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Table 4 Model fit statistics for the partial credit model of the HRL index

From: Assuming measurement invariance of background indicators in international comparative educational achievement studies: a challenge for the interpretation of achievement differences

Fit-statistics Model
1 2 3 4
Log likelihood −90,588.33 −89,914.61 −90,360.41 −88,523.81
AIC (smaller is better) 181,212.66 179,919.22 180,764.82 177,361.61
BIC (smaller is better) 181,389.71 180,361.83 180,981.21 178,905.83
  1. Model 1, constant discrimination parameter across countries and items; Model 2, constant discrimination parameters across items but vary across countries; Model 3 discrimination parameters are constant across countries but vary over items; Model 4, discrimination parameters vary across countries and across items