Check the validity of a graph-based MTP

Check that a given weight vector and transition matrix satisfy several conditions to determine if they form a valid graph. It verifies that the matrix is square, the dimensions match the length of the weight vector, the weight vector elements and matrix elements lie within the interval [0, 1], and that the weight vector sums to 1. Additionally, it checks the matrix is properly normalised, with all diagonal elements equal to 0 and each row summing to 1.

Usage

is_graph_valid(
  hyp_weight,
  trans_matrix,
  sum_to_one_constraint = TRUE,
  tolerance = sqrt(.Machine$double.eps)
)

Arguments

hyp_weight

A numeric vector representing the weights of the nodes (hypotheses) in the graph. All elements must be in the interval [0, 1] and the vector must sum to 1.

trans_matrix

A numeric matrix representing the transition matrix between nodes. All elements must be in the interval [0, 1], with diagonal elements equal to 0, and each row must sum to 1.

sum_to_one_constraint

A logical indicating whether to allow graphs where both the transition matrix rows are not constrained to sum-to-one, for example in a fixed sequence. Defaults to TRUE.

tolerance

numeric >= 0. The tolerance when evaluating the sum-to-one constraints of the hypothesis weights and transition matrix rows. The default value is close to 1.5e-8 - i.e. sqrt(.Machine$double.eps) (the standard R definition of "practically equal", as used by base::all.equal()).

Value

A logical value: TRUE if the graph is valid, otherwise FALSE. The function issues warnings if any of the validity checks fail.

Details

The function performs the following checks to determine graph validity:

• trans_matrix is a square matrix.

• the length of hyp_weight matches the number of rows and columns in trans_matrix.

• all diagonal elements of trans_matrix are 0.

• all elements of hyp_weight and trans_matrix lie in the interval [0, 1].

• the sum of hyp_weight equals 1.

• each row of trans_matrix sums to 1.

If any of these conditions are not satisfied, the function returns FALSE and issues the corresponding warning message.

Examples

hyp_weight <- c(0.4, 0.3, 0.3)
trans_matrix <- matrix(
                    c(0, 0.5, 0.5, 0.3, 0, 0.7, 0.6, 0.4, 0),
                    nrow = 3,
                    byrow = TRUE
                )
is_graph_valid(hyp_weight, trans_matrix)
#> [1] TRUE