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rpf (version 0.8)

An introduction: rpf - Response Probability Functions

Description

The purpose of this package is to factor out logic and math common to Item Response Theory fitting, diagnostics, and analysis. It is envisioned as core support code suitable for more specialized IRT packages to build upon.

Arguments

Warning

The API is not stable at this time. You have been warned. In particular, I anticipating transposing some of the input and output matrices.

Details

This package provides optimized, low-level functions to map parameters to response probabilities for dichotomous (1PL, 2PL and 3PL) rpf.drm and polytomous (graded response rpf.grm, partial credit/generalized partial credit rpf.gpcm, nominal rpf.nrm, and multiple-choice model rpf.mcm) items. Both unidimensional and multidimensional versions of the models are available.

Item model parameters are passed around as a numeric vector. A 1D matrix is also acceptable. Regardless of model, parameters are always ordered as follows: discrimination ("a"), difficulty ("b"), and guessing ("c"). If person ability ranges from low negative to high positive then probabilities are output from incorrect to correct. That is, a low ability person (e.g., ability = -2) will be more likely to get an item incorrect than correct. For example, a dichotomous model that returns [.25, .75] indicates a probability of .25 for incorrect and .75 for correct. A polytomous model will have the most incorrect probability at index 1 and the most correct probability at the maximum index.

All models are always in the logistic metric. To obtain normal ogive discrimination parameters, divide slope parameters by rpf.ogive. Item models are estimated in slope-intercept form unless the traditional parameterization is specifically requested.

This package could also accrete functions to support plotting (but not the actual plot functions).

References

Thissen, D. and Steinberg, L. (1986). A taxonomy of item response models. Psychometrika 51(4), 567-577.

See Also

See rpf.rparam to create item parameters.