This supplement provides the estimation infrastructure used in the manuscript, On the asymmetry, complexity, and predicted data pattern of nontraditional item response theory models.
It includes: (1) analysis settings, (2) Gauss-Hermite quadrature setup, (3) custom item definitions for AO, LPE, and RH with analytic gradients and Hessians, (4) prior specification and starting-value transfer routines, and (5) an LSAT7 illustration that demonstrates the full estimation pipeline from a baseline 2PLM fit through all three asymmetric models.
Gauss-Hermite quadrature N(0,1)
Custom link IRT models with analytic gradients/Hessians
Starting values and custom fits
Run LSAT7 illustration
# A tibble: 5 × 5
item a1 d g u
<int> <dbl> <dbl> <dbl> <dbl>
1 1 0.988 1.86 0 1
2 2 1.08 0.808 0 1
3 3 1.70 1.80 0 1
4 4 0.765 0.486 0 1
5 5 0.736 1.85 0 1
# A tibble: 5 × 4
item a1 d eta
<int> <dbl> <dbl> <dbl>
1 1 1.01 1.89 0.0212
2 2 0.973 0.607 -0.315
3 3 1.71 1.82 0.0139
4 4 0.937 0.850 0.459
5 5 0.720 1.80 -0.0449
# A tibble: 5 × 4
item a1 d S
<int> <dbl> <dbl> <dbl>
1 1 0.984 1.93 0.0664
2 2 1.19 0.414 -0.308
3 3 1.69 1.84 0.0329
4 4 0.707 0.920 0.349
5 5 0.742 1.82 -0.0311
# A tibble: 5 × 4
item a1 d delta
<int> <dbl> <dbl> <dbl>
1 1 0.637 1.12 0.639
2 2 0.649 0.433 -0.578
3 3 0.947 1.03 0.0182
4 4 0.426 0.379 1.27
5 5 0.437 1.10 0.0829
--- Built-in LPE (5PLM with g = 0, u = 1; for comparison) ---
# A tibble: 5 × 6
item a1 d g u logS
<int> <dbl> <dbl> <dbl> <dbl> <dbl>
1 1 0.985 1.94 0 1 0.0750
2 2 1.23 0.275 0 1 -0.410
3 3 1.68 1.83 0 1 0.0286
4 4 0.718 0.823 0 1 0.269
5 5 0.742 1.84 0 1 -0.0141