make_exposure_prob: Create exposure probabilities.
In szonszein/interference: Design-Based Estimation of Spillover Effects

Description Usage Arguments Details Value References Examples

Create matrices of exposure probabilities.

make_exposure_prob(
  potential_tr_vector,
  adj_matrix,
  exposure_map_fn,
  exposure_map_fn_add_args = NULL
)

`potential_tr_vector`	an `R` * `N` matrix of 0, 1 entries such as that produced by `make_tr_vec_permutation`, or an `R` * `N` matrix containing `R` permuted treatment assignments for `N` units.
`adj_matrix`	an `N` * `N` numeric matrix of 0, 1 entries such as those retuned by `make_adj_matrix`, or a `N` * `N` matrix, where `N` is the number of units.
`exposure_map_fn`	function which returns the exposure mapping such as `make_exposure_map_AS`.
`exposure_map_fn_add_args`	list of additional arguments which are passed to `exposure_map_fn`. `adj_matrix` and `tr_vector` should not be specified here because they are already passed with values derived from the arguments to `make_exposure_prob`. If using `make_exposure_map_AS`, `hop` must be specified here.

make_exposure_prob produces the units' probabilities of being subject to each of the possible exposure conditions which are used for estimating exposure-specific causal effects, and the joint exposure probabilities used for variance estimators.

A list of 3 lists:

I_exposure:: A list of K N * R numeric matrices of indicators for whether units N are in exposure condition k over each of the possible R treatment assignment vectors. The number of numeric matrices K corresponds to the number of exposure conditions.
prob_exposure_k_k:: A list of K symmetric N * N numeric matrices each containing individual exposure probabilities to condition k on the diagonal, and joint exposure probabilities to condition k on the off-diagonals.
prob_exposure_k_l:: A list of permutation(K,2) nonsymmetric N* N numeric matrices each containing joint probabilities across exposure conditions k and l on the off-diagonal, and zeroes on the diagonal. When K = 4, the number of numeric matrices is 12; permutation(4,2).

Aronow, P.M. & Samii, C. (2017). Estimating average causal effects under general interference, with application to a social network experiment. The Annals of Applied Statistics, 11(4), 1912–1947.

Aronow, P.M. et al. (2020). Spillover effects in experimental data. arXiv preprint, arXiv:2001.05444.

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potential_tr_vector <- make_tr_vec_permutation(N = 9, p = 0.2, R = 20, seed = 357)
adj_matrix <- make_adj_matrix(N = 9, model = 'sq_lattice')
make_exposure_prob(potential_tr_vector, adj_matrix, make_exposure_map_AS, list(hop=1))