Table 4.

Parameter estimates of the 9-item graded response model^a

Item	λ (SE)	τ 1 (SE)	τ 2 (SE)	τ 3 (SE)	τ 4 (SE)
Q100	4.49 (0.48)	3.92 (0.45)	5.55 (0.54)	7.56 (0.67)	9.76 (0.88)
Q105	4.68 (0.62)	5.45 (0.66)	7.57 (0.75)	9.99 (1.01)	14.85 (1.77)
Q109	3.77 (0.64)	5.34 (0.92)	7.04 (0.88)	8.98 (1.06)	10.62 (1.11)
Q112	5.31 (0.66)	4.90 (0.60)	7.40 (0.77)	9.13 (0.90)	11.97 (1.24)
Q123	4.65 (0.80)	6.10 (1.08)	7.55 (1.07)	8.87 (1.20)	9.75 (1.25)
Q124	6.96 (1.30)	9.51 (2.00)	12.13 (2.13)	14.70 (2.64)	16.37 (2.52)
Q128	4.10 (0.94)	9.23 (1.70)	10.02 (1.78)	10.76 (1.92)	11.70 (2.01)
Q130	2.90 (0.37)	5.46 (0.50)	6.48 (0.54)	7.56 (0.64)	8.15 (0.72)
Q137	5.58 (1.19)	9.10 (1.78)	13.39 (2.55)

^aThe parameters are of a mixture graded response model as specified in the MPlus [47] software where the cumulative probability Ρ _ij of an item i response at or above category j is expressed as follows: $P_{ij}\left(Y\ge j|\mathit{\theta }\right)=\frac{exp(-{\mathit{\tau }}_{ij}+{\mathit{\lambda }}_i\mathit{\theta })}{1+exp(-{\mathit{\tau }}_{ij}+{\mathit{\lambda }}_i\mathit{\theta })},$ where τ _ij denotes the thresholds between the categories of item i, and λ _i denotes the factor loading for item i. The following transformation can be applied to convert the Mplus thresholds (τ) and factor loadings (λ) into the difficulty (β) and discrimination (α) parameters of the graded response model: ${\mathit{\beta }}_{ij}=\frac{{\mathit{\tau }}_{ij}}{{\mathit{\lambda }}_i},$ and ${\mathit{\alpha }}_i={\mathit{\lambda }}_i$