ess_rand {FSM}

Randomization-based Effective Sample Size (ESS)

Description

Computes the randomization-based effective sample size (ESS) of a collection of assignments under a given set of potential outcomes.

Usage

ess_rand(assign_array, Y_mat, contrast = c(1, -1))

Arguments

assign_array

A three dimensional array containing a set of independent realizations of a collection the designs. The first coordinate of the array represents the iterations for each design. The second coordinate represents the units. The third coordinate represents the design.

Y_mat

A matrix of potential outcomes, where rows represent units and columns represent treatment levels (ordered).

contrast

A vector of the coefficients of the treatment contrast of interest. For example, for estimating the average treatment effect of treatment 1 versus treatment 2, contrast = c(1,-1).

Value

A vector of effective sample sizes for the given collection of assignments.

Author(s)

Ambarish Chattopadhyay, Carl N. Morris and Jose R. Zubizarreta.

References

Chattopadhyay, A., Morris, C. N., and Zubizarreta, J. R. (2020), “Randomized and Balanced Allocation of Units into Treatment Groups Using the Finite Selection Model for R".

Examples

# Consider N = 12, n1 = n2 = 6.
df_sample = data.frame(index = 1:12, x = c(20,30,40,40,50,60,20,30,40,40,50,60))
# Generate the potential outcomes.
Y_1 = 100 + (df_sample$x - mean(df_sample$x)) + rnorm(12, 0, 4)
Y_2 = Y_1 + 50
# Create matrix of potential outcomes.
Y_appended = cbind(Y_1, Y_2)
# Generate 100 assignments under CRD and the FSM.
Z_crd_iter = matrix(rep(0, 100 * 12), nrow = 100)
Z_fsm_iter = matrix(rep(0, 100 * 12), nrow = 100)
for(i in 1:100)
{
# Generate an assignment vector under CRD.
fc = crd(data_frame = df_sample, n_treat = 2, treat_sizes = c(6,6), control = FALSE)
Z_crd_iter[i,] = fc$Treat
# Generate an assignment vector under the FSM.
som_iter = som(data_frame = NULL, n_treat = 2, 
treat_sizes = c(6, 6),include_discard = FALSE,
method = 'SCOMARS', marginal_treat = rep((6/12), 12), control = FALSE)
f = fsm(data_frame = df_sample, SOM = som_iter, s_function = 'Dopt',eps = 0.0001, 
ties = 'random', intercept = TRUE, standardize = TRUE, units_print = FALSE)
Z_fsm_iter[i,] = f$data_frame_allocated$Treat
}
# Create a 3-dim array of assignments.
Z_array = array(0, dim = c(100, 12, 2))
Z_array[,,1] = Z_crd_iter
Z_array[,,2] = Z_fsm_iter
# Calculate the ESS.
ess_rand(assign_array = Z_array, Y_mat = Y_appended, contrast = c(1,-1))