.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula)
 155     fischer.info <- solve(mod.caroll.lik$hessian)
 156     coef <- mod.caroll.lik$par
 157     ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
 158     ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 159
 160     result <- append(result,
 161                      list(Bxy.est.mle = coef['x'],
 162                           Bxy.ci.upper.mle = ci.upper['x'],
 163                           Bxy.ci.lower.mle = ci.lower['x'],
 164                           Bzy.est.mle = coef['z'],
 165                           Bzy.ci.upper.mle = ci.upper['z'],
 166                           Bzy.ci.lower.mle = ci.lower['z']))
 167
 168     mod.caroll.profile.lik <- measerr_mle_dv(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, method='bbmle')
 169     coef <- coef(mod.caroll.profile.lik)
 170     ci <- confint(mod.caroll.profile.lik, method='spline')
 171     ci.lower <- ci[,'2.5 %']
 172     ci.upper <- ci[,'97.5 %']
 173
 174     result <- append(result,
 175                      list(Bxy.est.mle.profile = coef['x'],
 176                           Bxy.ci.upper.mle.profile = ci.upper['x'],
 177                           Bxy.ci.lower.mle.profile = ci.lower['x'],
 178                           Bzy.est.mle.profile = coef['z'],
 179                           Bzy.ci.upper.mle.profile = ci.upper['z'],
 180                           Bzy.ci.lower.mle.profile = ci.lower['z']))
 181
 182     ## my implementatoin of liklihood based correction
 183     mod.zhang <- zhang.mle.dv(df)
 184     coef <- coef(mod.zhang)
 185     ci <- confint(mod.zhang,method='quad')
 186
 187     result <- append(result,
 188                      list(Bxy.est.zhang = coef['Bxy'],
 189                           Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
 190                           Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
 191                           Bzy.est.zhang = coef['Bzy'],
 192                           Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
 193                           Bzy.ci.lower.zhang = ci['Bzy','2.5 %']))
 194
 195
 196
 197     # amelia says use normal distribution for binary variables.
 198     amelia_result <- list(Bxy.est.amelia.full = NA,
 199                           Bxy.ci.upper.amelia.full = NA,
 200                           Bxy.ci.lower.amelia.full = NA,
 201                           Bzy.est.amelia.full = NA,
 202                           Bzy.ci.upper.amelia.full = NA,
 203                           Bzy.ci.lower.amelia.full = NA
 204                           )
 205
 206     tryCatch({
 207         amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('y','ystar','w'),ords="y.obs")
 208         mod.amelia.k <- zelig(y.obs~x+z, model='logit', data=amelia.out.k$imputations, cite=FALSE)
 209         (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
 210         est.x.mi <- coefse['x','Estimate']
 211         est.x.se <- coefse['x','Std.Error']
 212
 213         est.z.mi <- coefse['z','Estimate']
 214         est.z.se <- coefse['z','Std.Error']
 215         amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
 216                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
 217                           Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
 218                           Bzy.est.amelia.full = est.z.mi,
 219                           Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
 220                           Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
 221                           )
 222     },
 223     error = function(e){
 224     result[['error']] <- e}
 225     )
 226     result <- append(result,amelia_result)
 227
 228     return(result)
 229
 230 }
 231
 232
 233 ## outcome_formula, proxy_formula, and truth_formula are passed to measerr_mle
 234 run_simulation <-  function(df, result, outcome_formula=y~x+z, proxy_formula=NULL, truth_formula=NULL, confint_method='quad'){
 235
 236     accuracy <- df[,mean(w_pred==x)]
 237     accuracy.y0 <- df[y<=0,mean(w_pred==x)]
 238     accuracy.y1 <- df[y>=0,mean(w_pred==x)]
 239     cor.y.xi <- cor(df$x - df$w_pred, df$y)
 240
 241     fnr <- df[w_pred==0,mean(w_pred!=x)]
 242     fnr.y0 <- df[(w_pred==0) & (y<=0),mean(w_pred!=x)]
 243     fnr.y1 <- df[(w_pred==0) & (y>=0),mean(w_pred!=x)]
 244
 245     fpr <- df[w_pred==1,mean(w_pred!=x)]
 246     fpr.y0 <- df[(w_pred==1) & (y<=0),mean(w_pred!=x)]
 247     fpr.y1 <- df[(w_pred==1) & (y>=0),mean(w_pred!=x)]
 248     cor.resid.w_pred <- cor(resid(lm(y~x+z,df)),df$w_pred)
 249
 250     result <- append(result, list(accuracy=accuracy,
 251                                   accuracy.y0=accuracy.y0,
 252                                   accuracy.y1=accuracy.y1,
 253                                   cor.y.xi=cor.y.xi,
 254                                   fnr=fnr,
 255                                   fnr.y0=fnr.y0,
 256                                   fnr.y1=fnr.y1,
 257                                   fpr=fpr,
 258                                   fpr.y0=fpr.y0,
 259                                   fpr.y1=fpr.y1,
 260                                   cor.resid.w_pred=cor.resid.w_pred
 261                                   ))
 262
 263     result <- append(result, list(cor.xz=cor(df$x,df$z)))
 264     (model.true <- lm(y ~ x + z, data=df))
 265     true.ci.Bxy <- confint(model.true)['x',]
 266     true.ci.Bzy <- confint(model.true)['z',]
 267
 268     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
 269                                   Bzy.est.true=coef(model.true)['z'],
 270                                   Bxy.ci.upper.true = true.ci.Bxy[2],
 271                                   Bxy.ci.lower.true = true.ci.Bxy[1],
 272                                   Bzy.ci.upper.true = true.ci.Bzy[2],
 273                                   Bzy.ci.lower.true = true.ci.Bzy[1]))
 274
 275     (model.feasible <- lm(y~x.obs+z,data=df))
 276
 277     feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
 278     result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
 279                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
 280                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
 281
 282     feasible.ci.Bzy <- confint(model.feasible)['z',]
 283     result <- append(result, list(Bzy.est.feasible=coef(model.feasible)['z'],
 284                                   Bzy.ci.upper.feasible = feasible.ci.Bzy[2],
 285                                   Bzy.ci.lower.feasible = feasible.ci.Bzy[1]))
 286
 287     (model.naive <- lm(y~w_pred+z, data=df))
 288
 289     naive.ci.Bxy <- confint(model.naive)['w_pred',]
 290     naive.ci.Bzy <- confint(model.naive)['z',]
 291
 292     result <- append(result, list(Bxy.est.naive=coef(model.naive)['w_pred'],
 293                                   Bzy.est.naive=coef(model.naive)['z'],
 294                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
 295                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
 296                                   Bzy.ci.upper.naive = naive.ci.Bzy[2],
 297                                   Bzy.ci.lower.naive = naive.ci.Bzy[1]))
 298
 299     amelia_result <- list(
 300         Bxy.est.amelia.full = NULL,
 301         Bxy.ci.upper.amelia.full = NULL,
 302         Bxy.ci.lower.amelia.full = NULL,
 303         Bzy.est.amelia.full = NULL,
 304         Bzy.ci.upper.amelia.full = NULL,
 305         Bzy.ci.lower.amelia.full = NULL
 306         )
 307
 308     tryCatch({
 309         amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w'))
 310         mod.amelia.k <- zelig(y~x.obs+z, model='ls', data=amelia.out.k$imputations, cite=FALSE)
 311         (coefse <- combine_coef_se(mod.amelia.k))
 312
 313         est.x.mi <- coefse['x.obs','Estimate']
 314         est.x.se <- coefse['x.obs','Std.Error']
 315         est.z.mi <- coefse['z','Estimate']
 316         est.z.se <- coefse['z','Std.Error']
 317
 318         amelia_result <- list(Bxy.est.amelia.full = est.x.mi,
 319                               Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
 320                               Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se,
 321                               Bzy.est.amelia.full = est.z.mi,
 322                               Bzy.ci.upper.amelia.full = est.z.mi + 1.96 * est.z.se,
 323                               Bzy.ci.lower.amelia.full = est.z.mi - 1.96 * est.z.se
 324                               )
 325
 326     },
 327
 328     error = function(e){
 329         result[['error']] <- e}
 330     )
 331
 332
 333     result <- append(result, amelia_result)
 334
 335
 336    mle_result <- list(Bxy.est.mle = NULL,
 337                       Bxy.ci.upper.mle = NULL,
 338                       Bxy.ci.lower.mle = NULL,
 339                       Bzy.est.mle = NULL,
 340                       Bzy.ci.upper.mle = NULL,
 341                       Bzy.ci.lower.mle = NULL)
 342
 343     tryCatch({
 344         temp.df <- copy(df)
 345         temp.df <- temp.df[,x:=x.obs]
 346         mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='optim')
 347         fischer.info <- solve(mod.caroll.lik$hessian)
 348         coef <- mod.caroll.lik$par
 349         ci.upper <- coef + sqrt(diag(fischer.info)) * 1.96
 350         ci.lower <- coef - sqrt(diag(fischer.info)) * 1.96
 351
 352         mle_result <- list(Bxy.est.mle = coef['x'],
 353                            Bxy.ci.upper.mle = ci.upper['x'],
 354                            Bxy.ci.lower.mle = ci.lower['x'],
 355                            Bzy.est.mle = coef['z'],
 356                            Bzy.ci.upper.mle = ci.upper['z'],
 357                            Bzy.ci.lower.mle = ci.lower['z'])
 358         },
 359         error=function(e) {result[['error']] <- as.character(e)
 360         })
 361
 362     result <- append(result, mle_result)
 363     mle_result_proflik <- list(Bxy.est.mle.profile = NULL,
 364                                Bxy.ci.upper.mle.profile = NULL,
 365                                Bxy.ci.lower.mle.profile = NULL,
 366                                Bzy.est.mle.profile = NULL,
 367                                Bzy.ci.upper.mle.profile = NULL,
 368                                Bzy.ci.lower.mle.profile = NULL)
 369
 370     tryCatch({
 371         ## confint_method == 'bbmle'
 372         mod.caroll.lik <- measerr_mle(temp.df, outcome_formula=outcome_formula, proxy_formula=proxy_formula, truth_formula=truth_formula, method='bbmle')
 373         coef <- coef(mod.caroll.lik)
 374         ci <- confint(mod.caroll.lik, method='spline')
 375         ci.lower <- ci[,'2.5 %']
 376         ci.upper <- ci[,'97.5 %']
 377
 378         mle_result_proflik <- list(Bxy.est.mle.profile = coef['x'],
 379                                    Bxy.ci.upper.mle.profile = ci.upper['x'],
 380                                    Bxy.ci.lower.mle.profile = ci.lower['x'],
 381                                    Bzy.est.mle.profile = coef['z'],
 382                                    Bzy.ci.upper.mle.profile = ci.upper['z'],
 383                                    Bzy.ci.lower.mle.profile = ci.lower['z'])
 384     },
 385
 386     error=function(e) {result[['error']] <- as.character(e)
 387     })
 388
 389     result <- append(result, mle_result_proflik)
 390
 391     zhang_result <- list(Bxy.est.mle.zhang = NULL,
 392                        Bxy.ci.upper.mle.zhang = NULL,
 393                        Bxy.ci.lower.mle.zhang = NULL,
 394                        Bzy.est.mle.zhang = NULL,
 395                        Bzy.ci.upper.mle.zhang = NULL,
 396                        Bzy.ci.lower.mle.zhang = NULL)
 397
 398     tryCatch({
 399     mod.zhang.lik <- zhang.mle.iv(df)
 400     coef <- coef(mod.zhang.lik)
 401     ci <- confint(mod.zhang.lik,method='quad')
 402     zhang_result <- list(Bxy.est.zhang = coef['Bxy'],
 403                          Bxy.ci.upper.zhang = ci['Bxy','97.5 %'],
 404                          Bxy.ci.lower.zhang = ci['Bxy','2.5 %'],
 405                          Bzy.est.zhang = coef['Bzy'],
 406                          Bzy.ci.upper.zhang = ci['Bzy','97.5 %'],
 407                          Bzy.ci.lower.zhang = ci['Bzy','2.5 %'])
 408     },
 409     error=function(e) {result[['error']] <- as.character(e)
 410     })
 411     result <- append(result, zhang_result)
 412
 413     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
 414     ## amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","w_pred"), noms=noms)
 415     ## mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
 416     ## (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
 417
 418     ## est.x.mi <- coefse['x.obs','Estimate']
 419     ## est.x.se <- coefse['x.obs','Std.Error']
 420     ## result <- append(result,
 421     ##                  list(Bxy.est.amelia.nok = est.x.mi,
 422     ##                       Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
 423     ##                       Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
 424     ##                       ))
 425
 426     ## est.g.mi <- coefse['g','Estimate']
 427     ## est.g.se <- coefse['g','Std.Error']
 428
 429     ## result <- append(result,
 430     ##                  list(Bgy.est.amelia.nok = est.g.mi,
 431     ##                       Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
 432     ##                       Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
 433     ##                       ))
 434
 435     N <- nrow(df)
 436     m <- nrow(df[!is.na(x.obs)])
 437     p <- v <- train <- rep(0,N)
 438     M <- m
 439     p[(M+1):(N)] <- 1
 440     v[1:(M)] <- 1
 441     df <- df[order(x.obs)]
 442     y <- df[,y]
 443     x <- df[,x.obs]
 444     z <- df[,z]
 445     w <- df[,w_pred]
 446     # gmm gets pretty close
 447     (gmm.res <- predicted_covariates(y, x, z, w, v, train, p, max_iter=100, verbose=TRUE))
 448
 449     result <- append(result,
 450                      list(Bxy.est.gmm = gmm.res$beta[1,1],
 451                           Bxy.ci.upper.gmm = gmm.res$confint[1,2],
 452                           Bxy.ci.lower.gmm = gmm.res$confint[1,1],
 453                           gmm.ER_pval = gmm.res$ER_pval
 454                           ))
 455
 456     result <- append(result,
 457                      list(Bzy.est.gmm = gmm.res$beta[2,1],
 458                           Bzy.ci.upper.gmm = gmm.res$confint[2,2],
 459                           Bzy.ci.lower.gmm = gmm.res$confint[2,1]))
 460
 461
 462     ## tryCatch({
 463     ## mod.calibrated.mle <- mecor(y ~ MeasError(w_pred, reference = x.obs) + z, df, B=400, method='efficient')
 464     ## (mod.calibrated.mle)
 465     ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
 466     ## result <- append(result, list(
 467     ##                              Bxy.est.mecor = mecor.ci['Estimate'],
 468     ##                              Bxy.ci.upper.mecor = mecor.ci['UCI'],
 469     ##                              Bxy.ci.lower.mecor = mecor.ci['LCI'])
 470     ##                  )
 471
 472     ## (mecor.ci <- summary(mod.calibrated.mle)$c$ci['z',])
 473
 474     ## result <- append(result, list(
 475     ##                              Bzy.est.mecor = mecor.ci['Estimate'],
 476     ##                              Bzy.ci.upper.mecor = mecor.ci['UCI'],
 477     ##                              Bzy.ci.lower.mecor = mecor.ci['LCI'])
 478     ##                  )
 479     ## },
 480     ## error = function(e){
 481     ##     message("An error occurred:\n",e)
 482     ##     result$error <- paste0(result$error, '\n', e)
 483     ## }
 484     ## )
 485 ##    clean up memory
 486 ##    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"))
 487
 488 ##    gc()
 489     return(result)
 490 }