Figure 1

Density of mixture distribution for\(J=5, a=-0{.}75, \sigma ^{2}_{\theta }=1\)and different values of\(\sigma ^{2}_{\delta _{j}}\). Vertical lines represent the values of the item difficulties drawn from the mixture distribution. Item difficulties for \(\sigma ^{2}_{\delta _{j}}=1\) (Figure a): δ _j =(−1.13,−0.37,0.39,0.67,0.9). Item difficulties for \(\sigma ^{2}_{\delta _{j}}=3\) (Figure b): δ _j =(−1.96,−0.63,0.68,1.16,1.55).