R/reg_est.R

In causaldrf: Estimating Causal Dose Response Functions

##' The regression prediction estimator
##'
##' This method estimates the linear or quadratic parameters of the ADRF by
##' estimating a least-squares fit on the basis functions which are composed of
##' combinations of the covariates and treatment values.
##'
##'
##' @param Y is the the name of the outcome variable contained in \code{data}.
##' @param treat is the name of the treatment variable contained in
##' \code{data}.
##' @param covar_formula is the formula to describe the covariates needed
##' to estimate the constant term:
##' \code{~ X.1 + ....}. Can include higher order terms or interactions.  i.e.
##' \code{~ X.1 + I(X.1^2) + X.1 * X.2 + ....}.  Don't forget the tilde before
##' listing the covariates.
##'
##' @param covar_lin_formula is the formula to describe the covariates needed
##' to estimate the linear term, t:
##' \code{~ X.1 + ....}. Can include higher order terms or interactions.  i.e.
##' \code{~ X.1 + I(X.1^2) + X.1 * X.2 + ....}.  Don't forget the tilde before
##' listing the covariates.
##'
##' @param covar_sq_formula is the formula to describe the covariates needed
##' to estimate the quadratic term, t^2:
##' \code{~ X.1 + ....}. Can include higher order terms or interactions.  i.e.
##' \code{~ X.1 + I(X.1^2) + X.1 * X.2 + ....}.  Don't forget the tilde before
##' listing the covariates.
##'
##' @param data is a dataframe containing \code{Y}, \code{treat}, and
##' \code{X}.
##' @param degree is 1 for linear and 2 for quadratic outcome model.
##' @param wt is weight used in lsfit for outcome regression.
##' Default is wt = NULL.
##' @param method is "same" if the same set of covariates are used to estimate
##' the constant, linear, and/or quadratic term.  If method = "different", then
##' different sets of covariates can be used to estimate the constant, linear,
##' and/or quadratic term.  covar_lin_formula and covar_sq_formula must be specified
##' if method = "different".
##'
##' @details
##' This function estimates the ADRF by the method described in Schafer and Galagate (2015)
##' that fits an outcome model using a function of the covariates.
##'
##' @return \code{reg_est} returns an object of class "causaldrf_lsfit",
##' a list that contains the following components:
##' \item{param}{the estimated parameters.}
##' \item{out_mod}{the result of the outcome model fit using lsfit.}
##' \item{call}{the matched call.}
##'
##' @seealso  \code{\link{iptw_est}}, \code{\link{ismw_est}},
##' \code{\link{aipwee_est}}, \code{\link{wtrg_est}},
##' etc. for other estimates.
##'
##' \code{\link{t_mod}}, \code{\link{overlap_fun}} to prepare the \code{data}
##' for use in the different estimates.
##'
##' @references Schafer, J.L., Galagate, D.L. (2015).  Causal inference with a
##' continuous treatment and outcome: alternative estimators for parametric
##' dose-response models. \emph{Manuscript in preparation}.
##'
##' Schafer, Joseph L, Kang, Joseph (2008).  Average causal effects from
##' nonrandomized studies: a practical guide and simulated example.
##' \emph{Psychological methods}, \bold{13.4}, 279.
##'
##' @examples
##'
##' ## Example from Schafer (2015).
##'
##' example_data <- sim_data
##'
##' reg_list <- reg_est(Y = Y,
##'                     treat = T,
##'                     covar_formula = ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
##'                     covar_lin_formula = ~ 1,
##'                     covar_sq_formula = ~ 1,
##'                     data = example_data,
##'                     degree = 1,
##'                     wt = NULL,
##'                     method = "same")
##'
##' sample_index <- sample(1:1000, 100)
##'
##' plot(example_data$T[sample_index],
##'       example_data$Y[sample_index],
##'       xlab = "T",
##'       ylab = "Y",
##'       main = "regression estimate")
##'
##' abline(reg_list$param[1],
##'         reg_list$param[2],
##'         lty = 2,
##'         col = "blue",
##'         lwd = 2)
##'
##' legend('bottomright',
##'         "regression estimate",
##'         lty = 2,
##'         bty = 'Y',
##'         cex = 1,
##'         col = "blue",
##'         lwd = 2)
##'
##' rm(example_data, reg_list, sample_index)
##'
##' @importFrom stats Gamma binomial coef dgamma dnbinom
##' dnorm dpois gaussian glm lm ls.print lsfit median model.frame model.matrix na.fail
##' na.omit predict predict.glm quantile var vcov
##'
##'
##' @usage
##'
##' reg_est(Y,
##'         treat,
##'         covar_formula,
##'         covar_lin_formula = NULL,
##'         covar_sq_formula = NULL,
##'         data,
##'         degree,
##'         wt = NULL,
##'         method = "same")
##'
##'
##' @export
##'
##'
##'





reg_est <- function(Y,
                    treat,
                    covar_formula,
                    covar_lin_formula = NULL,
                    covar_sq_formula = NULL,
                    data,
                    degree,
                    wt = NULL,
                    method = "same"){

  # Y is the name of the Y variable
  # treat is the name of the treatment variable
  # covar_formula is the formula for the covariates model of the form: ~ X.1 + ....
  # data will contain all the data: X, treat, and Y
  # degree is 1 for linear and 2 for quadratic outcome model

  # The outcome is the estimated parameters.


  #save input
  tempcall <- match.call()

  #some basic input checks
  if (!("Y" %in% names(tempcall))) stop("No Y variable specified")
  if (!("treat" %in% names(tempcall)))  stop("No treat variable specified")
  if (!("covar_formula" %in% names(tempcall))) stop("No covar_formula model specified")
  if (!("data" %in% names(tempcall))) stop("No data specified")
  if (!("degree" %in% names(tempcall)))  {if(!(tempcall$degree %in% c(1, 1))) stop("degree must be 1 or 2")}



  #make new dataframe for newly computed variables, to prevent variable name conflicts
  tempdat <- data.frame(
    Y = data[,as.character(tempcall$Y)],
    treat = data[,as.character(tempcall$treat)]

  )


  # make a formula for the treatment model
  if (method == "same"){  # this restricts the covariates for the linear and quadratic interactions to be the same.

    formula_covar = eval(parse(text = paste(deparse(tempcall$treat, width.cutoff = 500), deparse(tempcall$covar_formula, width.cutoff = 500), sep = "")))

  # utils::str(m_frame <- model.frame(formula_covar, data))
  m_frame <- model.frame(formula_covar, data)
  covar_sq_mat <- covar_lin_mat <- covar_mat <- model.matrix(formula_covar, m_frame)

  } else if (method == "different"){  # this allows the covariates for the constant, linear, and quadratic interactions to be different.


    formula_covar = eval(parse(text = paste(deparse(tempcall$treat, width.cutoff = 500), deparse(tempcall$covar_formula, width.cutoff = 500), sep = "")))
    formula_lin_covar = eval(parse(text = paste(deparse(tempcall$treat, width.cutoff = 500), deparse(tempcall$covar_lin_formula, width.cutoff = 500), sep = "")))
    formula_sq_covar = eval(parse(text = paste(deparse(tempcall$treat, width.cutoff = 500), deparse(tempcall$covar_sq_formula, width.cutoff = 500), sep = "")))

    m_frame <- model.frame(formula_covar, data)
    covar_mat <- model.matrix(formula_covar, m_frame)  # matrix containing covariates needed in constant term parameter.

    m_frame_lin <- model.frame(formula_lin_covar, data)
    covar_lin_mat <- model.matrix(formula_lin_covar, m_frame_lin)  # matrix containing covariates needed in linear term parameter.

    m_frame_sq <- model.frame(formula_sq_covar, data)
    covar_sq_mat <- model.matrix(formula_sq_covar, m_frame_sq)  # matrix containing covariates needed in square term parameter.

  } else {
    stop("Error: method is not recognized.")
  }


  if (degree == 2){
  # create the covariate matrix that will have:
  # intercept, main effects, treat, treat * (main effects), treat^2, treat^2 * (main effects)

  basis_mat <- cbind(covar_mat,
                     tempdat$treat * covar_lin_mat,
                     tempdat$treat^2 * covar_sq_mat)

  colnames(basis_mat) <- paste("x",
                               1:ncol(basis_mat),
                               sep="")

  ls_mod <- lsfit(basis_mat,
                  tempdat$Y,
                  wt,
                  intercept = FALSE)

  coef_reg_pred <- ls_mod$coefficients

  n_covars <- ncol(covar_mat)
  n_covars_lin <- ncol(covar_lin_mat)
  n_covars_sq <- ncol(covar_sq_mat)

  coef_0_reg <- coef_reg_pred[ c(1:n_covars) ]
  coef_1_reg <- coef_reg_pred[ c( (n_covars + 1):(n_covars + n_covars_lin) ) ]
  coef_2_reg <- coef_reg_pred[ c( (n_covars + n_covars_lin + 1):(n_covars + n_covars_lin + n_covars_sq) ) ]

  theta_0_covars <- basis_mat[,  c(1:n_covars) ]
  theta_1_covars <- basis_mat[,  c( (n_covars + 1):(n_covars + n_covars_lin) )   ]
  theta_2_covars <- basis_mat[,  c( (n_covars + n_covars_lin + 1):(n_covars + n_covars_lin + n_covars_sq) )  ]


  theta_0_est_reg <- mean(as.matrix(theta_0_covars) %*% coef_0_reg )
  theta_1_est_reg <- mean( (as.matrix(theta_1_covars) %*% coef_1_reg / tempdat$treat)[which(tempdat$treat != 0)]   )  # make sure not to divide by zero.
  theta_2_est_reg <- mean( (as.matrix(theta_2_covars) %*% coef_2_reg / tempdat$treat^2)[which(tempdat$treat != 0)] )

  reg_coefs <- c(theta_0_est_reg,
                 theta_1_est_reg,
                 theta_2_est_reg)

  } else if (degree == 1 ){
    # create the covariate matrix that will have:
    # intercept, main effects, treat, treat * (main effects)

    basis_mat <- cbind(covar_mat,
                       tempdat$treat * covar_lin_mat)

    colnames(basis_mat) <- paste("x",
                                 1:ncol(basis_mat),
                                 sep="")

    ls_mod <- lsfit(basis_mat,
                    tempdat$Y,
                    wt,
                    intercept = FALSE)

    coef_reg_pred <- ls_mod$coefficients

    n_covars <- ncol(covar_mat)
    n_covars_lin <- ncol(covar_lin_mat)

    coef_0_reg <- coef_reg_pred[ c(1:n_covars) ]
    coef_1_reg <- coef_reg_pred[ c( (n_covars + 1):(n_covars + n_covars_lin) ) ]

    theta_0_covars <- basis_mat[,  c(1:n_covars) ]
    theta_1_covars <- basis_mat[,  c( (n_covars + 1):(n_covars + n_covars_lin) )   ]

    theta_0_est_reg <- mean(as.matrix(theta_0_covars) %*% coef_0_reg )
    theta_1_est_reg <- mean( (as.matrix(theta_1_covars) %*% coef_1_reg / tempdat$treat)[which(tempdat$treat != 0)] )

    reg_coefs <- c(theta_0_est_reg,
                   theta_1_est_reg)


  }else{
    stop("Error: degree needs to be 1 or 2")
  }



  z_object <- list(param = reg_coefs,
                   out_mod = ls_mod,
                   call = tempcall)

  class(z_object) <- "causaldrf_lsfit"
  z_object

}


##' @export
summary.causaldrf_lsfit <- function(object,...){
  cat("\nEstimated parameter values:\n")
  print(object$param)
  cat("\nOutcome Summary:\n")
  print(ls.print(object$out_mod))

}


##' @export
print.summary.causaldrf_lsfit <- function(x, ...){
#   cat("\nTreatment Summary:\n")
#   print(summary(x$t_mod))
  cat("\nOutcome Summary:\n")
  print(ls.print(x$out_mod))
}


##' @export
print.causaldrf_lsfit <- function(x,...){
  #   cat("Call:\n")
  #   print(x$call)
  cat("\nEstimated values:\n")
  print(x$param)
}