R/gam_est.R

In causaldrf: Estimating Causal Dose Response Functions

##' The GAM estimator
##'
##' This estimates the ADRF using a method similar to that described in Hirano and Imbens (2004),
##' but with spline basis terms in the outcome model.
##'
##'
##'
##' @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 treat_formula an object of class "formula" (or one that can be
##' coerced to that class) that regresses \code{treat} on a linear combination
##' of \code{X}: a symbolic description of the model to be fitted.
##' @param data is a dataframe containing \code{Y} and \code{treat} and
##' \code{X}.
##' @param grid_val contains the treatment values to be evaluated.
##' @param treat_mod a description of the error distribution to be used in the
##' model for treatment. Options include: \code{"Normal"} for normal model,
##' \code{"LogNormal"} for lognormal model, \code{"Sqrt"} for square-root transformation
##' to a normal treatment, \code{"Poisson"} for Poisson model,
##' \code{"NegBinom"} for negative binomial model, \code{"Gamma"} for gamma
##' model.
##' @param link_function is either "log", "inverse", or "identity" for the
##' "Gamma" \code{treat_mod}.
##' @param ... additional arguments to be passed to the gam() outcome function.
##'
##' @details
##' This function estimates the ADRF similarly to the method described by
##' Hirano and Imbens (2004), but with a generalized additive model in the outcome
##' model.
##'
##'
##' @return \code{gam_est} returns an object of class "causaldrf",
##' a list that contains the following components:
##' \item{param}{parameter estimates for a gam fit.}
##' \item{t_mod}{the result of the treatment model fit.}
##' \item{out_mod}{the result of the outcome model fit.}
##' \item{call}{the matched call.}
##'
##' @seealso \code{\link{nw_est}}, \code{\link{iw_est}}, \code{\link{hi_est}}, \code{\link{gam_est}},
##' \code{\link{add_spl_est}},
##' \code{\link{bart_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}.
##'
##' Hirano, Keisuke, Imbens, Guido W (2004).  The propensity score with
##' continuous treatments.  \emph{Applied Bayesian modeling and
##' causal inference from incomplete-data perspectives.}
##'
##' Flores, Carlos A and Flores-Lagunes, Alfonso and Gonzalez, Arturo and Neumann, Todd C (2012).
##' Estimating the effects of length of
##' exposure to instruction in a training program: the case of job corps.
##' \emph{Review of Economics and Statistics}. \bold{94.1}, 153-171
##'
##'
##' @examples
##'
##' ## Example from Schafer (2015).
##'
##' example_data <- sim_data
##'
##' gam_list <- gam_est(Y = Y,
##'                 treat = T,
##'                 treat_formula = T ~ B.1 + B.2 + B.3 + B.4 + B.5 + B.6 + B.7 + B.8,
##'                 data = example_data,
##'                 grid_val = seq(8, 16, by = 1),
##'                 treat_mod = "Normal")
##'
##' sample_index <- sample(1:1000, 100)
##'
##' plot(example_data$T[sample_index],
##'       example_data$Y[sample_index],
##'       xlab = "T",
##'       ylab = "Y",
##'       main = "gam estimate")
##'
##' lines(seq(8, 16, by = 1),
##'       gam_list$param,
##'       lty = 2,
##'       lwd = 2,
##'       col = "blue")
##'
##' legend('bottomright',
##'         "gam estimate",
##'         lty=2,
##'         lwd = 2,
##'         col = "blue",
##'         bty='Y',
##'         cex=1)
##'
##' rm(example_data, gam_list, sample_index)
##'
##'
##' @usage
##'
##' gam_est(Y,
##'         treat,
##'         treat_formula,
##'         data,
##'         grid_val,
##'         treat_mod,
##'         link_function,
##'         ...)
##'
##' @export

gam_est <- function(Y,
                    treat,
                    treat_formula,
                    data,
                    grid_val,
                    treat_mod,
                    link_function,
                    ...
                    ){


  # Y is the name of the Y variable
  # treat is the name of the treatment variable
  # treat_formula is the formula for the treatment model
  # data will contain all the data: X, treat, and Y
  # grid_val is the set of grid points on T
  # treat_mod is th treatment model to fit
  # link_function is the link function used, if needed

  # The outcome is a list of 3 objects:
  #    (1) estimated values of ADRF at gridvalues
  #    (2) result of treatment model
  #    (3) result from the gam model


  #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 (!("data" %in% names(tempcall))) stop("No data specified")
  if (!("grid_val" %in% names(tempcall)))  stop("No grid_val specified")
  if (!("treat_mod" %in% names(tempcall)) | ("treat_mod" %in% names(tempcall) & !(tempcall$treat_mod %in% c("NegBinom", "Poisson", "Gamma", "LogNormal", "Sqrt", "Normal")))) stop("No valid family specified (\"NegBinom\", \"Poisson\", \"Gamma\", \"Log\",  \"Sqrt\", \"Normal\")")
  if (tempcall$treat_mod == "Gamma") {if(!(tempcall$link_function %in% c("log", "inverse"))) stop("No valid link function specified for family = Gamma (\"log\", \"inverse\")")}
  if (tempcall$treat_mod == "binomial") {if(!(tempcall$link_function %in% c("logit", "probit", "cauchit", "log", "cloglog"))) stop("No valid link function specified for family = binomial (\"logit\", \"probit\", \"cauchit\", \"log\", \"cloglog\")")}
  if (tempcall$treat_mod == "ordinal" ) {if(!(tempcall$link_function %in% c("logit", "probit", "cauchit", "cloglog"))) stop("No valid link function specified for family = ordinal (\"logit\", \"probit\", \"cauchit\", \"cloglog\")")}


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




  #-------------------------------------------------------------------------------

  # make a formula for the treatment model
  #   formula_t <- eval(parse(text = paste(deparse(tempcall$treat, width.cutoff = 500), deparse(tempcall$treat_formula, width.cutoff = 500), sep = "")))
  formula_t <- tempcall$treat_formula

  if (treat_mod == "NegBinom") {
    samp_dat <- data
    result <- MASS::glm.nb(formula = formula_t, link = log, data = samp_dat)
    cond_mean <- result$fitted.values
    cond_var <- cond_mean + cond_mean^2/result$theta
    prob_nb_est <- (cond_var - cond_mean)/cond_var
    gps_fun_NB <- function(tt) {
      dnbinom(x = tt, size = result$theta, mu = result$fitted.values,
              log = FALSE)
    }
    gps_fun <- gps_fun_NB
  }
  else if (treat_mod == "Poisson") {
    samp_dat <- data
    result <- glm(formula = formula_t, family = "poisson", data = samp_dat)
    cond_mean <- result$fitted.values
    samp_dat$gps_vals <- dpois(x = tempdat$treat, lambda = cond_mean)
    gps_fun_Pois <- function(t) {
      dpois(t, lambda = cond_mean)
    }
    gps_fun <- gps_fun_Pois
  }
  else if (treat_mod == "Gamma") {
    samp_dat <- data
    result <- glm(formula = formula_t, family = Gamma(link = link_function),
                  data = samp_dat)
    est_treat <- result$fitted
    shape_gamma <- as.numeric(MASS::gamma.shape(result)[1])
    theta_given_X <- result$fitted.values/shape_gamma
    theta_treat_X <- tempdat$treat/shape_gamma
    gps_fun_Gamma <- function(t) {
      dgamma(t, shape = shape_gamma, scale = theta_given_X)
    }
    gps_fun <- gps_fun_Gamma
  }
  else if (treat_mod == "LogNormal") {

    samp_dat <- data
    samp_dat[, as.character(tempcall$treat)] <- log(samp_dat[, as.character(tempcall$treat)])
    result <- lm(formula = formula_t, data = samp_dat)
    est_log_treat <- result$fitted
    sigma_est <- summary(result)$sigma
    gps_fun_Log <- function(tt) {
      dnorm(log(tt), mean = est_log_treat, sd = sigma_est)
    }
    gps_fun <- gps_fun_Log
  }
  else if (treat_mod == "Sqrt") {

    samp_dat <- data
    samp_dat[, as.character(tempcall$treat)] <- sqrt(samp_dat[, as.character(tempcall$treat)])
    result <- lm(formula = formula_t, data = samp_dat)
    est_sqrt_treat <- result$fitted
    sigma_est <- summary(result)$sigma
    gps_fun_sqrt <- function(tt) {
      dnorm(sqrt(tt), mean = est_sqrt_treat, sd = sigma_est)
    }
    gps_fun <- gps_fun_sqrt
  }
  else if (treat_mod == "Normal") {
    samp_dat <- data
    result <- lm(formula = formula_t, data = samp_dat)
    gps_fun_Normal <- function(tt) {
      dnorm(tt, mean = result$fitted, sd = summary(result)$sigma)
    }
    gps_fun <- gps_fun_Normal
  }
  else {
    stop("No valid treat_mod specified.  Please try again.")
  }



#--------------------------------------------------------

  out_data <- data.frame( cbind(tempdat$Y, tempdat$treat, gps_fun(tempdat$treat) ) )

  colnames(out_data) <- c("Y", "treat", "gps")

  gam_fit <- mgcv::gam(Y ~ s(treat, bs = "cr") + s(gps, bs = "cr"),
                       family = gaussian,
                       data = out_data,
                       ...)

  gps_at_grid <- matrix(numeric(length(grid_val) * nrow(out_data)), nrow = nrow(out_data) )
  for (i in 1:length(grid_val)) {
    gps_at_grid[, i] <-  gps_fun(grid_val[i])
  }

  GAM_Y_est <- numeric( length(grid_val) )
  for ( i in 1:length(grid_val) ) {
    gam_data_1 <- data.frame(cbind(tempdat$Y,
                                   grid_val[i],
                                   gps_at_grid[, i] )
    )

    colnames(gam_data_1) <- c("Y", "treat", "gps")

    pred_est <-predict(gam_fit,
                       type = "response",
                       newdata = gam_data_1
    )

    GAM_Y_est[i] <- mean(pred_est)

  }

  z_object <- list(param = GAM_Y_est,
                   t_mod = result,
                   out_mod = gam_fit,
                   call = tempcall)

  class(z_object) <- "causaldrf"
  z_object

}