ess_model {FSM}

Model-based Effective Sample Size (ESS)

Description

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

Usage

ess_model(X_cov, assign_matrix, Y_mat, contrast = c(1, -1))

Arguments

X_cov

A matrix of covariates or transformations thereof that will be used as explanatory variables in the linear outcome models within each treatment group.

assign_matrix

A matrix containing a collection of treatment assignment vectors, each column containing a particular assignment vector.

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 the Lalonde dataset.
# Get the full sample size.
N = nrow(Lalonde)
# Get the treatment group sizes.
n1 = floor(N/2)
n2 = N-n1
# Generate an SOM.
som_obs = som(n_treat = 2, treat_sizes = c(n1,n2),include_discard = FALSE,
method = 'SCOMARS', marginal_treat = rep((n2/N),N), control = FALSE)
# Generate a treatment assignment given som_obs.
f = fsm(data_frame = Lalonde, SOM = som_obs, s_function = 'Dopt', eps = 0.0001, 
ties = 'random', intercept = TRUE, standardize = TRUE, units_print = FALSE)
# Get assignment vector under the FSM.
Z_fsm_obs = f$data_frame_allocated$Treat
# Draw a random CRD.
Z_crd_obs = crd(data_frame = Lalonde, n_treat = 2, treat_sizes = c(n1, n2), 
control = FALSE)$Treat
Z_big = cbind(Z_crd_obs, Z_fsm_obs)
# Generate the potential outcomes.
Y_1 = 100 - Lalonde$Age + 6 * Lalonde$Education - 20 * Lalonde$Black + 
20 * Lalonde$Hispanic + 0.003 * Lalonde$Re75 + rnorm(N,0,4)
Y_1 = round(Y_1,2)
# Set unit level causal effect = tau = 0.
tau = 0
Y_2 = Y_1 + tau
# Get the matrix of potential outcomes.
Y_appended = cbind(Y_1, Y_2)
# Get the matrix of covariates.
X_cov = Lalonde[,-1]
ess = ess_model(X_cov = X_cov, assign_matrix = Z_big, Y_mat = Y_appended, contrast = c(1,-1))