The partial credit model (PCM) with a varying
slope parameter is developed and called the
generalized partial credit model (GPCM). The item
step parameter of this model is decomposed to a
location and a threshold parameter, following
Andrich’s (1978) rating scale formulation. The EM
algorithm for estimating the model parameters is
derived. The performance of this generalized
model is compared on both simulated and real
data to a Rasch family of polytomous item
response models. Simulated data were generated
and then analyzed by the various polytomous item
response models. The results demonstrate that the
rating formulation of the GPCM is quite adaptable
to the analysis of polytomous item responses.
The real data used in this study consisted of the
National Assessment of Educational Progress
(Johnson & Allen, 1992) mathematics data that
used both dichotomous and polytomous items.
The PCM was applied to these data using both
constant and varying slope parameters. The GPCM,
which provides for varying slope parameters,
yielded better fit to the data than did the PCM.
Index terms: item response model, National Assessment
of Educational Progress, nominal response
model, partial credit model, polytomous response
model, rating scale model.