generate_weights {tidysynth}

generate_weights

Description

Generates weights from the the aggregate-level predictors to generate the synthetic control. These weights determine which variable and which unit from the donor pool is important in generating the synthetic control.

Usage

generate_weights(
  data,
  optimization_window = NULL,
  custom_variable_weights = NULL,
  include_fit = FALSE,
  optimization_method = c("Nelder-Mead", "BFGS"),
  genoud = FALSE,
  quadopt = "ipop",
  margin_ipop = 5e-04,
  sigf_ipop = 5,
  bound_ipop = 10,
  verbose = FALSE,
  ...
)

Arguments

data

nested data of type tbl_df generated from sythetic_control(). See synthetic_control() documentation for more information. In addition, a matrix of predictors must be prespecified using the generate_predictor() function. See documentation for more information on how to generate a predictor function.

optimization_window

the temporal window of the pre-intervention outcome time series to be used in the optimization task. Default behavior uses the entire pre-intervention time period.

custom_variable_weights

a vector of provided weights that define a variable's importance in the optimization task. The weights are intended to reflect the users prior regarding the relative significance of each variable. Vector must sum to one. Note that the method is significantly faster when a custom variable weights are provided. Default behavior assumes no wieghts are provided and thus must be learned from the data.

include_fit

Boolean flag, if TRUE, then the optimization output is included in the outputted tbl_df.

optimization_method

string vector that specifies the optimization algorithms to be used. Permissable values are all optimization algorithms that are currently implemented in the optimx function (see this function for details). This list currently includes c('Nelder-Mead', 'BFGS', 'CG', 'L-BFGS-B', 'nlm', 'nlminb', 'spg', and 'ucminf"). If multiple algorithms are specified, synth will run the optimization with all chosen algorithms and then return the result for the best performing method. Default is c('Nelder-Mead','BFGS'). As an additional possibility, the user can also specify 'All' which means that synth will run the results over all algorithms in optimx.

genoud

Logical flag. If true, synth embarks on a two step optimization. In the first step, genoud, an optimization function that combines evolutionary algorithm methods with a derivative-based (quasi-Newton) method to solve difficult optimization problems, is used to obtain a solution. See genoud for details. In the second step, the genoud results are passed to the optimization algorithm(s) chosen in optimxmethod for a local optimization within the neighborhood of the genoud solution. This two step optimization procedure will require much more computing time, but may yield lower loss in cases where the search space is highly irregular.

quadopt

string vector that specifies the routine for quadratic optimization over w weights. possible values are "ipop" and "LowRankQP" (see ipop and LowRankQP for details). default is 'ipop'

margin_ipop

setting for ipop optimization routine: how close we get to the constrains (see ipop for details)

sigf_ipop

setting for ipop optimization routine: Precision (default: 7 significant figures (see ipop for details)

bound_ipop

setting for ipop optimization routine: Clipping bound for the variables (see ipop for details)

verbose

Logical flag. If TRUE then intermediate results will be shown.

...

Additional arguments to be passed to optimx and or genoud to adjust optimization.

Details

Optimization

The method completes the following nested minimization task:

W^*(V) = min \sum^M_{m=1} v_m (X_{1m} - \sum^{J+1}_{j=2}w_j X_{jm})^2

Where X_1 and X_0, which are matrices of aggregate-level covariates, are generated using the generate_predictor() function. V denotes the variable weights with M reflecting the total number of predictor variables. Thus, the optimal weights are a function of V.

The weights themselves are optimized via the following:

\sum^{T_0}_{t=1}(Y_{1t} - \sum^{J=1}_{j=2}w^*_j(V)Y_{jt})^2

where T_0 denotes the pre-intervention period (or a specific optimization window supplied by the argument time_window); J denotes the number of control units from the donor pool, where j=1 reflects the treated unit.

Thus, the weights are selected in a manner that produces a synthetic \hat{Y} that approximates the observed Y as closely as possible.

Variable Weights

As proposed in Abadie and Gardeazabal (2003) and Abadie, Diamond, Hainmueller (2010), the synth function routinely searches for the set of weights that generate the best fitting convex combination of the control units. In other words, the predictor weight matrix V (custom_variable_weights) is chosen among all positive definite diagonal matrices such that MSPE is minimized for the pre-intervention period. Instead of using this data-driven procedures to search for the best fitting synthetic control group, the user may supply their own weights using the custom_variable_weights argument. These weights reflect the user's subjective assessment of the predictive power of the variables generated by generate_predictor().

When generating weights for the placebo cases, the variable weights used for the fit of the treated unit optimization. This ensures comparability between the placebo and treated fits. In addition, it greatly decreases processing time as the variable weights do not be learned for every placebo entry.

Value

tbl_df with nested fields containing the following:

• .id: unit id for the intervention case (this will differ when a placebo unit).

• .placebo: indicator field taking on the value of 1 if a unit is a placebo unit, 0 if it's the specified treated unit.

• .type: type of the nested data construct: treated or controls. Keeps tract of which data construct is located in .outcome field.

• .outcome: nested data construct containing the outcome variable configured for the sythnetic control method. Data is configured into a wide format for the optimization task.

• .predictors: nested data construct containing the covariate matrices for the treated and control (donor) units. Data is configured into a wide format for the optimization task.

• .unit_weights: Nested column of unit weights (i.e. how each unit from the donor pool contributes to the synthetic control). Weights should sum to

• .predictor_weights: Nested column of predictor variable weights (i.e. the significance of each predictor in optimizing the weights that generate the synthetic control). Weights should sum to 1. If variable weights are provided, those variable weights are provided.

• .original_data: original impute data filtered by treated or control units. This allows for easy processing down stream when generating predictors.

• .meta: stores information regarding the unit and time index, the treated unit and time and the name of the outcome variable. Used downstream in subsequent functions.

• .loss: the RMPE loss for both sets of weights.

Examples

# Smoking example data
data(smoking)

smoking_out <-
smoking %>%

# initial the synthetic control object
synthetic_control(outcome = cigsale,
                  unit = state,
                  time = year,
                  i_unit = "California",
                  i_time = 1988,
                  generate_placebos= TRUE) %>%

# Generate the aggregate predictors used to generate the weights
  generate_predictor(time_window=1980:1988,
                     lnincome = mean(lnincome, na.rm = TRUE),
                     retprice = mean(retprice, na.rm = TRUE),
                     age15to24 = mean(age15to24, na.rm = TRUE)) %>%

  generate_predictor(time_window=1984:1988,
                     beer = mean(beer, na.rm = TRUE)) %>%

  generate_predictor(time_window=1975,
                     cigsale_1975 = cigsale) %>%

  generate_predictor(time_window=1980,
                     cigsale_1980 = cigsale) %>%

  generate_predictor(time_window=1988,
                     cigsale_1988 = cigsale) %>%


  # Generate the fitted weights for the synthetic control
  generate_weights(optimization_window =1970:1988,
                   Margin.ipop=.02,Sigf.ipop=7,Bound.ipop=6)

# Retrieve weights
smoking_out %>% grab_predictor_weights()
smoking_out %>% grab_unit_weights()

# Retrieve the placebo weights as well.
smoking_out %>% grab_predictor_weights(placebo= TRUE)
smoking_out %>% grab_unit_weights(placebo= TRUE)

# Plot the unit weights
smoking_out %>% plot_weights()