Function to implement permutation test for Distributional Synthetic Controls
Usage
DiSCo_per(
results.periods,
T0,
ww = 0,
peridx = 0,
evgrid = seq(from = 0, to = 1, length.out = 101),
graph = TRUE,
num.cores = 1,
weights = NULL,
qmethod = NULL,
qtype = qtype,
q_min = 0,
q_max = 1,
M = 1000,
simplex = FALSE,
mixture = FALSE
)Arguments
- results.periods
List of period-specific results from DiSCo
- T0
Integer indicating first year of treatment as counted from 1 (e.g, if treatment year 2002 was the 5th year in the sample, this parameter should be 5).
- ww
Optional vector of weights indicating the relative importance of each time period. If not specified, each time period is weighted equally.
- peridx
Optional integer indicating number of permutations. If not specified, by default equal to the number of units in the sample.
- graph
Logical, indicating whether to plot the permutation graph as in Figure 3 of the paper. Default is FALSE.
- num.cores
Integer, number of cores to use for parallel computation. Default is 1. If the
permutationorCIarguments are set to TRUE, this can be slow and it is recommended to set this to 4 or more, if possible. If you get an error in "all cores" or similar, try setting num.cores=1 to see the precise error value.- weights
Optional vector of weights to use for the "true" treated unit.
redo_weightshas to be set to FALSE for these weights to be used.- qmethod
Character, indicating the method to use for computing the quantiles of the target distribution. The default is NULL, which uses the
quantilefunction from the stats package. Other options are "qkden" (based on smoothed kernel density function) and "extreme" (based on parametric extreme value distributions). Both are substantially slower than the default method but may be useful for fat-tailed distributions with few data points at the upper quantiles. Alternatively, one could use the q_max option to restrict the range of quantiles used.- qtype
Integer, indicating the type of quantile to compute when using
quantilein theqmethodargument. The default 7. See the documentation for thequantilefunction for more information.- q_min
Numeric, minimum quantile to use. Set this together with
q_maxto restrict the range of quantiles used to construct the synthetic control. Default is 0 (all quantiles). Currently NOT implemented for themixtureapproach.- q_max
Numeric, maximum quantile to use. Set this together with
q_minto restrict the range of quantiles used to construct the synthetic control. Default is 1 (all quantiles). Currently NOT implemented for themixtureapproach.- M
Integer indicating the number of control quantiles to use in the DiSCo method. Default is 1000.
- simplex
Logical, indicating whether to use to constrain the optimal weights to the unit simplex. Default is FALSE, which only constrains the weights to sum up to 1 but allows them to be negative.
- mixture
Logical, indicating whether to use the mixture of distributions approach instead. See Section 4.3. in Gunsilius (2023) . This approach minimizes the distance between the CDFs instead of the quantile functions, and is preferred for categorical variables. When working with such variables, one should also provide a list of support points in the
grid.catparameter. When that is provided, this parameter is automatically set to TRUE. Default is FALSE.
Value
List of matrices containing synthetic time path of the outcome variable for the target unit together with the time paths of the control units
Details
This program iterates through all units and computes the optimal weights on the other units for replicating the unit of iteration's outcome variable, assuming that it is the treated unit. See Algorithm 1 in Gunsilius (2023) for more details. The only modification is that we take the ratio of post- and pre-treatment root mean squared Wasserstein distances to calculate the p-value, rather than the level in each period, following @abadie2010synthetic.