difference_in_means: Design-based difference-in-means estimator

Description

Difference-in-means estimators that selects the appropriate point estimate, standard errors, and degrees of freedom for a variety of designs: unit randomized, cluster randomized, block randomized, block-cluster randomized, matched-pairs, and matched-pair cluster randomized designs

Usage

difference_in_means(
  formula,
  data,
  blocks,
  clusters,
  weights,
  subset,
  se_type = c("default", "none"),
  condition1 = NULL,
  condition2 = NULL,
  ci = TRUE,
  alpha = 0.05
)

Value

Returns an object of class "difference_in_means".

The post-estimation commands functions summary and tidy

return results in a data.frame. To get useful data out of the return, you can use these data frames, you can use the resulting list directly, or you can use the generic accessor functions coef and confint.

An object of class "difference_in_means" is a list containing at least the following components:

coefficients: the estimated difference in means
std.error: the estimated standard error
statistic: the t-statistic
df: the estimated degrees of freedom
p.value: the p-value from a two-sided t-test using coefficients, std.error, and df
conf.low: the lower bound of the 1 - alpha percent confidence interval
conf.high: the upper bound of the 1 - alpha percent confidence interval
term: a character vector of coefficient names
alpha: the significance level specified by the user
N: the number of observations used
outcome: the name of the outcome variable
design: the name of the design learned from the arguments passed

Arguments

formula: an object of class formula, as in lm, such as Y ~ Z with only one variable on the right-hand side, the treatment.
data: A data.frame.
blocks: An optional bare (unquoted) name of the block variable. Use for blocked designs only.
clusters: An optional bare (unquoted) name of the variable that corresponds to the clusters in the data; used for cluster randomized designs. For blocked designs, clusters must nest within blocks.
weights: the bare (unquoted) names of the weights variable in the supplied data.
subset: An optional bare (unquoted) expression specifying a subset of observations to be used.
se_type: An optional string that can be one of c("default", "none"). If "default" (the default), it will use the default standard error estimator for the design, and if "none" then standard errors will not be computed which may speed up run time if only the point estimate is required.
condition1: value in the treatment vector of the condition to be the control. Effects are estimated with condition1 as the control and condition2 as the treatment. If unspecified, condition1 is the "first" condition and condition2 is the "second" according to levels if the treatment is a factor or according to a sortif it is a numeric or character variable (i.e if unspecified and the treatment is 0s and 1s, condition1 will by default be 0 and condition2 will be 1). See the examples for more.
condition2: value in the treatment vector of the condition to be the treatment. See condition1.
ci: logical. Whether to compute and return p-values and confidence intervals, TRUE by default.
alpha: The significance level, 0.05 by default.

Details

This function implements a difference-in-means estimator, with support for blocked, clustered, matched-pairs, block-clustered, and matched-pair clustered designs. One specifies their design by passing the blocks and clusters in their data and this function chooses which estimator is most appropriate.

If you pass only blocks, if all blocks are of size two, we will infer that the design is a matched-pairs design. If they are all size four or larger, we will infer that it is a regular blocked design. If you pass both blocks and clusters, we will similarly infer whether it is a matched-pairs clustered design or a block-clustered design the number of clusters per block. If the user passes only clusters, we will infer that the design was cluster-randomized. If the user specifies neither the blocks nor the clusters, a regular Welch's t-test will be performed.

Importantly, if the user specifies weights, the estimation is handed off to lm_robust with the appropriate robust standard errors as weighted difference-in-means estimators are not implemented here. More details of the about each of the estimators can be found in the mathematical notes.

References

Gerber, Alan S, and Donald P Green. 2012. Field Experiments: Design, Analysis, and Interpretation. New York: W.W. Norton.

Imai, Kosuke, Gary King, Clayton Nall. 2009. "The Essential Role of Pair Matching in Cluster-Randomized Experiments, with Application to the Mexican Universal Health Insurance Evaluation." Statistical Science 24 (1). Institute of Mathematical Statistics: 29-53. tools:::Rd_expr_doi("10.1214/08-STS274").

Examples

Run this code


library(fabricatr)
library(randomizr)
# Get appropriate standard errors for unit-randomized designs

# ----------
# 1. Unit randomized
# ----------
dat <- fabricate(
  N = 100,
  Y = rnorm(100),
  Z_comp = complete_ra(N, prob = 0.4),
)

table(dat$Z_comp)
difference_in_means(Y ~ Z_comp, data = dat)

# ----------
# 2. Cluster randomized
# ----------
# Accurates estimates and standard errors for clustered designs
dat$clust <- sample(20, size = nrow(dat), replace = TRUE)
dat$Z_clust <- cluster_ra(dat$clust, prob = 0.6)

table(dat$Z_clust, dat$clust)
summary(difference_in_means(Y ~ Z_clust, clusters = clust, data = dat))

# ----------
# 3. Block randomized
# ----------
dat$block <- rep(1:10, each = 10)
dat$Z_block <- block_ra(dat$block, prob = 0.5)

table(dat$Z_block, dat$block)
difference_in_means(Y ~ Z_block, blocks = block, data = dat)

# ----------
# 4. Block cluster randomized
# ----------
# Learns this design if there are two clusters per block
dat$small_clust <- rep(1:50, each = 2)
dat$big_blocks <- rep(1:5, each = 10)

dat$Z_blcl <- block_and_cluster_ra(
  blocks = dat$big_blocks,
  clusters = dat$small_clust
 )

difference_in_means(
  Y ~ Z_blcl,
  blocks = big_blocks,
  clusters = small_clust,
  data = dat
 )

# ----------
# 5. Matched-pairs
# ----------
# Matched-pair estimates and standard errors are also accurate
# Specified same as blocked design, function learns that
# it is matched pair from size of blocks!
dat$pairs <- rep(1:50, each = 2)
dat$Z_pairs <- block_ra(dat$pairs, prob = 0.5)

table(dat$pairs, dat$Z_pairs)
difference_in_means(Y ~ Z_pairs, blocks = pairs, data = dat)

# ----------
# 6. Matched-pair cluster randomized
# ----------
# Learns this design if there are two clusters per block
dat$small_clust <- rep(1:50, each = 2)
dat$cluster_pairs <- rep(1:25, each = 4)
table(dat$cluster_pairs, dat$small_clust)

dat$Z_mpcl <- block_and_cluster_ra(
  blocks = dat$cluster_pairs,
  clusters = dat$small_clust
 )

difference_in_means(
  Y ~ Z_mpcl,
  blocks = cluster_pairs,
  clusters = small_clust,
  data = dat
 )

# ----------
# Other examples
# ----------

# Also works with multi-valued treatments if users specify
# comparison of interest
dat$Z_multi <- simple_ra(
  nrow(dat),
  conditions = c("Treatment 2", "Treatment 1", "Control"),
  prob_each = c(0.4, 0.4, 0.2)
)

# Only need to specify which condition is treated `condition2` and
# which is control `condition1`
difference_in_means(
  Y ~ Z_multi,
  condition1 = "Treatment 2",
  condition2 = "Control",
  data = dat
)
difference_in_means(
  Y ~ Z_multi,
  condition1 = "Treatment 1",
  condition2 = "Control",
  data = dat
)

# Specifying weights will result in estimation via lm_robust()
dat$w <- runif(nrow(dat))
difference_in_means(Y ~ Z_comp, weights = w, data = dat)
lm_robust(Y ~ Z_comp, weights = w, data = dat)

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