Builds a two-arm design with blocks and clusters.

block_cluster_two_arm_designer(N = NULL, N_blocks = 1,
N_clusters_in_block = ifelse(is.null(N), 100, round(N/N_blocks)),
N_i_in_cluster = ifelse(is.null(N), 1, round(N/mean(N_blocks *
N_clusters_in_block))), sd = 1, sd_block = 0.5773 * sd,
sd_cluster = max(0, (sd^2 - sd_block^2)/2)^0.5, sd_i_0 = max(0, sd^2
- sd_block^2 - sd_cluster^2)^0.5, sd_i_1 = sd_i_0, rho = 1,
assignment_probs = 0.5, control_mean = 0, ate = 0,
treatment_mean = control_mean + ate, verbose = TRUE)

## Arguments

N An integer. Total number of units. Usually not specified as N is determined by N_blocks, N_clusters_in_block, and N_i_in_cluster. If N_blocks, and N_clusters_in_block, and N_i_in_cluster are specified then N is overridden. If these are not specified and N is specified then designer attempts to guess sizes of levels to approximate N, with preference for a design without blocks or clusters. An integer. Number of blocks. Defaults to 1 for no blocks. An integer or vector of integers of length N_blocks. Number of clusters in each block. This is the total N when N_blocks and N_i_in_cluster are at default values. An integer or vector of integers of length sum(N_clusters_in_block). Individuals per cluster. Defaults to 1 for no clusters. A nonnegative number. Overall standard deviation (combining individual level, cluster level, and block level shocks). Defaults to 1. Overridden if incompatible with other user-specified shocks. A nonnegative number. Standard deviation of block level shocks. A nonnegative number. Standard deviation of cluster level shock. A nonnegative number. Standard deviation of individual level shock in control. If not specified, and when possible given sd_block and sd_cluster, sd_i_0 defaults to make total variance = sd. A nonnegative number. Standard deviation of individual level shock in treatment. Defaults to sd_i_0. A number in [-1,1]. Correlation in individual shock between potential outcomes for treatment and control. A number or vector of numbers in (0,1). Treatment assignment probability for each block (specified in order of N_clusters_in_block). A number. Average outcome in control. A number. Average treatment effect. Alternative to specifying treatment_mean. Note that ate is an argument for the designer but it does not appear as an argument in design code (design code uses control_mean and treatment_mean only). A number. Average outcome in treatment. If treatment_mean is not provided then it is calculated as control_mean + ate. If both ate and treatment_mean are provided then only treatment_mean is used. Logical. If TRUE, prints intra-cluster correlation implied by design parameters.

## Value

A block cluster two-arm design.

## Details

Units are assigned to treatment using complete block cluster random assignment. Treatment effects can be specified either by providing control_mean and treatment_mean or by specifying an ate. Estimation uses differences in means accounting for blocks and clusters.

In the usual case N is not provided by the user but is determined by N_blocks, N_clusters_in_block, N_i_in_cluster (when these are integers N is the product of these three numbers).

Normal shocks can be specified at the individual, cluster, and block levels. If individual level shocks are not specified and cluster and block level variances sum to less than 1, then individual level shocks are set such that total variance in outcomes equals 1.

Key limitations: The designer assumes covariance between potential outcomes at the individual level only.

See vignette online.

## Examples

# Generate a design using default arguments:
block_cluster_two_arm_design <- block_cluster_two_arm_designer()#> [1] "The implied ICC in (control) is 0.667"
#> [1] "The implied ICC in (control) conditional on block is  0.5"block_cluster_uneven <- block_cluster_two_arm_designer(
N_blocks = 3, N_clusters_in_block = 2:4, N_i_in_cluster = 1:9)#> [1] "The implied ICC in (control) is 0.667"
#> [1] "The implied ICC in (control) conditional on block is  0.5"# A design in which number of clusters of cluster size is not specified
# but N and block size are:
block_cluster_guess <- block_cluster_two_arm_designer(N = 24, N_blocks = 3)#> [1] "The implied ICC in (control) is 0.667"
#> [1] "The implied ICC in (control) conditional on block is  0.5"# A design in which cluster size is not specified but N and block size are
# and target N is not met returns an error:
# NOT RUN {
block_cluster_guess_2 <- block_cluster_two_arm_designer(N = 24,
N_blocks = 3, N_clusters_in_block = 3)
# }


## Author

DeclareDesign Team