Automatic Construction of Ab-Representation for Common Inequality Constraints
Constructs the matrix A and vector b of the Ab-representation A*x < b for common inequality constraints such as "the probability j is larger than all others (Ab_max)" or "the probabilities are ordered (Ab_monotonicity)").
Ab_max( which_max, options, exclude = c(), exclude_fixed = FALSE, drop_fixed = TRUE )
which_max: vector of indices refering to probabilities that are assumed to be larger than the remaining probabilities (e.g., which_max=c(1,2) means that p1>p3, p1>p4,..., p2>p3, ...). Note that the indices refer to all probabilities/categories (including one fixed probability within each multinomial distribution).options: number of observable categories/probabilities for each item type/multinomial distribution, e.g., c(3,2) for a ternary and binary item.exclude: vector of indices refering to probabilities that are excluded from the construction of the order constraints (including the fixed probabilities).exclude_fixed: whether to exclude the fixed probabilities (i.e., the last probability within each multinomial) from the construction of the order constraints. For example, if options=c(2,2,3) then the probabilities/columns 2, 4, and 7 are dropped (which is equivalent to exclude=c(2,4,7)). This option is usually appropriate for binomial probabilities (i.e., if options = c(2,2,2,...)), e.g., when the interest is in the probability of correct responding across different item types.drop_fixed: whether to drop columns of A containing the fixed probabilities (i.e., the last probability within each multinomial). after construction of the inequalities.a list with the matrix A and the vectors b and options
# Example 1: Multinomial with 5 categories # Hypothesis: p1 is larger than p2,p3,p4,p5 Ab_max(which_max = 1, options = 5) # Example 2: Four binomial probabilities # Hypothesis: p1 is larger than p2,p3,p4 Ab_max(which_max = 1, options = c(2, 2, 2, 2), exclude_fixed = TRUE)