R/hmi_imp_cont_single_2018-02-23.R

In matthiasspeidel/hmi: Hierarchical Multiple Imputation

#' The function for imputation of continuous variables.
#'
#' The function is called by the wrapper (hmi). It uses \code{mice} with the method "norm".
#' @param y_imp A vector with the variable to impute.
#' @param X_imp A data.frame with the fixed effects variables.
#' @param pvalue A numeric between 0 and 1 denoting the threshold of p-values a variable in the imputation
#' model should not exceed. If they do, they are excluded from the imputation model.
#' @param rounding_degrees A numeric vector with the presumed rounding degrees.
#' @return A n x 1 data.frame with the original and imputed values.
imp_cont_single <- function(y_imp,
                      X_imp,
                      pvalue = 0.2,
                      rounding_degrees = c(1, 10, 100, 1000)){


  #the missing indactor indicates, which values of y are missing.
  missind <- is.na(y_imp)
  # ----------------------------- preparing the X data ------------------

  # remove excessive variables
  X_imp <- cleanup(X_imp)

  # standardise the covariates in X (which are numeric and no intercept)
  X <- stand(X_imp, rounding_degrees = rounding_degrees)

  n <- length(y_imp)

  # ----------- set up a maximal model matrix with all possible relevant (dummy) variables -----
  # In the imputation model only actually relevant (dummy) variables shall be present.
  # THis is done by setting up a mirror of the initial model matrix.
  # Then step by step this model matrix is reduced to all actually relevant (dummy) variables.
  # This reduction is based on models using the observed data.
  # The last step prior to the imputation-parameters estimation is to restrict the initial mode matrix
  # to those variables, left in the reduced mirror model matrix.
  #define a place holder (ph)
  ph <- sample_imp(y_imp)[, 1]

  y_mean <- mean(ph, na.rm = TRUE)
  y_sd <- stats::sd(ph, na.rm = TRUE)

  ph <- (ph - y_mean)/y_sd + 1

  tmp_0_all <- data.frame(target = ph, X)
  xnames_1 <- colnames(X)

  tmp_formula <- paste("target~ 0 + ", paste(xnames_1, collapse = "+"), sep = "")
  reg_1_all <- stats::lm(stats::formula(tmp_formula), data = tmp_0_all)

  X_model_matrix_1_all <- stats::model.matrix(reg_1_all)
  xnames_1 <- paste("X", 1:ncol(X_model_matrix_1_all), sep = "")
  colnames(X_model_matrix_1_all) <- xnames_1

  tmp_0_all <- data.frame(target = ph)
  tmp_0_all[, xnames_1] <- X_model_matrix_1_all

  #From this initial model matrix X_model_matrix_1_all
  #now step by step irrelavant variables are removed.
  X_model_matrix_1_sub <- X_model_matrix_1_all[!missind, , drop = FALSE]

  # The first step of the reduction is to remove variables having a non-measurable effect
  # (e.g. due to colinearity) on y.
  # tmp_1 shall include the covariates (like X_model_matrix) and additionally the target variable
  ph_sub <- ph[!missind]
  tmp_1_sub <- data.frame(target = ph_sub)
  xnames_1 <- colnames(X_model_matrix_1_sub)
  tmp_1_sub[, xnames_1] <- X_model_matrix_1_sub

  tmp_formula <- paste("target~ 0 + ", paste(xnames_1, collapse = "+"), sep = "")
  reg_1_sub <- stats::lm(stats::formula(tmp_formula) , data = tmp_1_sub)

  #remove unneeded variables
  X_model_matrix_1_sub <- X_model_matrix_1_sub[, !is.na(stats::coefficients(reg_1_sub)),
                                               drop = FALSE]

  # Remove insignificant variables from the imputation model
  check <- TRUE
  while(check){
    tmp_1_sub <- data.frame(target = ph_sub)
    xnames_1 <- colnames(X_model_matrix_1_sub)
    tmp_1_sub[, xnames_1] <- X_model_matrix_1_sub
    tmp_formula <- paste("target~ 0 + ", paste(xnames_1, collapse = "+"), sep = "")
    reg_1_sub <- stats::lm(stats::formula(tmp_formula), data = tmp_1_sub)

    pvalues <- summary(reg_1_sub)$coefficients[, 4]
    insignificant_variables <- which(pvalues > pvalue)
    most_insignificant <- insignificant_variables[which.max(pvalues[insignificant_variables])]

    if(length(most_insignificant) == 0){
      check <- FALSE
    }else{
      #.. drop the insignificant variable from the model.matrix, but only if at least 1 variable remains
      tmp_MM <- stats::model.matrix(reg_1_sub)[, -most_insignificant, drop = FALSE]
      if(ncol(tmp_MM) == 0){
        check <- FALSE
      }else{
        X_model_matrix_1_sub <- tmp_MM
      }
    }
  }

  tmp_2_all <- tmp_0_all[, colnames(tmp_1_sub), drop = FALSE]
  tmp_2_all$target[missind] <- NA
  everything <- mice::mice(data = tmp_2_all, m = 1,
                     method = "norm",
                     predictorMatrix = (1 - diag(1, ncol(tmp_2_all))),
                     visitSequence = (1:ncol(tmp_2_all))[apply(is.na(tmp_2_all),2,any)],
                     post = vector("character", length = ncol(tmp_2_all)),
                     defaultMethod = "norm",
                     maxit = 10,
                     diagnostics = TRUE,
                     printFlag = FALSE,
                     seed = NA,
                     imputationMethod = NULL,
                     defaultImputationMethod = NULL,
                     data.init = NULL)


  y_ret <- data.frame(y_ret = y_imp)
  y_ret[missind, 1] <- (everything$imp[[1]][, 1] - 1) * y_sd + y_mean

  return(y_ret)

}


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