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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

\(\alpha _{j}\left (\theta _{i}-\delta _{jm}\right)\)


Generalized partial credit model

\(\alpha _{j}\left (\theta _{i}-\delta _{jm}\right)\)


  1. Index q denotes the number of kind of item parameters considered in the IRT model and a the number of random effects