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
   8 logistic <- function(x) {1/(1+exp(-1*x))}
   9
  10 run_simulation <-  function(df, result){
  11
  12     accuracy <- df[,mean(w_pred==x)]
  13     result <- append(result, list(accuracy=accuracy))
  14
  15     (model.true <- lm(y ~ x + g, data=df))
  16     true.ci.Bxy <- confint(model.true)['x',]
  17     true.ci.Bgy <- confint(model.true)['g',]
  18
  19     result <- append(result, list(Bxy.est.true=coef(model.true)['x'],
  20                                   Bgy.est.true=coef(model.true)['g'],
  21                                   Bxy.ci.upper.true = true.ci.Bxy[2],
  22                                   Bxy.ci.lower.true = true.ci.Bxy[1],
  23                                   Bgy.ci.upper.true = true.ci.Bgy[2],
  24                                   Bgy.ci.lower.true = true.ci.Bgy[1]))
  25
  26     (model.feasible <- lm(y~x.obs+g,data=df))
  27
  28     feasible.ci.Bxy <- confint(model.feasible)['x.obs',]
  29     result <- append(result, list(Bxy.est.feasible=coef(model.feasible)['x.obs'],
  30                                   Bxy.ci.upper.feasible = feasible.ci.Bxy[2],
  31                                   Bxy.ci.lower.feasible = feasible.ci.Bxy[1]))
  32
  33     feasible.ci.Bgy <- confint(model.feasible)['g',]
  34     result <- append(result, list(Bgy.est.feasible=coef(model.feasible)['g'],
  35                                   Bgy.ci.upper.feasible = feasible.ci.Bgy[2],
  36                                   Bgy.ci.lower.feasible = feasible.ci.Bgy[1]))
  37
  38     (model.naive <- lm(y~w+g, data=df))
  39
  40     naive.ci.Bxy <- confint(model.naive)['w',]
  41     naive.ci.Bgy <- confint(model.naive)['g',]
  42
  43     result <- append(result, list(Bxy.est.naive=coef(model.naive)['w'],
  44                                   Bgy.est.naive=coef(model.naive)['g'],
  45                                   Bxy.ci.upper.naive = naive.ci.Bxy[2],
  46                                   Bxy.ci.lower.naive = naive.ci.Bxy[1],
  47                                   Bgy.ci.upper.naive = naive.ci.Bgy[2],
  48                                   Bgy.ci.lower.naive = naive.ci.Bgy[1]))
  49
  50
  51     ## multiple imputation when k is observed
  52     ## amelia does great at this one.
  53     noms <- c()
  54     if(length(unique(df$x.obs)) <=2){
  55         noms <- c(noms, 'x.obs')
  56     }
  57
  58     if(length(unique(df$g)) <=2){
  59         noms <- c(noms, 'g')
  60     }
  61
  62
  63     amelia.out.k <- amelia(df, m=200, p2s=0, idvars=c('x','w_pred'),noms=noms)
  64     mod.amelia.k <- zelig(y~x.obs+g, model='ls', data=amelia.out.k$imputations, cite=FALSE)
  65     (coefse <- combine_coef_se(mod.amelia.k, messages=FALSE))
  66
  67     est.x.mi <- coefse['x.obs','Estimate']
  68     est.x.se <- coefse['x.obs','Std.Error']
  69     result <- append(result,
  70                      list(Bxy.est.amelia.full = est.x.mi,
  71                           Bxy.ci.upper.amelia.full = est.x.mi + 1.96 * est.x.se,
  72                           Bxy.ci.lower.amelia.full = est.x.mi - 1.96 * est.x.se
  73                           ))
  74
  75     est.g.mi <- coefse['g','Estimate']
  76     est.g.se <- coefse['g','Std.Error']
  77
  78     result <- append(result,
  79                      list(Bgy.est.amelia.full = est.g.mi,
  80                           Bgy.ci.upper.amelia.full = est.g.mi + 1.96 * est.g.se,
  81                           Bgy.ci.lower.amelia.full = est.g.mi - 1.96 * est.g.se
  82                           ))
  83
  84     ## What if we can't observe k -- most realistic scenario. We can't include all the ML features in a model.
  85     amelia.out.nok <- amelia(df, m=200, p2s=0, idvars=c("x","k","w_pred"), noms=noms)
  86     mod.amelia.nok <- zelig(y~x.obs+g, model='ls', data=amelia.out.nok$imputations, cite=FALSE)
  87     (coefse <- combine_coef_se(mod.amelia.nok, messages=FALSE))
  88
  89     est.x.mi <- coefse['x.obs','Estimate']
  90     est.x.se <- coefse['x.obs','Std.Error']
  91     result <- append(result,
  92                      list(Bxy.est.amelia.nok = est.x.mi,
  93                           Bxy.ci.upper.amelia.nok = est.x.mi + 1.96 * est.x.se,
  94                           Bxy.ci.lower.amelia.nok = est.x.mi - 1.96 * est.x.se
  95                           ))
  96
  97     est.g.mi <- coefse['g','Estimate']
  98     est.g.se <- coefse['g','Std.Error']
  99
 100     result <- append(result,
 101                      list(Bgy.est.amelia.nok = est.g.mi,
 102                           Bgy.ci.upper.amelia.nok = est.g.mi + 1.96 * est.g.se,
 103                           Bgy.ci.lower.amelia.nok = est.g.mi - 1.96 * est.g.se
 104                           ))
 105
 106     N <- nrow(df)
 107     m <- nrow(df[!is.na(x.obs)])
 108     p <- v <- train <- rep(0,N)
 109     M <- m
 110     p[(M+1):(N)] <- 1
 111     v[1:(M)] <- 1
 112     df <- df[order(x.obs)]
 113     y <- df[,y]
 114     x <- df[,x.obs]
 115     g <- df[,g]
 116     w <- df[,w]
 117     # gmm gets pretty close
 118     (gmm.res <- predicted_covariates(y, x, g, w, v, train, p, max_iter=100, verbose=TRUE))
 119
 120     result <- append(result,
 121                      list(Bxy.est.gmm = gmm.res$beta[1,1],
 122                           Bxy.ci.upper.gmm = gmm.res$confint[1,2],
 123                           Bxy.ci.lower.gmm = gmm.res$confint[1,1],
 124                           gmm.ER_pval = gmm.res$ER_pval
 125                           ))
 126
 127     result <- append(result,
 128                      list(Bgy.est.gmm = gmm.res$beta[2,1],
 129                           Bgy.ci.upper.gmm = gmm.res$confint[2,2],
 130                           Bgy.ci.lower.gmm = gmm.res$confint[2,1]))
 131
 132
 133     mod.calibrated.mle <- mecor(y ~ MeasError(w, reference = x.obs) + g, df, B=400, method='efficient')
 134     (mod.calibrated.mle)
 135     (mecor.ci <- summary(mod.calibrated.mle)$c$ci['x.obs',])
 136     result <- append(result, list(
 137                                  Bxy.est.mecor = mecor.ci['Estimate'],
 138                                  Bxy.upper.mecor = mecor.ci['UCI'],
 139                                  Bxy.lower.mecor = mecor.ci['LCI'])
 140                      )
 141
 142     (mecor.ci <- summary(mod.calibrated.mle)$c$ci['g',])
 143
 144     result <- append(result, list(
 145                                  Bgy.est.mecor = mecor.ci['Estimate'],
 146                                  Bgy.upper.mecor = mecor.ci['UCI'],
 147                                  Bgy.lower.mecor = mecor.ci['LCI'])
 148                      )
 149
 150 ##    clean up memory
 151     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"))
 152
 153     gc()
 154     return(result)
 155 }