Nothing
R/weightit2cbps.R
In WeightIt: Weighting for Covariate Balance in Observational Studies
Defines functions
weightit2cbps
#' Covariate Balancing Propensity Score Weighting
#' @name method_cbps
#' @aliases method_cbps
#' @usage NULL
#'
#' @description
#'
#' This page explains the details of estimating weights from covariate balancing propensity scores by setting `method = "cbps"` in the call to [weightit()] or [weightitMSM()]. This method can be used with binary, multi-category, and continuous treatments.
#'
#' In general, this method relies on estimating propensity scores using generalized method of moments and then converting those propensity scores into weights using a formula that depends on the desired estimand. This method relies on code written for \pkg{WeightIt} using [optim()].
#'
#' ## Binary Treatments
#'
#' For binary treatments, this method estimates the propensity scores and weights using `optim()` using formulas described by Imai and Ratkovic (2014). The following estimands are allowed: ATE, ATT, and ATC.
#'
#' ## Multi-Category Treatments
#'
#' For multi-category treatments, this method estimates the generalized propensity scores and weights using `optim()` using formulas described by Imai and Ratkovic (2014). The following estimands are allowed: ATE and ATT.
#'
#' ## Continuous Treatments
#'
#' For continuous treatments, this method estimates the generalized propensity scores and weights using `optim()` using a modification of the formulas described by Fong, Hazlett, and Imai (2018). See Details.
#'
#' ## Longitudinal Treatments
#'
#' For longitudinal treatments, the weights are computed using methods similar to those described by Huffman and van Gameren (2018). This involves specifying moment conditions for the models at each time point as with single-time point treatments but using the product of the time-specific weights as the weights that are used in the balance moment conditions. This yields weights that balance the covariate at each time point. This is not the same implementation as is implemented in `CBPS::CBMSM()`, and results should not be expected to align between the two methods. Any combination of treatment types is supported.
#'
#' For the over-identified version (i.e., setting `over = TRUE`), the empirical variance is used in the objective function, whereas the expected variance averaging over the treatment is used with binary and multi-category point treatments.
#'
#' ## Sampling Weights
#'
#' Sampling weights are supported through `s.weights` in all scenarios.
#'
#' ## Missing Data
#'
#' In the presence of missing data, the following value(s) for `missing` are allowed:
#' \describe{
#' \item{`"ind"` (default)}{
#' First, for each variable with missingness, a new missingness indicator variable is created which takes the value 1 if the original covariate is `NA` and 0 otherwise. The missingness indicators are added to the model formula as main effects. The missing values in the covariates are then replaced with the covariate medians (this value is arbitrary and does not affect estimation). The weight estimation then proceeds with this new formula and set of covariates. The covariates output in the resulting `weightit` object will be the original covariates with the `NA`s.
#' }
#' }
#'
#' ## M-estimation
#'
#' M-estimation is supported for the just-identified CBPS (the default, setting `over = FALSE`) for binary and multi-category treatments. See [glm_weightit()] and `vignette("estimating-effects")` for details.
#'
#' @section Additional Arguments:
#'
#' The following additional arguments can be specified:
#' \describe{
#' \item{`over`}{`logical`; whether to request the over-identified CBPS, which combines the generalized linear model regression score equations (for binary treatments), multinomial logistic regression score equations (for multi-category treatments), or linear regression score equations (for continuous treatments) to the balance moment conditions. Default is `FALSE` to use the just-identified CBPS.
#' }
#' \item{`twostep`}{`logical`; when `over = TRUE`, whether to use the two-step approximation to the generalized method of moments variance. Default is `TRUE`. Ignored when `over = FALSE`.
#' }
#' \item{`link`}{`"string"`; the link used in the generalized linear model for the propensity scores when treatment is binary. Default is `"logit"` for logistic regression, which is used in the original description of the method by Imai and Ratkovic (2014), but others are allowed: `"logit"`, `"probit"`, `"cauchit"`, and `"cloglog"` all use the binomial likelihood, `"log"` uses the Poisson likelihood, and `"identity"` uses the Gaussian likelihood (i.e., the linear probability model). Note that negative weights are possible with these last two and they should be used with caution. Ignored for multi-category, continuous, and longitudinal treatments.
#' }
#' \item{`reltol`}{the relative tolerance for convergence of the optimization. Passed to the `control` argument of `optim()`. Default is `sqrt(.Machine$double.eps)`.
#' }
#' \item{`maxit`}{the maximum number of iterations for convergence of the optimization. Passed to the `control` argument of `optim()`. Default is 1000.
#' }
#' }
#'
#' @section Additional Outputs:
#' \describe{
#' \item{`obj`}{When `include.obj = TRUE`, the output of the final call to `optim()` used to produce the model parameters. Note that because of variable transformations, the resulting parameter estimates may not be interpretable.
#' }
#' }
#'
#' @details
#' CBPS estimates the coefficients of a generalized linear model (for binary treatments), multinomial logistic regression model (for multi-category treatments), or linear regression model (for continuous treatments) that is used to compute (generalized) propensity scores, from which the weights are computed. It involves replacing (or augmenting, in the case of the over-identified version) the standard regression score equations with the balance constraints in a generalized method of moments estimation. The idea is to nudge the estimation of the coefficients toward those that produce balance in the weighted sample. The just-identified version (with `exact = FALSE`) does away with the score equations for the coefficients so that only the balance constraints are used. The just-identified version will therefore produce superior balance on the means (i.e., corresponding to the balance constraints) for binary and multi-category treatments and linear terms for continuous treatments than will the over-identified version.
#'
#' Just-identified CBPS is very similar to entropy balancing and inverse probability tilting. For the ATT, all three methods will yield identical estimates. For other estimands, the results will differ.
#'
#' Note that \pkg{WeightIt} provides different functionality from the \pkg{CBPS} package in terms of the versions of CBPS available; for extensions to CBPS (e.g., optimal CBPS and CBPS for instrumental variables), the \pkg{CBPS} package may be preferred. Note that for longitudinal treatments, `CBPS::CBMSM()` uses different methods and produces different results from `weightitMSM()` called with `method = "cbps"`.
#'
#' @note
#' This method used to rely on functionality in the \pkg{CBPS} package, but no longer does. Slight differences may be found between the two packages in some cases due to numerical imprecision (or, for continuous and longitudinal treatments, due to a difference in the estimator). \pkg{WeightIt} supports arbitrary numbers of groups for the multi-category CBPS and any estimand, whereas \pkg{CBPS} only supports up to four groups and only the ATE. The implementation of the just-identified CBPS for continuous treatments also differs from that of \pkg{CBPS}, and departs slightly from that described by Fong et al. (2018). The treatment mean and treatment variance are treated as random parameters to be estimated and are included in the balance moment conditions. In Fong et al. (2018), the treatment mean and variance are fixed to their empirical counterparts. For continuous treatments with the over-identified CBPS, \pkg{WeightIt} and \pkg{CBPS} use different methods of specifying the GMM variance matrix, which may lead to differing results.
#'
#' Note that the default method differs between the two implementations; by default \pkg{WeightIt} uses the just-identified CBPS, which is faster to fit, yields better balance, and is compatible with M-estimation for estimating the standard error of the treatment effect, whereas \pkg{CBPS} uses the over-identified CBPS by default. However, both the just-identified and over-identified versions are available in both packages.
#'
#' @seealso
#' [weightit()], [weightitMSM()]
#'
#' [method_ebal] and [method_ipt] for entropy balancing and inverse probability tilting, which work similarly.
#'
#' @references
#' ## Binary treatments
#'
#' Imai, K., & Ratkovic, M. (2014). Covariate balancing propensity score. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 76(1), 243–263.
#'
#' ## Multi-Category treatments
#'
#' Imai, K., & Ratkovic, M. (2014). Covariate balancing propensity score. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 76(1), 243–263.
#'
#' ## Continuous treatments
#'
#' Fong, C., Hazlett, C., & Imai, K. (2018). Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements. *The Annals of Applied Statistics*, 12(1), 156–177. \doi{10.1214/17-AOAS1101}
#'
#' ## Longitudinal treatments
#'
#' Huffman, C., & van Gameren, E. (2018). Covariate Balancing Inverse Probability Weights for Time-Varying Continuous Interventions. *Journal of Causal Inference*, 6(2). \doi{10.1515/jci-2017-0002}
#'
#' Note: one should not cite Imai & Ratkovic (2015) when using CBPS for longitudinal treatments.
#'
#' Some of the code was inspired by the source code of the \pkg{CBPS} package.
#'
#' @examples
#' data("lalonde", package = "cobalt")
#'
#' #Balancing covariates between treatment groups (binary)
#' (W1a <- weightit(treat ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATT"))
#' summary(W1a)
#' cobalt::bal.tab(W1a)
#'
#' #Balancing covariates between treatment groups (binary)
#' #using over-identified CBPS with probit link
#' (W1b <- weightit(treat ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATT",
#' over = TRUE, link = "probit"))
#' summary(W1b)
#' cobalt::bal.tab(W1b)
#'
#' #Balancing covariates with respect to race (multi-category)
#' (W2 <- weightit(race ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATE"))
#' summary(W2)
#' cobalt::bal.tab(W2)
#'
#' #Balancing covariates with respect to re75 (continuous)
#' (W3 <- weightit(re75 ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps"))
#' summary(W3)
#' cobalt::bal.tab(W3)
#'
#' #Longitudinal treatments
#' data("msmdata")
#' (W4 <- weightitMSM(list(A_1 ~ X1_0 + X2_0,
#' A_2 ~ X1_1 + X2_1 +
#' A_1 + X1_0 + X2_0),
#' data = msmdata,
#' method = "cbps"))
#' summary(W4)
#' cobalt::bal.tab(W4)
NULL
weightit2cbps <- function(covs, treat, s.weights, estimand, focal, subset,
stabilize, subclass, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- treat[subset]
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
focal = focal, treat = treat))
t.lev <- get_treated_level(treat)
treat <- binarize(treat, one = t.lev)
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
mod_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
bal_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e3 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
if (is_null(A$link)) A$link <- "logit"
link <- A$link
chk::chk_string(link)
chk::chk_subset(link, c("logit", "probit", "cauchit", "cloglog", "log", "identity"))
.fam <- switch(link,
"log" = quasipoisson("log"),
"identity" = gaussian("identity"),
quasibinomial(link))
#Generalized linear model score
psi_glm <- function(B, Xm, A, SW) {
lin_pred <- drop(Xm %*% B)
p <- .fam$linkinv(lin_pred)
(SW * (A - p) * .fam$mu.eta(lin_pred) / .fam$variance(p)) * Xm
}
if (estimand == "ATE") {
# Balance condition for ATE
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * (A/p - (1-A)/(1-p)) * Xb
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- glm.fit(mod_covs, treat, family = .fam, weights = s.weights)$coefficients
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_glm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
lp <- drop(Xm %*% B)
p <- .fam$linkinv(lp)
sw.5 <- sqrt(SW)
g <- .fam$mu.eta(lp) / .fam$variance(p)
S11 <- crossprod(sw.5 * g * sqrt(p * (1 - p)) * Xm)
S12 <- crossprod(sw.5 * g * Xm, sw.5 * Xb)
S21 <- t(S12)
S22 <- crossprod(sw.5 / sqrt(p * (1 - p)) * Xb)
rbind(cbind(S11, S12),
cbind(S21, S22)) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
p.score <- .fam$linkinv(drop(mod_covs %*% par))
}
else {
# Balance condition for ATT
psi_bal <- switch(estimand,
"ATT" = function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * ((A - p) / (1 - p)) * Xb
},
"ATC" = function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * ((A - p) / p) * Xb
})
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- glm.fit(mod_covs, treat, family = .fam, weights = s.weights)$coefficients
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_glm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
lp <- drop(Xm %*% B)
p <- .fam$linkinv(lp)
sw.5 <- sqrt(SW)
g <- .fam$mu.eta(lp) / .fam$variance(p)
S11 <- crossprod(sw.5 * g * sqrt(p * (1 - p)) * Xm)
S12 <- switch(estimand,
"ATT" = crossprod(sw.5 * g * Xm, sw.5 * p * Xb),
"ATC" = crossprod(sw.5 * g * Xm, sw.5 * (1 - p) * Xb))
S21 <- t(S12)
S22 <- switch(estimand,
"ATT" = crossprod(sw.5 * sqrt(p / (1 - p)) * Xb),
"ATC" = crossprod(sw.5 * sqrt((1 - p) / p) * Xb))
rbind(cbind(S11, S12),
cbind(S21, S22)) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
p.score <- .fam$linkinv(drop(mod_covs %*% par))
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
w <- .get_w_from_ps_internal_bin(p.score, treat, estimand = estimand,
subclass = subclass,
stabilize = stabilize)
Mparts <- NULL
if (!over) {
Mparts <- list(
psi_treat = function(Btreat, A, Xtreat, SW) {
psi_bal(Btreat, Xtreat, Xtreat, A, SW)
},
wfun = function(Btreat, Xtreat, A) {
ps <- .fam$linkinv(drop(Xtreat %*% Btreat))
.get_w_from_ps_internal_bin(ps, A, estimand = estimand,
subclass = subclass, stabilize = stabilize)
},
Xtreat = mod_covs,
A = treat,
btreat = par
)
}
list(w = w, ps = p.score, fit.obj = out,
Mparts = Mparts)
}
weightit2cbps.multi <- function(covs, treat, s.weights, estimand, focal, subset,
stabilize, subclass, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- factor(treat[subset])
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
focal = focal, treat = treat))
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
mod_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
bal_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e3 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
treat_num <- as.integer(treat)
K <- nlevels(treat)
kk <- seq_len(K)
coef_ind <- setNames(lapply(kk[-K], function(i) {
(i - 1) * ncol(mod_covs) + seq_len(ncol(mod_covs))
}), levels(treat)[-K])
get_pp <- function(B, Xm) {
qq <- lapply(kk[-K], function(i) {
exp(drop(Xm %*% B[coef_ind[[i]]]))
})
pden <- 1 + rowSums(do.call("cbind", qq))
out <- do.call("cbind", c(qq, list(1))) / pden
colnames(out) <- levels(treat)
out
}
#Multinomial logistic regression score
psi_mlr <- function(B, Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(levels(treat), function(i) {
SW * ((A == i) - pp[,i]) * Xm
}))
}
if (estimand == "ATE") {
combs <- utils::combn(levels(treat), 2, simplify = FALSE)
# combs <- lapply(kk, function(i) c(i, i - 1))
# Balance condition for ATE
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(combs, function(co) {
SW * ((A == co[1]) / pp[,co[1]] - (A == co[2]) / pp[,co[2]]) * Xb
}))
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- unlist(lapply(kk[-K], function(i) {
glm.fit(mod_covs, treat_num == i, family = binomial(), weights = s.weights)$coefficients
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, Xm = mod_covs, Xb = bal_covs,
A = treat, SW = s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_mlr(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
sw.5 <- sqrt(SW)
swXmXb <- crossprod(sw.5 * Xm, sw.5 * Xb)
S <- list()
for (i in levels(treat)) {
for (j in levels(treat)) {
S[[sprintf("m%s_m%s", i, j)]] <- {
if (i == j) crossprod(sw.5 * sqrt(pp[,i] * (1 - pp[,i])) * Xm)
else if (i < j) -crossprod(sw.5 * sqrt(pp[,i] * pp[,j]) * Xm)
else t(S[[sprintf("m%s_m%s", j, i)]])
}
}
}
for (i in levels(treat)) {
for (jj in combs) {
m <- {
if (i == jj[1]) swXmXb
else if (i == jj[2]) -swXmXb
else matrix(0, ncol(Xm), ncol(Xb))
}
S[[sprintf("m%s_b%s%s", i, jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_m%s", jj[1], jj[2], i)]] <- t(m)
}
}
for (ii in combs) {
for (jj in combs) {
m <- {
if (identical(ii, jj)) crossprod(sw.5 * sqrt(1 / pp[,ii[1]] + 1 / pp[,ii[2]]) * Xb)
else if (ii[1] == jj[1]) crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * Xb)
else if (ii[1] == jj[2]) -crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * Xb)
else if (ii[2] == jj[1]) -crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * Xb)
else if (ii[2] == jj[2]) crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * Xb)
else matrix(0, ncol(Xb), ncol(Xb))
}
S[[sprintf("b%s%s_b%s%s", ii[1], ii[2], jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_b%s%s", jj[1], jj[2], ii[1], ii[2])]] <- m
}
}
nms <- c(sprintf("m%s", levels(treat)), sprintf("b%s", vapply(combs, paste0, character(1L), collapse = "")))
do.call("rbind", lapply(nms, function(i) {
do.call("cbind", lapply(nms, function(j) {
S[[sprintf("%s_%s", i, j)]]
}))
})) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat_num, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
}
else {
# combs <- lapply(setdiff(levels(treat), focal), function(i) c(focal, i))
combs <- utils::combn(levels(treat), 2, simplify = FALSE)
# Balance condition for ATT
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(combs, function(co) {
SW * pp[,focal] * ((A == co[1]) / pp[,co[1]] - (A == co[2]) / pp[,co[2]]) * Xb
}))
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2)) #use sqrt to improve convergence
}
# Initialize coefs using logistic regression
par_glm <- unlist(lapply(kk[-K], function(i) {
glm.fit(mod_covs, treat_num == i, family = binomial(), weights = s.weights)$coefficients
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, Xm = mod_covs, Xb = bal_covs,
A = treat, SW = s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_mlr(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
sw.5 <- sqrt(SW)
swXmXb <- crossprod(sw.5 * Xm, sw.5 * pp[,focal] * Xb)
S <- list()
for (i in levels(treat)) {
for (j in levels(treat)) {
S[[sprintf("m%s_m%s", i, j)]] <- {
if (i == j) crossprod(sw.5 * sqrt(pp[,i] * (1 - pp[,i])) * Xm)
else if (i < j) -crossprod(sw.5 * sqrt(pp[,i] * pp[,j]) * Xm)
else t(S[[sprintf("m%s_m%s", j, i)]])
}
}
}
for (i in levels(treat)) {
for (jj in combs) {
m <- {
if (i == jj[1]) swXmXb
else if (i == jj[2]) -swXmXb
else matrix(0, ncol(Xm), ncol(Xb))
}
S[[sprintf("m%s_b%s%s", i, jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_m%s", jj[1], jj[2], i)]] <- t(m)
}
}
for (ii in combs) {
for (jj in combs) {
m <- {
if (identical(ii, jj)) crossprod(sw.5 * sqrt(1 / pp[,ii[1]] + 1 / pp[,ii[2]]) * pp[,focal] * Xb)
else if (ii[1] == jj[1]) crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * pp[,focal] * Xb)
else if (ii[1] == jj[2]) -crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * pp[,focal] * Xb)
else if (ii[2] == jj[1]) -crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * pp[,focal] * Xb)
else if (ii[2] == jj[2]) crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * pp[,focal] * Xb)
else matrix(0, ncol(Xb), ncol(Xb))
}
S[[sprintf("b%s%s_b%s%s", ii[1], ii[2], jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_b%s%s", jj[1], jj[2], ii[1], ii[2])]] <- m
}
}
nms <- c(sprintf("m%s", levels(treat)), sprintf("b%s", vapply(combs, paste0, character(1L), collapse = "")))
do.call("rbind", lapply(nms, function(i) {
do.call("cbind", lapply(nms, function(j) {
S[[sprintf("%s_%s", i, j)]]
}))
})) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar)) #use sqrt to improve convergence
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat_num, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
pp <- get_pp(par, mod_covs)
w <- .get_w_from_ps_internal_multi(pp, treat, estimand = estimand, subclass = subclass,
focal = focal, stabilize = stabilize)
out$pp <- pp
Mparts <- NULL
if (!over) {
Mparts <- list(
psi_treat = function(Btreat, A, Xtreat, SW) {
psi_bal(Btreat, Xtreat, Xtreat, A, SW)
},
wfun = function(Btreat, Xtreat, A) {
ps <- get_pp(Btreat, Xtreat)
.get_w_from_ps_internal_multi(ps, A, estimand = estimand, focal = focal,
subclass = subclass, stabilize = stabilize)
},
Xtreat = mod_covs,
A = treat,
btreat = par
)
}
list(w = w, fit.obj = out,
Mparts = Mparts)
}
weightit2cbps.cont <- function(covs, treat, s.weights, subset, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- treat[subset]
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE, orthogonal_poly = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
treat = treat))
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
treat <- (treat - w.m(treat, s.weights)) / sqrt(col.w.v(treat, s.weights))
covs <- scale(covs,
center = col.w.m(covs, s.weights),
scale = sqrt(col.w.v(covs, s.weights)))
mod_covs <- cbind(`(Intercept)` = 1,
scale(svd(covs)$u))
bal_covs <- mod_covs
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) (.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e4 else A$maxit
chk::chk_count(maxit)
s.weights <- s.weights / mean_fast(s.weights)
# dens.num <- dnorm(treat, log = TRUE)
#Linear regression score + score for marginal mean + var and conditional var
psi_lm <- function(B, Xm, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
s2 <- exp(B[3])
p <- drop(Xm %*% B[-(1:3)])
cbind(#SW * (A - un_p)^2 - un_s2,
#SW * (A - un_p),
#SW * (A - p)^2 - s2,
SW * (A - p) * Xm)
}
# un_s2 <- mean((treat - mean(treat)) ^ 2)
# un_p <- mean(treat)
squish_tol <- 25
# Balance condition
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
dens.num <- squish(dnorm(A, un_p, sqrt(un_s2), log = TRUE),
lo = -squish_tol, hi = squish_tol)
s2 <- exp(B[3])
p <- drop(Xm %*% B[-(1:3)])
dens.denom <- squish(dnorm(A, p, sqrt(s2), log = TRUE),
lo = -squish_tol, hi = squish_tol)
w <- exp(dens.num - dens.denom)
cbind(SW * (A - un_p)^2 - un_s2,
SW * (A - un_p),
SW * (A - p)^2 - s2,
# SW * (A - p),
# SW * w * Xm,
SW * w * A * Xm)
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
init.fit <- lm.wfit(mod_covs, treat, w = s.weights)
par_glm <- c(0, 0, log(var(init.fit$residuals)), init.fit$coefficients)
names(par_glm)[1:3] <- c("log(s^2)", "E[A]", "log(s_r^2)")
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_lm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
crossprod(psi(B, Xm, Xb, A, SW))
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
psi0 <- psi(B, Xm, Xb, A, SW)
if (is.null(invS)) {
invS <- generalized_inverse(crossprod(psi0))
}
gbar <- colMeans(psi0)
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
un_s2 <- exp(par[1])
un_p <- par[2]
dens.num <- dnorm(treat, un_p, sqrt(un_s2), log = TRUE)
s2 <- exp(par[3])
p <- drop(mod_covs %*% par[-(1:3)])
dens.denom <- dnorm(treat, p, sqrt(s2), log = TRUE)
w <- exp(dens.num - dens.denom)
Mparts <- NULL
list(w = w, fit.obj = out,
Mparts = Mparts)
}
weightitMSM2cbps <- function(covs.list, treat.list, s.weights, subset, missing, moments, int, verbose, ...) {
A <- list(...)
s.weights <- s.weights[subset]
treat.types <- character(length(treat.list))
for (i in seq_along(covs.list)) {
covs.list[[i]] <- covs.list[[i]][subset, , drop = FALSE]
treat.list[[i]] <- treat.list[[i]][subset]
if (missing == "ind") {
covs.list[[i]] <- add_missing_indicators(covs.list[[i]])
}
covs.list[[i]] <- cbind(covs.list[[i]], .int_poly_f(covs.list[[i]], poly = moments,
int = int, center = TRUE))
covs.list[[i]] <- cbind(covs.list[[i]], .quantile_f(covs.list[[i]], qu = A[["quantile"]],
s.weights = s.weights,
treat = treat.list[[i]]))
colinear.covs.to.remove <- setdiff(colnames(covs.list[[i]]), colnames(make_full_rank(covs.list[[i]])))
covs.list[[i]] <- covs.list[[i]][, colnames(covs.list[[i]]) %nin% colinear.covs.to.remove, drop = FALSE]
if (!has_treat_type(treat.list[[i]])) {
treat.list[[i]] <- assign_treat_type(treat.list[[i]])
}
treat.types[i] <- get_treat_type(treat.list[[i]])
treat.list[[i]] <- switch(
treat.types[i],
"binary" = binarize(treat.list[[i]], one = get_treated_level(treat.list[[i]])),
"multinomial" = factor(treat.list[[i]]),
"continuous"= (treat.list[[i]] - w.m(treat.list[[i]], s.weights)) / sqrt(col.w.v(treat.list[[i]], s.weights))
)
covs.list[[i]] <- cbind(`(Intercept)` = 1,
scale(svd(scale(covs.list[[i]],
center = col.w.m(covs.list[[i]], s.weights),
scale = sqrt(col.w.v(covs.list[[i]], s.weights))))$u))
}
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e4 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
coef_ind <- vector("list", length(treat.list))
for (i in seq_along(treat.list)) {
coef_ind[[i]] <- length(unlist(coef_ind)) + switch(
treat.types[i],
"binary" = seq_len(ncol(covs.list[[i]])),
"multinomial" = seq_len((nlevels(treat.list[[i]]) - 1) * ncol(covs.list[[i]])),
"continuous" = seq_len(3 + ncol(covs.list[[i]]))
)
}
get_p <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(B, X, A) {
plogis(drop(X %*% B))
},
"multinomial" = function(B, X, A) {
qq <- lapply(seq_len(nlevels(A) - 1), function(j) {
coef_ind_i <- (j - 1) * ncol(X) + seq_len(ncol(X))
exp(drop(X %*% B[coef_ind_i]))
})
pden <- 1 + rowSums(do.call("cbind", qq))
p <- do.call("cbind", c(qq, list(1))) / pden
colnames(p) <- levels(A)
p
},
"continuous" = function(B, X, A) {
drop(X %*% B[-(1:3)])
})
})
squish_tol <- 25
get_w <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(p, A, B) {
A / p + (1 - A) / (1 - p)
},
"multinomial" = function(p, A, B) {
w <- numeric(length(A))
for (a in levels(A)) {
w[A == a] <- 1 / p[A == a, a]
}
w
},
"continuous" = function(p, A, B) {
un_s2 <- exp(B[1])
un_p <- B[2]
dens.num <- squish(dnorm(A, un_p, sqrt(un_s2), log = TRUE),
lo = -Inf, hi = squish_tol)
s2 <- exp(B[3])
dens.denom <- squish(dnorm(A, p, sqrt(s2), log = TRUE),
lo = -squish_tol, hi = Inf)
exp(dens.num - dens.denom)
})
})
get_psi_bal <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(w, B, X, A, SW) {
SW * w * (A - (1 - A)) * X
},
"multinomial" = function(w, B, X, A, SW) {
do.call("cbind", lapply(utils::combn(levels(treat.list[[i]]), 2, simplify = FALSE), function(co) {
SW * w * ((A == co[1]) - (A == co[2])) * X
}))
},
"continuous" = function(w, B, X, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
s2 <- exp(B[3])
p <- drop(X %*% B[-(1:3)])
cbind(
SW * (A - un_p)^2 - un_s2,
SW * (A - un_p),
SW * (A - p)^2 - s2,
SW * w * A * X)
})
})
# Balance condition
psi_bal <- function(B, X.list, A.list, SW) {
w <- Reduce("*", lapply(seq_along(A.list), function(i) {
Bi <- B[coef_ind[[i]]]
p <- get_p[[i]](Bi, X.list[[i]], A.list[[i]])
get_w[[i]](p, A.list[[i]], Bi)
}), init = 1)
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_bal[[i]](w, B[coef_ind[[i]]], X.list[[i]], A.list[[i]], SW)
}))
}
obj_bal <- function(B, X.list, A.list, SW) {
gbar <- colMeans(psi_bal(B, X.list, A.list, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using GLMs
par_glm <- unlist(lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = glm.fit(covs.list[[i]], treat.list[[i]], family = binomial(),
weights = s.weights)$coefficients,
"multinomial" = unlist(lapply(seq_len(nlevels(treat.list[[i]]) - 1), function(j) {
glm.fit(covs.list[[i]], treat.list[[i]] == levels(treat.list[[i]])[j],
family = binomial(), weights = s.weights)$coefficients
})),
"continuous" = {
init.fit <- lm.wfit(covs.list[[i]], treat.list[[i]], w = s.weights)
b <- c(0, 0, log(var(init.fit$residuals)), init.fit$coefficients)
names(b)[1:3] <- c("log(s^2)", "E[A]", "log(s_r^2)")
b
})
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, covs.list, treat.list, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol,
trace = as.integer(verbose)),
X.list = covs.list,
A.list = treat.list,
SW = s.weights)
par <- out$par
if (over) {
get_psi_glm <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(p, X, A, SW) {
SW * (A - p) * X
},
"multinomial" = function(p, X, A, SW) {
do.call("cbind", lapply(levels(A), function(i) {
SW * ((A == i) - p[,i]) * X
}))
},
"continuous" = function(p, X, A, SW) {
SW * (A - p) * X
})
})
psi <- function(B, X.list, A.list, SW) {
p.list <- lapply(seq_along(A.list), function(i) {
get_p[[i]](B[coef_ind[[i]]], X.list[[i]], A.list[[i]])
})
w <- Reduce("*", lapply(seq_along(A.list), function(i) {
get_w[[i]](p.list[[i]], A.list[[i]], B[coef_ind[[i]]])
}), init = 1)
cbind(
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_bal[[i]](w, B[coef_ind[[i]]], X.list[[i]], A.list[[i]], SW)
})),
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_glm[[i]](p.list[[i]], X.list[[i]], A.list[[i]], SW)
}))
)
}
Sigma <- function(B, X.list, A.list, SW) {
crossprod(psi(B, X.list, A.list, SW))
}
obj <- function(B, X.list, A.list, SW, invS = NULL) {
psi0 <- psi(B, X.list, A.list, SW)
if (is.null(invS)) {
invS <- generalized_inverse(crossprod(psi0))
}
gbar <- colMeans(psi0)
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, covs.list, treat.list, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol,
trace = as.integer(verbose)),
X.list = covs.list,
A.list = treat.list,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
w <- Reduce("*", lapply(seq_along(treat.list), function(i) {
Bi <- par[coef_ind[[i]]]
p <- get_p[[i]](Bi, covs.list[[i]], treat.list[[i]])
get_w[[i]](p, treat.list[[i]], Bi)
}), init = 1)
Mparts <- NULL
list(w = w, fit.obj = out,
Mparts = Mparts)
}
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Defines functions weightit2cbps
#' Covariate Balancing Propensity Score Weighting
#' @name method_cbps
#' @aliases method_cbps
#' @usage NULL
#'
#' @description
#'
#' This page explains the details of estimating weights from covariate balancing propensity scores by setting `method = "cbps"` in the call to [weightit()] or [weightitMSM()]. This method can be used with binary, multi-category, and continuous treatments.
#'
#' In general, this method relies on estimating propensity scores using generalized method of moments and then converting those propensity scores into weights using a formula that depends on the desired estimand. This method relies on code written for \pkg{WeightIt} using [optim()].
#'
#' ## Binary Treatments
#'
#' For binary treatments, this method estimates the propensity scores and weights using `optim()` using formulas described by Imai and Ratkovic (2014). The following estimands are allowed: ATE, ATT, and ATC.
#'
#' ## Multi-Category Treatments
#'
#' For multi-category treatments, this method estimates the generalized propensity scores and weights using `optim()` using formulas described by Imai and Ratkovic (2014). The following estimands are allowed: ATE and ATT.
#'
#' ## Continuous Treatments
#'
#' For continuous treatments, this method estimates the generalized propensity scores and weights using `optim()` using a modification of the formulas described by Fong, Hazlett, and Imai (2018). See Details.
#'
#' ## Longitudinal Treatments
#'
#' For longitudinal treatments, the weights are computed using methods similar to those described by Huffman and van Gameren (2018). This involves specifying moment conditions for the models at each time point as with single-time point treatments but using the product of the time-specific weights as the weights that are used in the balance moment conditions. This yields weights that balance the covariate at each time point. This is not the same implementation as is implemented in `CBPS::CBMSM()`, and results should not be expected to align between the two methods. Any combination of treatment types is supported.
#'
#' For the over-identified version (i.e., setting `over = TRUE`), the empirical variance is used in the objective function, whereas the expected variance averaging over the treatment is used with binary and multi-category point treatments.
#'
#' ## Sampling Weights
#'
#' Sampling weights are supported through `s.weights` in all scenarios.
#'
#' ## Missing Data
#'
#' In the presence of missing data, the following value(s) for `missing` are allowed:
#' \describe{
#' \item{`"ind"` (default)}{
#' First, for each variable with missingness, a new missingness indicator variable is created which takes the value 1 if the original covariate is `NA` and 0 otherwise. The missingness indicators are added to the model formula as main effects. The missing values in the covariates are then replaced with the covariate medians (this value is arbitrary and does not affect estimation). The weight estimation then proceeds with this new formula and set of covariates. The covariates output in the resulting `weightit` object will be the original covariates with the `NA`s.
#' }
#' }
#'
#' ## M-estimation
#'
#' M-estimation is supported for the just-identified CBPS (the default, setting `over = FALSE`) for binary and multi-category treatments. See [glm_weightit()] and `vignette("estimating-effects")` for details.
#'
#' @section Additional Arguments:
#'
#' The following additional arguments can be specified:
#' \describe{
#' \item{`over`}{`logical`; whether to request the over-identified CBPS, which combines the generalized linear model regression score equations (for binary treatments), multinomial logistic regression score equations (for multi-category treatments), or linear regression score equations (for continuous treatments) to the balance moment conditions. Default is `FALSE` to use the just-identified CBPS.
#' }
#' \item{`twostep`}{`logical`; when `over = TRUE`, whether to use the two-step approximation to the generalized method of moments variance. Default is `TRUE`. Ignored when `over = FALSE`.
#' }
#' \item{`link`}{`"string"`; the link used in the generalized linear model for the propensity scores when treatment is binary. Default is `"logit"` for logistic regression, which is used in the original description of the method by Imai and Ratkovic (2014), but others are allowed: `"logit"`, `"probit"`, `"cauchit"`, and `"cloglog"` all use the binomial likelihood, `"log"` uses the Poisson likelihood, and `"identity"` uses the Gaussian likelihood (i.e., the linear probability model). Note that negative weights are possible with these last two and they should be used with caution. Ignored for multi-category, continuous, and longitudinal treatments.
#' }
#' \item{`reltol`}{the relative tolerance for convergence of the optimization. Passed to the `control` argument of `optim()`. Default is `sqrt(.Machine$double.eps)`.
#' }
#' \item{`maxit`}{the maximum number of iterations for convergence of the optimization. Passed to the `control` argument of `optim()`. Default is 1000.
#' }
#' }
#'
#' @section Additional Outputs:
#' \describe{
#' \item{`obj`}{When `include.obj = TRUE`, the output of the final call to `optim()` used to produce the model parameters. Note that because of variable transformations, the resulting parameter estimates may not be interpretable.
#' }
#' }
#'
#' @details
#' CBPS estimates the coefficients of a generalized linear model (for binary treatments), multinomial logistic regression model (for multi-category treatments), or linear regression model (for continuous treatments) that is used to compute (generalized) propensity scores, from which the weights are computed. It involves replacing (or augmenting, in the case of the over-identified version) the standard regression score equations with the balance constraints in a generalized method of moments estimation. The idea is to nudge the estimation of the coefficients toward those that produce balance in the weighted sample. The just-identified version (with `exact = FALSE`) does away with the score equations for the coefficients so that only the balance constraints are used. The just-identified version will therefore produce superior balance on the means (i.e., corresponding to the balance constraints) for binary and multi-category treatments and linear terms for continuous treatments than will the over-identified version.
#'
#' Just-identified CBPS is very similar to entropy balancing and inverse probability tilting. For the ATT, all three methods will yield identical estimates. For other estimands, the results will differ.
#'
#' Note that \pkg{WeightIt} provides different functionality from the \pkg{CBPS} package in terms of the versions of CBPS available; for extensions to CBPS (e.g., optimal CBPS and CBPS for instrumental variables), the \pkg{CBPS} package may be preferred. Note that for longitudinal treatments, `CBPS::CBMSM()` uses different methods and produces different results from `weightitMSM()` called with `method = "cbps"`.
#'
#' @note
#' This method used to rely on functionality in the \pkg{CBPS} package, but no longer does. Slight differences may be found between the two packages in some cases due to numerical imprecision (or, for continuous and longitudinal treatments, due to a difference in the estimator). \pkg{WeightIt} supports arbitrary numbers of groups for the multi-category CBPS and any estimand, whereas \pkg{CBPS} only supports up to four groups and only the ATE. The implementation of the just-identified CBPS for continuous treatments also differs from that of \pkg{CBPS}, and departs slightly from that described by Fong et al. (2018). The treatment mean and treatment variance are treated as random parameters to be estimated and are included in the balance moment conditions. In Fong et al. (2018), the treatment mean and variance are fixed to their empirical counterparts. For continuous treatments with the over-identified CBPS, \pkg{WeightIt} and \pkg{CBPS} use different methods of specifying the GMM variance matrix, which may lead to differing results.
#'
#' Note that the default method differs between the two implementations; by default \pkg{WeightIt} uses the just-identified CBPS, which is faster to fit, yields better balance, and is compatible with M-estimation for estimating the standard error of the treatment effect, whereas \pkg{CBPS} uses the over-identified CBPS by default. However, both the just-identified and over-identified versions are available in both packages.
#'
#' @seealso
#' [weightit()], [weightitMSM()]
#'
#' [method_ebal] and [method_ipt] for entropy balancing and inverse probability tilting, which work similarly.
#'
#' @references
#' ## Binary treatments
#'
#' Imai, K., & Ratkovic, M. (2014). Covariate balancing propensity score. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 76(1), 243–263.
#'
#' ## Multi-Category treatments
#'
#' Imai, K., & Ratkovic, M. (2014). Covariate balancing propensity score. *Journal of the Royal Statistical Society: Series B (Statistical Methodology)*, 76(1), 243–263.
#'
#' ## Continuous treatments
#'
#' Fong, C., Hazlett, C., & Imai, K. (2018). Covariate balancing propensity score for a continuous treatment: Application to the efficacy of political advertisements. *The Annals of Applied Statistics*, 12(1), 156–177. \doi{10.1214/17-AOAS1101}
#'
#' ## Longitudinal treatments
#'
#' Huffman, C., & van Gameren, E. (2018). Covariate Balancing Inverse Probability Weights for Time-Varying Continuous Interventions. *Journal of Causal Inference*, 6(2). \doi{10.1515/jci-2017-0002}
#'
#' Note: one should not cite Imai & Ratkovic (2015) when using CBPS for longitudinal treatments.
#'
#' Some of the code was inspired by the source code of the \pkg{CBPS} package.
#'
#' @examples
#' data("lalonde", package = "cobalt")
#'
#' #Balancing covariates between treatment groups (binary)
#' (W1a <- weightit(treat ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATT"))
#' summary(W1a)
#' cobalt::bal.tab(W1a)
#'
#' #Balancing covariates between treatment groups (binary)
#' #using over-identified CBPS with probit link
#' (W1b <- weightit(treat ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATT",
#' over = TRUE, link = "probit"))
#' summary(W1b)
#' cobalt::bal.tab(W1b)
#'
#' #Balancing covariates with respect to race (multi-category)
#' (W2 <- weightit(race ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps", estimand = "ATE"))
#' summary(W2)
#' cobalt::bal.tab(W2)
#'
#' #Balancing covariates with respect to re75 (continuous)
#' (W3 <- weightit(re75 ~ age + educ + married +
#' nodegree + re74, data = lalonde,
#' method = "cbps"))
#' summary(W3)
#' cobalt::bal.tab(W3)
#'
#' #Longitudinal treatments
#' data("msmdata")
#' (W4 <- weightitMSM(list(A_1 ~ X1_0 + X2_0,
#' A_2 ~ X1_1 + X2_1 +
#' A_1 + X1_0 + X2_0),
#' data = msmdata,
#' method = "cbps"))
#' summary(W4)
#' cobalt::bal.tab(W4)
NULL
weightit2cbps <- function(covs, treat, s.weights, estimand, focal, subset,
stabilize, subclass, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- treat[subset]
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
focal = focal, treat = treat))
t.lev <- get_treated_level(treat)
treat <- binarize(treat, one = t.lev)
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
mod_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
bal_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e3 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
if (is_null(A$link)) A$link <- "logit"
link <- A$link
chk::chk_string(link)
chk::chk_subset(link, c("logit", "probit", "cauchit", "cloglog", "log", "identity"))
.fam <- switch(link,
"log" = quasipoisson("log"),
"identity" = gaussian("identity"),
quasibinomial(link))
#Generalized linear model score
psi_glm <- function(B, Xm, A, SW) {
lin_pred <- drop(Xm %*% B)
p <- .fam$linkinv(lin_pred)
(SW * (A - p) * .fam$mu.eta(lin_pred) / .fam$variance(p)) * Xm
}
if (estimand == "ATE") {
# Balance condition for ATE
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * (A/p - (1-A)/(1-p)) * Xb
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- glm.fit(mod_covs, treat, family = .fam, weights = s.weights)$coefficients
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_glm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
lp <- drop(Xm %*% B)
p <- .fam$linkinv(lp)
sw.5 <- sqrt(SW)
g <- .fam$mu.eta(lp) / .fam$variance(p)
S11 <- crossprod(sw.5 * g * sqrt(p * (1 - p)) * Xm)
S12 <- crossprod(sw.5 * g * Xm, sw.5 * Xb)
S21 <- t(S12)
S22 <- crossprod(sw.5 / sqrt(p * (1 - p)) * Xb)
rbind(cbind(S11, S12),
cbind(S21, S22)) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
p.score <- .fam$linkinv(drop(mod_covs %*% par))
}
else {
# Balance condition for ATT
psi_bal <- switch(estimand,
"ATT" = function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * ((A - p) / (1 - p)) * Xb
},
"ATC" = function(B, Xm, Xb = Xm, A, SW) {
p <- .fam$linkinv(drop(Xm %*% B))
SW * ((A - p) / p) * Xb
})
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- glm.fit(mod_covs, treat, family = .fam, weights = s.weights)$coefficients
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_glm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
lp <- drop(Xm %*% B)
p <- .fam$linkinv(lp)
sw.5 <- sqrt(SW)
g <- .fam$mu.eta(lp) / .fam$variance(p)
S11 <- crossprod(sw.5 * g * sqrt(p * (1 - p)) * Xm)
S12 <- switch(estimand,
"ATT" = crossprod(sw.5 * g * Xm, sw.5 * p * Xb),
"ATC" = crossprod(sw.5 * g * Xm, sw.5 * (1 - p) * Xb))
S21 <- t(S12)
S22 <- switch(estimand,
"ATT" = crossprod(sw.5 * sqrt(p / (1 - p)) * Xb),
"ATC" = crossprod(sw.5 * sqrt((1 - p) / p) * Xb))
rbind(cbind(S11, S12),
cbind(S21, S22)) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
p.score <- .fam$linkinv(drop(mod_covs %*% par))
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
w <- .get_w_from_ps_internal_bin(p.score, treat, estimand = estimand,
subclass = subclass,
stabilize = stabilize)
Mparts <- NULL
if (!over) {
Mparts <- list(
psi_treat = function(Btreat, A, Xtreat, SW) {
psi_bal(Btreat, Xtreat, Xtreat, A, SW)
},
wfun = function(Btreat, Xtreat, A) {
ps <- .fam$linkinv(drop(Xtreat %*% Btreat))
.get_w_from_ps_internal_bin(ps, A, estimand = estimand,
subclass = subclass, stabilize = stabilize)
},
Xtreat = mod_covs,
A = treat,
btreat = par
)
}
list(w = w, ps = p.score, fit.obj = out,
Mparts = Mparts)
}
weightit2cbps.multi <- function(covs, treat, s.weights, estimand, focal, subset,
stabilize, subclass, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- factor(treat[subset])
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
focal = focal, treat = treat))
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
mod_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
bal_covs <- svd(cbind(`(Intercept)` = 1, scale(covs)))$u
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e3 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
treat_num <- as.integer(treat)
K <- nlevels(treat)
kk <- seq_len(K)
coef_ind <- setNames(lapply(kk[-K], function(i) {
(i - 1) * ncol(mod_covs) + seq_len(ncol(mod_covs))
}), levels(treat)[-K])
get_pp <- function(B, Xm) {
qq <- lapply(kk[-K], function(i) {
exp(drop(Xm %*% B[coef_ind[[i]]]))
})
pden <- 1 + rowSums(do.call("cbind", qq))
out <- do.call("cbind", c(qq, list(1))) / pden
colnames(out) <- levels(treat)
out
}
#Multinomial logistic regression score
psi_mlr <- function(B, Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(levels(treat), function(i) {
SW * ((A == i) - pp[,i]) * Xm
}))
}
if (estimand == "ATE") {
combs <- utils::combn(levels(treat), 2, simplify = FALSE)
# combs <- lapply(kk, function(i) c(i, i - 1))
# Balance condition for ATE
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(combs, function(co) {
SW * ((A == co[1]) / pp[,co[1]] - (A == co[2]) / pp[,co[2]]) * Xb
}))
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
par_glm <- unlist(lapply(kk[-K], function(i) {
glm.fit(mod_covs, treat_num == i, family = binomial(), weights = s.weights)$coefficients
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, Xm = mod_covs, Xb = bal_covs,
A = treat, SW = s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_mlr(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
sw.5 <- sqrt(SW)
swXmXb <- crossprod(sw.5 * Xm, sw.5 * Xb)
S <- list()
for (i in levels(treat)) {
for (j in levels(treat)) {
S[[sprintf("m%s_m%s", i, j)]] <- {
if (i == j) crossprod(sw.5 * sqrt(pp[,i] * (1 - pp[,i])) * Xm)
else if (i < j) -crossprod(sw.5 * sqrt(pp[,i] * pp[,j]) * Xm)
else t(S[[sprintf("m%s_m%s", j, i)]])
}
}
}
for (i in levels(treat)) {
for (jj in combs) {
m <- {
if (i == jj[1]) swXmXb
else if (i == jj[2]) -swXmXb
else matrix(0, ncol(Xm), ncol(Xb))
}
S[[sprintf("m%s_b%s%s", i, jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_m%s", jj[1], jj[2], i)]] <- t(m)
}
}
for (ii in combs) {
for (jj in combs) {
m <- {
if (identical(ii, jj)) crossprod(sw.5 * sqrt(1 / pp[,ii[1]] + 1 / pp[,ii[2]]) * Xb)
else if (ii[1] == jj[1]) crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * Xb)
else if (ii[1] == jj[2]) -crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * Xb)
else if (ii[2] == jj[1]) -crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * Xb)
else if (ii[2] == jj[2]) crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * Xb)
else matrix(0, ncol(Xb), ncol(Xb))
}
S[[sprintf("b%s%s_b%s%s", ii[1], ii[2], jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_b%s%s", jj[1], jj[2], ii[1], ii[2])]] <- m
}
}
nms <- c(sprintf("m%s", levels(treat)), sprintf("b%s", vapply(combs, paste0, character(1L), collapse = "")))
do.call("rbind", lapply(nms, function(i) {
do.call("cbind", lapply(nms, function(j) {
S[[sprintf("%s_%s", i, j)]]
}))
})) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat_num, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
}
else {
# combs <- lapply(setdiff(levels(treat), focal), function(i) c(focal, i))
combs <- utils::combn(levels(treat), 2, simplify = FALSE)
# Balance condition for ATT
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
do.call("cbind", lapply(combs, function(co) {
SW * pp[,focal] * ((A == co[1]) / pp[,co[1]] - (A == co[2]) / pp[,co[2]]) * Xb
}))
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2)) #use sqrt to improve convergence
}
# Initialize coefs using logistic regression
par_glm <- unlist(lapply(kk[-K], function(i) {
glm.fit(mod_covs, treat_num == i, family = binomial(), weights = s.weights)$coefficients
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, Xm = mod_covs, Xb = bal_covs,
A = treat, SW = s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_mlr(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
pp <- get_pp(B, Xm)
sw.5 <- sqrt(SW)
swXmXb <- crossprod(sw.5 * Xm, sw.5 * pp[,focal] * Xb)
S <- list()
for (i in levels(treat)) {
for (j in levels(treat)) {
S[[sprintf("m%s_m%s", i, j)]] <- {
if (i == j) crossprod(sw.5 * sqrt(pp[,i] * (1 - pp[,i])) * Xm)
else if (i < j) -crossprod(sw.5 * sqrt(pp[,i] * pp[,j]) * Xm)
else t(S[[sprintf("m%s_m%s", j, i)]])
}
}
}
for (i in levels(treat)) {
for (jj in combs) {
m <- {
if (i == jj[1]) swXmXb
else if (i == jj[2]) -swXmXb
else matrix(0, ncol(Xm), ncol(Xb))
}
S[[sprintf("m%s_b%s%s", i, jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_m%s", jj[1], jj[2], i)]] <- t(m)
}
}
for (ii in combs) {
for (jj in combs) {
m <- {
if (identical(ii, jj)) crossprod(sw.5 * sqrt(1 / pp[,ii[1]] + 1 / pp[,ii[2]]) * pp[,focal] * Xb)
else if (ii[1] == jj[1]) crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * pp[,focal] * Xb)
else if (ii[1] == jj[2]) -crossprod(sw.5 * sqrt(1 / pp[,ii[1]]) * pp[,focal] * Xb)
else if (ii[2] == jj[1]) -crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * pp[,focal] * Xb)
else if (ii[2] == jj[2]) crossprod(sw.5 * sqrt(1 / pp[,ii[2]]) * pp[,focal] * Xb)
else matrix(0, ncol(Xb), ncol(Xb))
}
S[[sprintf("b%s%s_b%s%s", ii[1], ii[2], jj[1], jj[2])]] <- m
S[[sprintf("b%s%s_b%s%s", jj[1], jj[2], ii[1], ii[2])]] <- m
}
}
nms <- c(sprintf("m%s", levels(treat)), sprintf("b%s", vapply(combs, paste0, character(1L), collapse = "")))
do.call("rbind", lapply(nms, function(i) {
do.call("cbind", lapply(nms, function(j) {
S[[sprintf("%s_%s", i, j)]]
}))
})) / N
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
if (is.null(invS)) {
invS <- generalized_inverse(Sigma(B, Xm, Xb, A, SW))
}
gbar <- colMeans(psi(B, Xm, Xb, A, SW))
sqrt(drop(t(gbar) %*% invS %*% gbar)) #use sqrt to improve convergence
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat_num, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
pp <- get_pp(par, mod_covs)
w <- .get_w_from_ps_internal_multi(pp, treat, estimand = estimand, subclass = subclass,
focal = focal, stabilize = stabilize)
out$pp <- pp
Mparts <- NULL
if (!over) {
Mparts <- list(
psi_treat = function(Btreat, A, Xtreat, SW) {
psi_bal(Btreat, Xtreat, Xtreat, A, SW)
},
wfun = function(Btreat, Xtreat, A) {
ps <- get_pp(Btreat, Xtreat)
.get_w_from_ps_internal_multi(ps, A, estimand = estimand, focal = focal,
subclass = subclass, stabilize = stabilize)
},
Xtreat = mod_covs,
A = treat,
btreat = par
)
}
list(w = w, fit.obj = out,
Mparts = Mparts)
}
weightit2cbps.cont <- function(covs, treat, s.weights, subset, missing, moments, int, verbose, ...) {
A <- list(...)
covs <- covs[subset, , drop = FALSE]
treat <- treat[subset]
s.weights <- s.weights[subset]
if (missing == "ind") {
covs <- add_missing_indicators(covs)
}
covs <- cbind(covs, .int_poly_f(covs, poly = moments, int = int, center = TRUE, orthogonal_poly = TRUE))
covs <- cbind(covs, .quantile_f(covs, qu = A[["quantile"]], s.weights = s.weights,
treat = treat))
colinear.covs.to.remove <- setdiff(colnames(covs), colnames(make_full_rank(covs)))
covs <- covs[, colnames(covs) %nin% colinear.covs.to.remove, drop = FALSE]
treat <- (treat - w.m(treat, s.weights)) / sqrt(col.w.v(treat, s.weights))
covs <- scale(covs,
center = col.w.m(covs, s.weights),
scale = sqrt(col.w.v(covs, s.weights)))
mod_covs <- cbind(`(Intercept)` = 1,
scale(svd(covs)$u))
bal_covs <- mod_covs
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) (.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e4 else A$maxit
chk::chk_count(maxit)
s.weights <- s.weights / mean_fast(s.weights)
# dens.num <- dnorm(treat, log = TRUE)
#Linear regression score + score for marginal mean + var and conditional var
psi_lm <- function(B, Xm, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
s2 <- exp(B[3])
p <- drop(Xm %*% B[-(1:3)])
cbind(#SW * (A - un_p)^2 - un_s2,
#SW * (A - un_p),
#SW * (A - p)^2 - s2,
SW * (A - p) * Xm)
}
# un_s2 <- mean((treat - mean(treat)) ^ 2)
# un_p <- mean(treat)
squish_tol <- 25
# Balance condition
psi_bal <- function(B, Xm, Xb = Xm, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
dens.num <- squish(dnorm(A, un_p, sqrt(un_s2), log = TRUE),
lo = -squish_tol, hi = squish_tol)
s2 <- exp(B[3])
p <- drop(Xm %*% B[-(1:3)])
dens.denom <- squish(dnorm(A, p, sqrt(s2), log = TRUE),
lo = -squish_tol, hi = squish_tol)
w <- exp(dens.num - dens.denom)
cbind(SW * (A - un_p)^2 - un_s2,
SW * (A - un_p),
SW * (A - p)^2 - s2,
# SW * (A - p),
# SW * w * Xm,
SW * w * A * Xm)
}
obj_bal <- function(B, Xm, Xb = Xm, A, SW) {
gbar <- colMeans(psi_bal(B, Xm, Xb, A, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using logistic regression
init.fit <- lm.wfit(mod_covs, treat, w = s.weights)
par_glm <- c(0, 0, log(var(init.fit$residuals)), init.fit$coefficients)
names(par_glm)[1:3] <- c("log(s^2)", "E[A]", "log(s_r^2)")
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, mod_covs, bal_covs, treat, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights)
par <- out$par
if (over) {
# Combine LR and balance
psi <- function(B, Xm, Xb = Xm, A, SW) {
cbind(psi_lm(B, Xm, A, SW), psi_bal(B, Xm, Xb, A, SW))
}
Sigma <- function(B, Xm, Xb = Xm, A, SW) {
crossprod(psi(B, Xm, Xb, A, SW))
}
obj <- function(B, Xm, Xb = Xm, A, SW, invS = NULL) {
psi0 <- psi(B, Xm, Xb, A, SW)
if (is.null(invS)) {
invS <- generalized_inverse(crossprod(psi0))
}
gbar <- colMeans(psi0)
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, mod_covs, bal_covs, treat, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol),
Xm = mod_covs,
Xb = bal_covs,
A = treat,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
un_s2 <- exp(par[1])
un_p <- par[2]
dens.num <- dnorm(treat, un_p, sqrt(un_s2), log = TRUE)
s2 <- exp(par[3])
p <- drop(mod_covs %*% par[-(1:3)])
dens.denom <- dnorm(treat, p, sqrt(s2), log = TRUE)
w <- exp(dens.num - dens.denom)
Mparts <- NULL
list(w = w, fit.obj = out,
Mparts = Mparts)
}
weightitMSM2cbps <- function(covs.list, treat.list, s.weights, subset, missing, moments, int, verbose, ...) {
A <- list(...)
s.weights <- s.weights[subset]
treat.types <- character(length(treat.list))
for (i in seq_along(covs.list)) {
covs.list[[i]] <- covs.list[[i]][subset, , drop = FALSE]
treat.list[[i]] <- treat.list[[i]][subset]
if (missing == "ind") {
covs.list[[i]] <- add_missing_indicators(covs.list[[i]])
}
covs.list[[i]] <- cbind(covs.list[[i]], .int_poly_f(covs.list[[i]], poly = moments,
int = int, center = TRUE))
covs.list[[i]] <- cbind(covs.list[[i]], .quantile_f(covs.list[[i]], qu = A[["quantile"]],
s.weights = s.weights,
treat = treat.list[[i]]))
colinear.covs.to.remove <- setdiff(colnames(covs.list[[i]]), colnames(make_full_rank(covs.list[[i]])))
covs.list[[i]] <- covs.list[[i]][, colnames(covs.list[[i]]) %nin% colinear.covs.to.remove, drop = FALSE]
if (!has_treat_type(treat.list[[i]])) {
treat.list[[i]] <- assign_treat_type(treat.list[[i]])
}
treat.types[i] <- get_treat_type(treat.list[[i]])
treat.list[[i]] <- switch(
treat.types[i],
"binary" = binarize(treat.list[[i]], one = get_treated_level(treat.list[[i]])),
"multinomial" = factor(treat.list[[i]]),
"continuous"= (treat.list[[i]] - w.m(treat.list[[i]], s.weights)) / sqrt(col.w.v(treat.list[[i]], s.weights))
)
covs.list[[i]] <- cbind(`(Intercept)` = 1,
scale(svd(scale(covs.list[[i]],
center = col.w.m(covs.list[[i]], s.weights),
scale = sqrt(col.w.v(covs.list[[i]], s.weights))))$u))
}
over <- if (is_null(A$over)) FALSE else A$over
chk::chk_logical(over)
twostep <- if (is_null(A$twostep)) TRUE else A$twostep
if (over) chk::chk_logical(twostep)
reltol <- if (is_null(A$reltol)) sqrt(.Machine$double.eps) else A$reltol
chk::chk_number(reltol)
maxit <- if (is_null(A$maxit)) 1e4 else A$maxit
chk::chk_count(maxit)
N <- sum(s.weights)
coef_ind <- vector("list", length(treat.list))
for (i in seq_along(treat.list)) {
coef_ind[[i]] <- length(unlist(coef_ind)) + switch(
treat.types[i],
"binary" = seq_len(ncol(covs.list[[i]])),
"multinomial" = seq_len((nlevels(treat.list[[i]]) - 1) * ncol(covs.list[[i]])),
"continuous" = seq_len(3 + ncol(covs.list[[i]]))
)
}
get_p <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(B, X, A) {
plogis(drop(X %*% B))
},
"multinomial" = function(B, X, A) {
qq <- lapply(seq_len(nlevels(A) - 1), function(j) {
coef_ind_i <- (j - 1) * ncol(X) + seq_len(ncol(X))
exp(drop(X %*% B[coef_ind_i]))
})
pden <- 1 + rowSums(do.call("cbind", qq))
p <- do.call("cbind", c(qq, list(1))) / pden
colnames(p) <- levels(A)
p
},
"continuous" = function(B, X, A) {
drop(X %*% B[-(1:3)])
})
})
squish_tol <- 25
get_w <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(p, A, B) {
A / p + (1 - A) / (1 - p)
},
"multinomial" = function(p, A, B) {
w <- numeric(length(A))
for (a in levels(A)) {
w[A == a] <- 1 / p[A == a, a]
}
w
},
"continuous" = function(p, A, B) {
un_s2 <- exp(B[1])
un_p <- B[2]
dens.num <- squish(dnorm(A, un_p, sqrt(un_s2), log = TRUE),
lo = -Inf, hi = squish_tol)
s2 <- exp(B[3])
dens.denom <- squish(dnorm(A, p, sqrt(s2), log = TRUE),
lo = -squish_tol, hi = Inf)
exp(dens.num - dens.denom)
})
})
get_psi_bal <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(w, B, X, A, SW) {
SW * w * (A - (1 - A)) * X
},
"multinomial" = function(w, B, X, A, SW) {
do.call("cbind", lapply(utils::combn(levels(treat.list[[i]]), 2, simplify = FALSE), function(co) {
SW * w * ((A == co[1]) - (A == co[2])) * X
}))
},
"continuous" = function(w, B, X, A, SW) {
un_s2 <- exp(B[1])
un_p <- B[2]
s2 <- exp(B[3])
p <- drop(X %*% B[-(1:3)])
cbind(
SW * (A - un_p)^2 - un_s2,
SW * (A - un_p),
SW * (A - p)^2 - s2,
SW * w * A * X)
})
})
# Balance condition
psi_bal <- function(B, X.list, A.list, SW) {
w <- Reduce("*", lapply(seq_along(A.list), function(i) {
Bi <- B[coef_ind[[i]]]
p <- get_p[[i]](Bi, X.list[[i]], A.list[[i]])
get_w[[i]](p, A.list[[i]], Bi)
}), init = 1)
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_bal[[i]](w, B[coef_ind[[i]]], X.list[[i]], A.list[[i]], SW)
}))
}
obj_bal <- function(B, X.list, A.list, SW) {
gbar <- colMeans(psi_bal(B, X.list, A.list, SW))
sqrt(sum(gbar^2))
}
# Initialize coefs using GLMs
par_glm <- unlist(lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = glm.fit(covs.list[[i]], treat.list[[i]], family = binomial(),
weights = s.weights)$coefficients,
"multinomial" = unlist(lapply(seq_len(nlevels(treat.list[[i]]) - 1), function(j) {
glm.fit(covs.list[[i]], treat.list[[i]] == levels(treat.list[[i]])[j],
family = binomial(), weights = s.weights)$coefficients
})),
"continuous" = {
init.fit <- lm.wfit(covs.list[[i]], treat.list[[i]], w = s.weights)
b <- c(0, 0, log(var(init.fit$residuals)), init.fit$coefficients)
names(b)[1:3] <- c("log(s^2)", "E[A]", "log(s_r^2)")
b
})
}))
# Slightly improve glm coefs to move closer to optimal
alpha.func <- function(alpha) obj_bal(par_glm * alpha, covs.list, treat.list, s.weights)
par_alpha <- par_glm * optimize(alpha.func, interval = c(.8, 1.1))$min
# Optimize balance objective
out <- optim(par = par_alpha,
fn = obj_bal,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol,
trace = as.integer(verbose)),
X.list = covs.list,
A.list = treat.list,
SW = s.weights)
par <- out$par
if (over) {
get_psi_glm <- lapply(seq_along(treat.list), function(i) {
switch(treat.types[i],
"binary" = function(p, X, A, SW) {
SW * (A - p) * X
},
"multinomial" = function(p, X, A, SW) {
do.call("cbind", lapply(levels(A), function(i) {
SW * ((A == i) - p[,i]) * X
}))
},
"continuous" = function(p, X, A, SW) {
SW * (A - p) * X
})
})
psi <- function(B, X.list, A.list, SW) {
p.list <- lapply(seq_along(A.list), function(i) {
get_p[[i]](B[coef_ind[[i]]], X.list[[i]], A.list[[i]])
})
w <- Reduce("*", lapply(seq_along(A.list), function(i) {
get_w[[i]](p.list[[i]], A.list[[i]], B[coef_ind[[i]]])
}), init = 1)
cbind(
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_bal[[i]](w, B[coef_ind[[i]]], X.list[[i]], A.list[[i]], SW)
})),
do.call("cbind", lapply(seq_along(A.list), function(i) {
get_psi_glm[[i]](p.list[[i]], X.list[[i]], A.list[[i]], SW)
}))
)
}
Sigma <- function(B, X.list, A.list, SW) {
crossprod(psi(B, X.list, A.list, SW))
}
obj <- function(B, X.list, A.list, SW, invS = NULL) {
psi0 <- psi(B, X.list, A.list, SW)
if (is.null(invS)) {
invS <- generalized_inverse(crossprod(psi0))
}
gbar <- colMeans(psi0)
sqrt(drop(t(gbar) %*% invS %*% gbar))
}
invS <- {
if (twostep) generalized_inverse(Sigma(par_alpha, covs.list, treat.list, s.weights))
else NULL
}
out <- lapply(list(par_alpha, par), function(par_) {
optim(par = par_,
fn = obj,
method = "BFGS",
control = list(maxit = maxit,
reltol = reltol,
trace = as.integer(verbose)),
X.list = covs.list,
A.list = treat.list,
SW = s.weights,
invS = invS)
})
out <- out[[which.min(unlist(grab(out, "value")))]]
par <- out$par
}
if (out$converge != 0) {
.wrn("the optimziation failed to converge; try again with a higher value of `maxit`")
}
w <- Reduce("*", lapply(seq_along(treat.list), function(i) {
Bi <- par[coef_ind[[i]]]
p <- get_p[[i]](Bi, covs.list[[i]], treat.list[[i]])
get_w[[i]](p, treat.list[[i]], Bi)
}), init = 1)
Mparts <- NULL
list(w = w, fit.obj = out,
Mparts = Mparts)
}
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