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Table 2 Specification of the famous IRT model following the components: (r,F, Z q ,U a ) for the GLMM and (r,F,nl) for IRT model with no longer linear predictor

From: Item response models for the longitudinal analysis of health-related quality of life in cancer clinical trials

IRT models \(\eta _{im}^{(j)}\) (r,F, Z q ,U a )
Rating scale model \(\theta _{i}-\left (\delta _{m}+\tau _{j}\right)\) (adjacent,logistic, Z 2,U 1 )
Partial credit model θ i δ jm (adjacent,logistic, Z 1,U 1 )
Sequential Rasch model θ i δ jm (sequential,logistic, Z 1,U 1 )
Graded response model \(\alpha _{j}\left (\theta _{i}-\delta _{jm}\right)\) (cumulative,logistic,nl)
Generalized partial credit model \(\alpha _{j}\left (\theta _{i}-\delta _{jm}\right)\) (adjacent,logistic,nl)
  1. Index q denotes the number of kind of item parameters considered in the IRT model and a the number of random effects