Figure 2

Density of mixture distribution for\(J=5, \sigma ^{2}_{\theta }=1, \sigma ^{2}_{\delta _{j}}=1\)and different values ofa. Vertical lines represent the values of the item difficulties drawn from the mixture distribution. Item difficulties for a=−0.75 (Figure a): δ _j =(−1.13,−0.37,0.39,0.67,0.9). Item difficulties for a=0 (Figure b): δ _j =(−0.74,−0.29,0,0.29,0.74). Item difficulties for a=0.5 (Figure c): δ _j =(−0.81,−0.52,−0.26,0.13,1).