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