PROC IRT supports several response models for binary and ordinal responses, and it allows different items to have different response models. Details about these response models and their relationships follow:
One-parameter model: This model assumes that items are binary. The distinctive feature of the one-parameter model, compared with the two-parameter model, is that the slopes (or the discrimination parameters) of the items are the same in the model. Statistically, the one-parameter model is equivalent to the Rasch model. They give the same model fit for the same data set.
Two-parameter model: This model assumes that items are binary. The slopes (or the discrimination parameters) and the difficulty (or the intercept parameters) of the items are free parameters in the model. If all slopes of the two-parameter model are constrained to be same, it reduces to the one-parameter model.
Three-parameter model: This model assumes that items are binary. The slopes (or the discrimination parameters), the difficulty (or the intercept parameters), and the guessing parameters of the items are free parameters in the model. If all the guessing parameters are fixed to 0, the three-parameter model reduces to the two-parameter model.
Four-parameter model: This model assumes that items are binary. The slopes (or the discrimination parameters), the difficulty (or the intercept parameters), the guessing parameters, and the ceiling parameters of the items are free parameters in the model. If all the guessing parameters are fixed to 0 and all the ceiling parameters are fixed to 1, the four-parameter model reduces to the two-parameter model.
Rasch model: This model assumes that items are binary. The distinctive feature of the Rasch model, compared with the two-parameter model, is that the slopes (or the discrimination parameters) of the items are all fixed to 1 (and with free factor variance parameters) in the model. Statistically, the Rasch model is equivalent to the one-parameter model. They give the same model fit for the same data set.
Graded response model: This model assumes that items are ordinal-categorical with at most 19 levels. The slopes (or discrimination) and the thresholds parameters of the items are free parameters in the model.
Generalized partial credit model: This model assumes that items are ordinal-categorical with at most 19 levels. The slopes (or discrimination) and the step parameters of the items are free parameters in the model.
You can specify the response function or model for all the variables that are listed in the VAR statement by using the RESFUNC= option in the PROC IRT statement. To specify different response functions or models for different set of variables, you can use the MODEL statement.