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