#' Build our auxiliary matrices to estimate entry models
#'
#' @param data A \code{data.frame} object containing your data
#' @param y A string indicating the outcome variable
#' @param N_max An \code{integer} indicating the maximum number of competitors
#' @param n Number of observations in \code{data}
#' @return A list of the auxiliary matrices
#'
#' @importFrom dplyr select
#' @importFrom magrittr %>%
aux_matrix <- function(data, y, N_max, n) {
# auxiliary matrix A1
A1 <- (-1)*matrix(1, nrow = N_max, ncol = N_max, byrow = TRUE)
for (i in 1:N_max){
A1[i,1] <- 1
}
for (i in 1:N_max){
for (j in 1:N_max){
if (i < j){
A1[i, j] <- 0
}
}
}
# auxiliary matrix A2
A2 <- matrix(1, nrow = N_max, ncol = N_max, byrow = TRUE)
for (i in 1:N_max){
for (j in 1:N_max){
if (i < j){
A2[i, j] <- 0
}
}
}
return(list(A1, A2))
}
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