Table 2.
Item parameter estimates of the 21 trended anchor items in 1999, 2003, and 2007 TIMSS: Two-class mixture 3PL IRT model.
| Class | Item | Discrimination (a) | Difficulty (b) | Lower asymptote (c) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1999 | 2003 | 2007 | 1999 | 2003 | 2007 | 1999 | 2003 | 2007 | ||
| 1 | 1 | 1.44 (0.05) | 0.46 (0.01) | 0.80 (0.07) | −0.43 (0.13) | −3.16 (0.09) | −2.55 (0.12) | 0.23 (0.00) | 0.26 (0.00) | 0.26 (0.00) |
| 2 | 1.68 (0.04) | 1.61 (0.11) | 0.30 (0.01) | −1.08 (0.13) | −2.48 (0.12) | −1.37 (0.12) | 0.23 (0.00) | 0.24 (0.00) | 0.27 (0.00) | |
| 3 | 1.39 (0.06) | 0.42 (0.02) | 1.61 (0.06) | −0.71 (0.12) | −2.15 (0.10) | −0.45 (0.06) | 0.24 (0.00) | 0.27 (0.01) | 0.24 (0.00) | |
| 4 | 1.24 (0.05) | 2.01 (0.10) | 1.26 (0.05) | −0.25 (0.10) | −0.06 (0.02) | −0.49 (0.07) | 0.24 (0.00) | 0.19 (0.01) | 0.25 (0.00) | |
| 5 | 1.30 (0.04) | 1.58 (0.07) | 0.73 (0.05) | 0.08 (0.11) | 0.50 (0.07) | −0.82 (0.10) | 0.24 (0.00) | 0.22 (0.01) | 0.26 (0.00) | |
| 6 | 1.38 (0.05) | 1.40 (0.07) | 2.37 (0.06) | −0.42 (0.13) | −0.47 (0.04) | −1.43 (0.06) | 0.23 (0.00) | 0.25 (0.01) | 0.23 (0.00) | |
| 7 | 1.57 (0.04) | 1.84 (0.07) | 1.59 (0.06) | 0.75 (0.11) | 2.32 (0.09) | 0.33 (0.07) | 0.22 (0.00) | 0.19 (0.00) | 0.22 (0.00) | |
| 8 | 1.53 (0.06) | 1.31 (0.06) | 1.36 (0.06) | −1.03 (0.18) | −1.44 (0.08) | −1.48 (0.09) | 0.24 (0.00) | 0.24 (0.00) | 0.24 (0.00) | |
| 9 | 1.71 (0.04) | 0.99 (0.04) | 1.57 (0.06) | −1.96 (0.11) | −2.62 (0.11) | −0.74 (0.10) | 0.24 (0.00) | 0.25 (0.00) | 0.23 (0.00) | |
| 10 | 1.78 (0.04) | 0.78 (0.05) | 1.12 (0.07) | −0.51 (0.15) | −2.48 (0.12) | −1.13 (0.10) | 0.23 (0.00) | 0.25 (0.01) | 0.25 (0.00) | |
| 11 | 1.68 (0.06) | 1.91 (0.12) | 1.76 (0.07) | −0.15 (0.18) | −2.62 (0.10) | −1.48 (0.11) | 0.22 (0.00) | 0.23 (0.00) | 0.24 (0.00) | |
| 12 | 1.47 (0.05) | 1.85 (0.07) | 1.56 (0.05) | 0.98 (0.11) | 1.77 (0.10) | 1.45 (0.10) | 0.22 (0.00) | 0.24 (0.01) | 0.22 (0.00) | |
| 13 | 1.34 (0.05) | 1.22 (0.06) | 1.82 (0.06) | −0.09 (0.11) | 1.42 (0.12) | 0.72 (0.11) | 0.24 (0.00) | 0.21 (0.01) | 0.20 (0.00) | |
| 14 | 1.43 (0.04) | 1.25 (0.07) | 1.28 (0.06) | −0.43 (0.10) | −0.12 (0.07) | −0.37 (0.10) | 0.24 (0.00) | 0.23 (0.01) | 0.24 (0.00) | |
| 15 | 1.15 (0.04) | 0.52 (0.04) | 1.17 (0.06) | −0.48 (0.08) | −0.09 (0.10) | −1.37 (0.10) | 0.24 (0.00) | 0.24 (0.01) | 0.25 (0.00) | |
| 16 | 1.97 (0.05) | 2.03 (0.12) | 1.44 (0.06) | −0.74 (0.12) | −1.67 (0.10) | −0.74 (0.15) | 0.23 (0.00) | 0.25 (0.01) | 0.24 (0.00) | |
| 17 | 1.65 (0.04) | 0.79 (0.06) | 1.79 (0.04) | 1.27 (0.11) | 0.25 (0.07) | 20.46 (0.06) | 0.22 (0.00) | 0.22 (0.01) | 0.21 (0.00) | |
| 18 | 1.59 (0.05) | 1.38 (0.07) | 1.17 (0.06) | 0.97 (0.11) | 0.78 (0.06) | 0.30 (0.10) | 0.21 (0.00) | 0.23 (0.01) | 0.25 (0.00) | |
| 19 | 1.50 (0.07) | 2.02 (0.07) | 1.12 (0.08) | −0.05 (0.19) | 0.67 (0.04) | 1.12 (0.09) | 0.23 (0.00) | 0.19 (0.00) | 0.25 (0.00) | |
| 20 | 1.32 (0.04) | 2.06 (0.09) | 2.13 (0.05) | 0.37 (0.13) | 0.92 (0.05) | −0.38 (0.07) | 0.24 (0.00) | 0.21 (0.01) | 0.22 (0.00) | |
| 21 | 1.68 (0.05) | 1.44 (0.06) | 1.26 (0.05) | −0.92 (0.16) | −0.91 (0.05) | −0.84 (0.07) | 0.23 (0.00) | 0.24 (0.01) | 0.24 (0.00) | |
| 2 | 1 | 0.67 (0.01) | 1.10 (0.03) | 0.71 (0.02) | −1.29 (0.03) | −1.06 (0.03) | −1.72 (0.04) | 0.19 (0.00) | 0.21 (0.01) | 0.23 (0.00) |
| 2 | 1.37 (0.05) | 1.46 (0.02) | 1.60 (0.05) | −0.54 (0.02) | −0.20 (0.02) | −0.65 (0.02) | 0.16 (0.00) | 0.16 (0.00) | 0.20 (0.00) | |
| 3 | 0.66 (0.02) | 0.97 (0.02) | 0.55 (0.01) | −0.55 (0.03) | 0.14 (0.04) | −0.21 (0.03) | 0.19 (0.00) | 0.29 (0.01) | 0.20 (0.00) | |
| 4 | 0.95 (0.02) | 1.41 (0.03) | 0.92 (0.02) | 1.67 (0.02) | 1.15 (0.03) | 1.55 (0.03) | 0.15 (0.00) | 0.17 (0.00) | 0.19 (0.00) | |
| 5 | 2.27 (0.06) | 3.52 (0.06) | 2.64 (0.05) | 1.22 (0.01) | 0.77 (0.01) | 1.39 (0.01) | 0.03 (0.00) | 0.03 (0.00) | 0.05 (0.00) | |
| 6 | 0.58 (0.02) | 0.86 (0.02) | 0.47 (0.01) | −1.58 (0.05) | −0.76 (0.03) | −0.74 (0.05) | 0.22 (0.01) | 0.22 (0.01) | 0.24 (0.01) | |
| 7 | 1.35 (0.04) | 2.80 (0.08) | 1.80 (0.05) | 2.30 (0.03) | 1.25 (0.01) | 2.54 (0.03) | 0.10 (0.00) | 0.10 (0.00) | 0.12 (0.00) | |
| 8 | 1.79 (0.02) | 2.39 (0.03) | 1.80 (0.04) | 0.24 (0.02) | 0.42 (0.01) | 0.64 (0.01) | 0.08 (0.00) | 0.10 (0.00) | 0.10 (0.00) | |
| 9 | 1.59 (0.03) | 2.51 (0.06) | 2.14 (0.06) | −0.97 (0.02) | −0.56 (0.02) | −0.84 (0.02) | 0.19 (0.00) | 0.19 (0.01) | 0.18 (0.00) | |
| 10 | 0.93 (0.02) | 1.44 (0.03) | 0.86 (0.02) | −1.93 (0.04) | −1.05 (0.03) | −2.18 (0.04) | 0.23 (0.00) | 0.22 (0.01) | 0.24 (0.00) | |
| 11 | 1.54 (0.03) | 1.74 (0.02) | 1.69 (0.06) | −0.92 (0.03) | −0.71 (0.02) | −0.96 (0.03) | 0.22 (0.01) | 0.17 (0.01) | 0.21 (0.01) | |
| 12 | 0.82 (0.02) | 1.58 (0.05) | 1.37 (0.05) | 1.70 (0.03) | 0.96 (0.02) | 1.44 (0.03) | 0.11 (0.00) | 0.15 (0.00) | 0.19 (0.00) | |
| 13 | 1.14 (0.03) | 2.54 (0.04) | 1.46 (0.04) | 1.36 (0.02) | 0.82 (0.01) | 1.16 (0.02) | 0.09 (0.00) | 0.08 (0.00) | 0.12 (0.00) | |
| 14 | 0.97 (0.03) | 1.61 (0.04) | 0.78 (0.03) | 1.20 (0.02) | 0.60 (0.02) | 0.55 (0.03) | 0.25 (0.00) | 0.27 (0.00) | 0.21 (0.00) | |
| 15 | 0.76 (0.02) | 1.47 (0.04) | 0.46 (0.01) | 1.14 (0.02) | 0.85 (0.02) | −2.83 (0.07) | 0.15 (0.00) | 0.17 (0.00) | 0.27 (0.00) | |
| 16 | 1.83 (0.06) | 2.23 (0.05) | 1.49 (0.04) | −1.14 (0.04) | −1.00 (0.02) | −2.18 (0.04) | 0.29 (0.01) | 0.25 (0.01) | 0.24 (0.01) | |
| 17 | 1.23 (0.03) | 2.03 (0.03) | 1.24 (0.04) | 1.99 (0.03) | 1.35 (0.02) | 1.98 (0.04) | 0.02 (0.00) | 0.03 (0.00) | 0.04 (0.00) | |
| 18 | 1.89 (0.06) | 3.15 (0.07) | 1.95 (0.05) | 1.70 (0.02) | 1.31 (0.02) | 1.73 (0.02) | 0.01 (0.00) | 0.02 (0.00) | 0.03 (0.00) | |
| 19 | 2.26 (0.07) | 3.31 (0.06) | 2.31 (0.06) | 1.88 (0.02) | 1.49 (0.02) | 2.01 (0.02) | 0.01 (0.00) | 0.01 (0.00) | 0.02 (0.00) | |
| 20 | 1.30 (0.03) | 2.91 (0.07) | 1.77 (0.04) | 1.65 (0.02) | 1.02 (0.01) | 1.74 (0.02) | 0.06 (0.00) | 0.06 (0.00) | 0.07 (0.00) | |
| 21 | 2.92 (0.05) | 2.99 (0.06) | 2.56 (0.06) | 0.85 (0.02) | 0.46 (0.01) | 0.43 (0.01) | 0.26 (0.00) | 0.22 (0.00) | 0.13 (0.00) | |
Estimated using MCMC with 10,000 samples and 4000 samples burn-in; values in parenthesis represent MC Error.