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. 2016 Feb 24;7:255. doi: 10.3389/fpsyg.2016.00255

Table 5.

Conditions for the simulation study: generating values.

Condition Item Time 1 Time 2
Group 1 Group 2 Group 1 Group 2
a11 b11 a12 b12 a21 b21 a22 b22
1 (Increase in Item Difficulty for Group 1 at Time 2) 1 1.44 −0.43 0.67 −1.29 1.44 0.57 0.67 −1.29
2 1.68 −1.08 1.37 −0.54 1.68 −0.08 1.37 −0.54
3 1.39 −0.71 0.66 −0.55 1.39 0.29 0.66 −0.55
4 1.24 −0.25 0.95 1.67 1.24 0.75 0.95 1.67
5 1.30 0.08 2.27 1.22 1.30 1.08 2.27 1.22
6 1.38 −0.42 0.58 −1.58 1.38 0.58 0.58 −1.58
7 1.57 0.75 1.35 2.30 1.57 1.75 1.35 2.30
8 1.53 −1.03 1.79 0.24 1.53 −0.03 1.79 0.24
9 1.71 −1.96 1.59 −0.97 1.71 −0.96 1.59 −0.97
10 1.78 −0.51 0.93 −1.93 1.78 0.49 0.93 −1.93
11 1.68 −0.15 1.54 −0.92 1.68 0.85 1.54 −0.92
12 1.47 0.98 0.82 1.70 1.47 1.98 0.82 1.70
13 1.34 −0.09 1.14 1.36 1.34 0.91 1.14 1.36
14 1.43 −0.43 0.97 1.20 1.43 0.57 0.97 1.20
15 1.15 −0.48 0.76 1.14 1.15 0.52 0.76 1.14
16 1.97 −0.74 1.83 −1.14 1.97 0.26 1.83 −1.14
17 1.65 1.27 1.23 1.99 1.65 2.27 1.23 1.99
18 1.59 0.97 1.89 1.70 1.59 1.97 1.89 1.70
19 1.50 −0.05 2.26 1.88 1.50 0.95 2.26 1.88
20 1.32 0.37 1.30 1.65 1.32 1.37 1.30 1.65
2 (Increase in Item Discrimination for Group 1 atTime 2) 1 1.44 −0.43 0.67 −1.29 2.44 −0.43 0.67 −1.29
2 1.68 −1.08 1.37 −0.54 2.68 −1.08 1.37 −0.54
3 1.39 −0.71 0.66 −0.55 2.39 −0.71 0.66 −0.55
4 1.24 −0.25 0.95 1.67 2.24 −0.25 0.95 1.67
5 1.30 0.08 2.27 1.22 2.30 0.08 2.27 1.22
6 1.38 −0.42 0.58 −1.58 2.38 −0.42 0.58 −1.58
7 1.57 0.75 1.35 2.30 2.57 0.75 1.35 2.30
8 1.53 −1.03 1.79 0.24 2.53 −1.03 1.79 0.24
9 1.71 −1.96 1.59 −0.97 2.71 −1.96 1.59 −0.97
10 1.78 −0.51 0.93 −1.93 2.78 −0.51 0.93 −1.93
11 1.68 −0.15 1.54 −0.92 2.68 −0.15 1.54 −0.92
12 1.47 0.98 0.82 1.70 2.47 0.98 0.82 1.70
13 1.34 −0.09 1.14 1.36 2.34 −0.09 1.14 1.36
14 1.43 −0.43 0.97 1.20 2.43 −0.43 0.97 1.20
15 1.15 −0.48 0.76 1.14 2.15 −0.48 0.76 1.14
16 1.97 −0.74 1.83 −1.14 2.97 −0.74 1.83 −1.14
17 1.65 1.27 1.23 1.99 2.65 1.27 1.23 1.99
18 1.59 0.97 1.89 1.70 2.59 0.97 1.89 1.70
19 1.50 −0.05 2.26 1.88 2.50 −0.05 2.26 1.88
20 1.32 0.37 1.30 1.65 2.32 0.37 1.30 1.65
3 (Increase in both Item Difficulty and Discrimination for Group 1 at Time 2) 1 1.44 −0.43 0.67 −1.29 2.44 0.57 0.67 −1.29
2 1.68 −1.08 1.37 −0.54 2.68 −0.08 1.37 −0.54
3 1.39 −0.71 0.66 −0.55 2.39 0.29 0.66 −0.55
4 1.24 −0.25 0.95 1.67 2.24 0.75 0.95 1.67
5 1.30 0.08 2.27 1.22 2.30 1.08 2.27 1.22
6 1.38 −0.42 0.58 −1.58 2.38 0.58 0.58 −1.58
7 1.57 0.75 1.35 2.30 2.57 1.75 1.35 2.30
8 1.53 −1.03 1.79 0.24 2.53 −0.03 1.79 0.24
9 1.71 −1.96 1.59 −0.97 2.71 −0.96 1.59 −0.97
10 1.78 −0.51 0.93 −1.93 2.78 0.49 0.93 −1.93
11 1.68 −0.15 1.54 −0.92 2.68 0.85 1.54 −0.92
12 1.47 0.98 0.82 1.70 2.47 1.98 0.82 1.70
13 1.34 −0.09 1.14 1.36 2.34 0.91 1.14 1.36
14 1.43 −0.43 0.97 1.20 2.43 0.57 0.97 1.20
15 1.15 −0.48 0.76 1.14 2.15 0.52 0.76 1.14
16 1.97 −0.74 1.83 −1.14 2.97 0.26 1.83 −1.14
17 1.65 1.27 1.23 1.99 2.65 2.27 1.23 1.99
18 1.59 0.97 1.89 1.70 2.59 1.97 1.89 1.70
19 1.50 −0.05 2.26 1.88 2.50 0.95 2.26 1.88
20 1.32 0.37 1.30 1.65 2.32 1.37 1.30 1.65

1. Generating values for Group 1 and Group 2 for Time 1 were obtained from estimated item parameters using the mixture 3PL IRT model of TIMSS 1999 data (items 1 to 20).

2. All simulations in Conditions 1–3 used ability as normally distributed with mean 0 and variance 1, θ ~N(0,1).

3. In addition to the conditions listed above two additional conditions were examined:

Condition 4: Change in ability distribution for one group at Time 2

- Time 1: Same generating values used at Time 1 of Condition 1

- Time 2: Same generating values used at Time 1 of Condition 1 with θ ~N(1,0.5) for Group 1

Condition 5: Change in ability distribution for one group at Time 2 and increased discrimination

- Time 1: Same generating values used at Time 1 of Condition 1

- Time 2: Same generating values used at Time 2 of Condition 2 (increase in discrimination for Group 1) with θ ~N(1,0.5).