Build the item-response probability matrix for the simulation

Returns a T x K matrix rho where rho[t, k] = P(Y_k = 1 | X = t).

Usage

make_rho(pi_)

Arguments

pi_

Numeric scalar in (0.5, 1). Probability of the "likely" response. Use bk2018_params$separation_levels for the three simulation levels.

Value

A 3 x 6 numeric matrix.

Details

The three-class structure is:

• Class 1: pi_ on all 6 items (high responders).

• Class 2: pi_ on items 1-3, 1 - pi_ on items 4-6 (mixed).

• Class 3: 1 - pi_ on all 6 items (low responders).

Examples

# High separation: P(Y=1|class) = 0.9 for the "high" class
make_rho(0.9)
#>        [,1] [,2] [,3] [,4] [,5] [,6]
#> class1  0.9  0.9  0.9  0.9  0.9  0.9
#> class2  0.9  0.9  0.9  0.1  0.1  0.1
#> class3  0.1  0.1  0.1  0.1  0.1  0.1

# Low separation
make_rho(0.7)
#>        [,1] [,2] [,3] [,4] [,5] [,6]
#> class1  0.7  0.7  0.7  0.7  0.7  0.7
#> class2  0.7  0.7  0.7  0.3  0.3  0.3
#> class3  0.3  0.3  0.3  0.3  0.3  0.3