% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/classes.R
\docType{package}
\name{An introduction}
\alias{An introduction}
\alias{An introduction-package}
\title{rpf - Response Probability Functions}
\description{
Factor out logic and math common
to Item Factor Analysis fitting, diagnostics, and analysis.  It is
envisioned as core support code suitable for more specialized IFA
packages to build upon.
}
\details{
This package provides optimized, low-level functions to map
parameters to response probabilities for dichotomous (1PL, 2PL and
3PL) \code{\link{rpf.drm}} and polytomous (graded response
\code{\link{rpf.grm}}, partial credit/generalized partial credit
(via the nominal model), and nominal \code{\link{rpf.nrm}} items.

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/slope ("a"),
difficulty/intercept ("b"), and pseudo guessing/upper-bound ("g"/"u"). If
person ability ranges from negative to 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
\code{\link{rpf.ogive}}. Item models are estimated in
slope-intercept form. Input/output matrices arranged in the way
most convenient for low-level processing in C. The maximum
absolute logit is 35 because f(x) := 1-exp(x) loses accuracy around f(-35)
and equals 1 at f(-38) due to the limited accuracy of double
precision floating point.

This package could also accrete functions to support plotting (but
not the actual plot functions).
}
\references{
Pritikin, J. N., Hunter, M. D., & Boker, S. M.
(2015). Modular open-source software for Item Factor Analysis.
Educational and Psychological Measurement, 75(3), 458-474

Thissen, D. and Steinberg, L. (1986). A taxonomy of
item response models. \emph{Psychometrika 51}(4), 567-577.
}
\seealso{
See \code{\link{rpf.rparam}} to create item parameters.
}
