Residual balancing is a method of constructing weights for marginal structural models, which can be used to estimate marginal effects of time-varying treatments and controlled direct/mediator effects in causal mediation analysis. Compared with inverse probability-of-treatment weights (IPW), residual balancing weights tend to be more robust and more efficient, and are easier to use with continuous exposures. This package provides three main functions, rbwPoint(), rbwPanel() and rbwMed(), that produce residual balancing weights for analyzing point treatments, time-varying treatments, and causal mediation, respectively.
Reference
You can install the released version of rbw from CRAN with:
And the development version from GitHub with:
The rbwPoint() function constructs residual balancing weights for estimating the average effect of a point treatment. The following example illustrates its use by estimating the average effect of televised political advertisements (treat) on campaign contributions (Cont) among 16,265 zipcodes in the 2004 and 2008 US presidential elections.
library(rbw)
# install.packages("survey")
library(survey)
# residual balancing weights
rbwPoint_fit <- rbwPoint(treat, baseline_x = c(log_TotalPop, PercentOver65, log_Inc, PercentHispanic, PercentBlack, density, per_collegegrads, CanCommute), data = advertisement)
#> Entropy minimization converged within tolerance level
# attach residual balancing weights to data
advertisement$rbw_point <- rbwPoint_fit$weights
# fit marginal structural model
rbw_design <- svydesign(ids = ~ 1, weights = ~ rbw_point, data = advertisement)
# the outcome model includes the treatment, the square of the treatment,
# and state-level fixed effects (Fong, Hazlett, and Imai 2018)
msm_rbwPoint <- svyglm(Cont ~ treat + I(treat^2) + factor(StFIPS), design = rbw_design)
summary(msm_rbwPoint)
#>
#> Call:
#> svyglm(formula = Cont ~ treat + I(treat^2) + factor(StFIPS),
#> design = rbw_design)
#>
#> Survey design:
#> svydesign(ids = ~1, weights = ~rbw_point, data = advertisement)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 3.57549 2.79045 1.281 0.200095
#> treat 0.43986 1.70909 0.257 0.796901
#> I(treat^2) 0.01552 0.16555 0.094 0.925332
#> factor(StFIPS)5 -1.25821 1.07914 -1.166 0.243656
#> factor(StFIPS)6 64.54555 5.42773 11.892 < 2e-16 ***
#> factor(StFIPS)10 12.25245 6.06566 2.020 0.043403 *
#> factor(StFIPS)13 11.14059 2.98022 3.738 0.000186 ***
#> factor(StFIPS)17 20.98707 4.37924 4.792 1.66e-06 ***
#> factor(StFIPS)20 -1.89078 1.17473 -1.610 0.107516
#> factor(StFIPS)21 -1.75188 1.21534 -1.441 0.149469
#> factor(StFIPS)23 -2.07515 1.60297 -1.295 0.195489
#> factor(StFIPS)24 36.79553 8.26927 4.450 8.66e-06 ***
#> factor(StFIPS)25 48.39716 7.34165 6.592 4.47e-11 ***
#> factor(StFIPS)27 2.31899 2.11116 1.098 0.272027
#> factor(StFIPS)28 -0.11943 1.25105 -0.095 0.923948
#> factor(StFIPS)30 -4.49525 1.58284 -2.840 0.004517 **
#> factor(StFIPS)31 -3.16796 1.00206 -3.161 0.001573 **
#> factor(StFIPS)34 23.32090 4.04985 5.758 8.64e-09 ***
#> factor(StFIPS)36 29.47346 4.29735 6.859 7.21e-12 ***
#> factor(StFIPS)40 0.58593 1.16360 0.504 0.614588
#> factor(StFIPS)45 1.14183 1.46973 0.777 0.437230
#> factor(StFIPS)46 -4.75496 1.99265 -2.386 0.017033 *
#> factor(StFIPS)47 5.66276 1.84947 3.062 0.002203 **
#> factor(StFIPS)48 18.32801 2.37261 7.725 1.19e-14 ***
#> factor(StFIPS)50 -0.50451 1.93071 -0.261 0.793860
#> factor(StFIPS)56 2.17016 3.10951 0.698 0.485244
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 13738.91)
#>
#> Number of Fisher Scoring iterations: 2The rbwPanel() function constructs residual balancing weights for estimating marginal effects of time-varying treatments. The following example illustrates its use by estimating the effect of negative campaign advertising (d.gone.neg) on election outcomes (demprcnt) for 113 Democratic candidates in US Senate and Gubernatorial elections.
# models for time-varying confounders
m1 <- lm(dem.polls ~ (d.gone.neg.l1 + dem.polls.l1 + undother.l1) * factor(week), data = campaign_long)
m2 <- lm(undother ~ (d.gone.neg.l1 + dem.polls.l1 + undother.l1) * factor(week), data = campaign_long)
xmodels <- list(m1, m2)
# residual balancing weights
rbwPanel_fit <- rbwPanel(treatment = d.gone.neg, xmodels = xmodels, id = id, time = week, data = campaign_long)
#> Entropy minimization converged within tolerance level
# merge weights into wide-format data
campaign_wide2 <- merge(campaign_wide, rbwPanel_fit$weights, by = "id")
# fit a marginal structural model (adjusting for baseline confounders)
rbw_design <- svydesign(ids = ~ 1, weights = ~ rbw, data = campaign_wide2)
msm_rbw <- svyglm(demprcnt ~ cum_neg * deminc + camp.length + factor(year) + office, design = rbw_design)
summary(msm_rbw)
#>
#> Call:
#> svyglm(formula = demprcnt ~ cum_neg * deminc + camp.length +
#> factor(year) + office, design = rbw_design)
#>
#> Survey design:
#> svydesign(ids = ~1, weights = ~rbw, data = campaign_wide2)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 50.39769 2.52269 19.978 < 2e-16 ***
#> cum_neg 0.96579 0.45496 2.123 0.036143 *
#> deminc 17.04229 2.66426 6.397 4.62e-09 ***
#> camp.length -0.09085 0.06175 -1.471 0.144222
#> factor(year)2002 -5.57359 1.53081 -3.641 0.000425 ***
#> factor(year)2004 -6.22630 1.67340 -3.721 0.000322 ***
#> factor(year)2006 -1.51220 1.93697 -0.781 0.436751
#> office 0.02811 1.11988 0.025 0.980026
#> cum_neg:deminc -2.99678 0.65932 -4.545 1.49e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 25.21453)
#>
#> Number of Fisher Scoring iterations: 2In causal mediation analysis, the rbwMed() function can be used to construct residual balancing weights for estimating the controlled direct effect or the controlled mediator effect with a marginal structural model. The following example illustrates its use by estimating the controlled direct effect of shared democracy (democ) on public support for war (strike) at different levels of perceived morality of war (immoral) for a sample of respondents in a survey experiment.
# models for post-treatment confounders
m1 <- lm(threatc ~ ally + trade + h1 + i1 + p1 + e1 + r1 +
male + white + age + ed4 + democ, data = peace)
m2 <- lm(cost ~ ally + trade + h1 + i1 + p1 + e1 + r1 +
male + white + age + ed4 + democ, data = peace)
m3 <- lm(successc ~ ally + trade + h1 + i1 + p1 + e1 + r1 +
male + white + age + ed4 + democ, data = peace)
# residual balancing weights
rbwMed_fit <- rbwMed(treatment = democ, mediator = immoral,
zmodels = list(m1, m2, m3), interact = TRUE,
baseline_x = c(ally, trade, h1, i1, p1, e1, r1, male, white, age, ed4),
data = peace)
#> Entropy minimization converged within tolerance level
# attach residual balancing weights to data
peace$rbw_cde <- rbwMed_fit$weights
# fit marginal structural model
rbw_design <- svydesign(ids = ~ 1, weights = ~ rbw_cde, data = peace)
msm_rbwMed <- svyglm(strike ~ democ * immoral, design = rbw_design)
summary(msm_rbwMed)
#>
#> Call:
#> svyglm(formula = strike ~ democ * immoral, design = rbw_design)
#>
#> Survey design:
#> svydesign(ids = ~1, weights = ~rbw_cde, data = peace)
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 2.74428 0.06255 43.875 < 2e-16 ***
#> democ -0.37399 0.09893 -3.780 0.000164 ***
#> immoral -1.36569 0.15082 -9.055 < 2e-16 ***
#> democ:immoral 0.09091 0.19782 0.460 0.645899
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for gaussian family taken to be 1.384994)
#>
#> Number of Fisher Scoring iterations: 2