In rpf: Response Probability Functions

library(knitr)
library(rpf)
library(ggplot2)
library(reshape2)
library(gridExtra)
opts_chunk$set(echo=FALSE)

Basic 1 dimensional plots

This template is suitable for plotting a single group of 1 dimensional items. Refer to the Rmd source code to see how to adapt this template to your project.

Load data

Normally you would obtain model parameters from OpenMx (or flexMIRT with flexmirt.read), but here are some inline parameters for demonstration purposes.

small <- structure(list(param = structure(c(1, 1, 0, 0, -0.5789195, -2.412259,  -1.3471789, 1, 1, 0, 0, 1.0983234, -2.0991327, -2.9482965, 1,  1, 0, 0, 0.4078264, -0.9824549, -1.5905594, 1, 1, 0, 0, -1.0650001,  -0.2100243, -3.2034577), .Dim = c(7L, 4L), .Dimnames = list(NULL,      c("X2", "X6", "X7", "X10"))), mean = 0, cov = structure(9.8238066, .Dim = c(1L,  1L))), .Names = c("param", "mean", "cov"))
small$spec <- list()
small$spec[1:4] <- rpf.nrm(outcomes=4, T.c= lower.tri(diag(3),TRUE) * -1)

Item characteristic curve plots

width <- 5
small$icc <- list()
small$iif <- list()

tcc <- expand.grid(theta=seq(-width,width,.1), score=0)
tic <- expand.grid(theta=seq(-width,width,.1), info=0)

for (ix in 1:length(small$spec)) {
    name <- colnames(small$param)[ix]
    ii <- small$spec[[ix]]
    ii.p <- small$param[,ix]
    grid <- expand.grid(theta=seq(-width,width,.1))
    grid <- cbind(grid, t(rpf.prob(ii, ii.p, grid$theta)))
    tcc$score <- tcc$score + c(0:(ii@outcomes-1) %*% rpf.prob(ii, ii.p, grid$theta))
    colnames(grid) <- c("theta", paste0("k", 0:3))
    grid2 <- melt(grid, id.vars=c("theta"), variable.name="category", value.name="p")

    small$icc[[ix]] <- ggplot(grid2, aes(theta, p, color=category)) + geom_line() +
            ggtitle(paste("Item", name)) + ylim(0,1) + xlim(-width, width)

    grid <- expand.grid(theta=seq(-width,width,.1))
    grid$info <- rpf.info(ii, ii.p, t(grid$theta))
    tic$info <- tic$info + grid$info
    small$iif[[ix]] <- ggplot(grid, aes(theta, info)) + geom_line() +
            ggtitle(paste("Item", name)) + xlim(-width, width)
  }
do.call(grid.arrange, c(small$icc, ncol=2))

Item information curve plots

do.call(grid.arrange, c(small$iif, ncol=2))

Whole test plots

tcc.plot <- ggplot(tcc, aes(theta, score)) + geom_line() +
  ggtitle("Test Characteristic Curve") + xlim(-width, width)
tic.plot <- ggplot(tic, aes(theta, info)) + geom_line() +
  ggtitle("Test Information Curve") + xlim(-width, width)
grid.arrange(tcc.plot, tic.plot, ncol=2)