# R/interaction.R In irtoys: A Collection of Functions Related to Item Response Theory (IRT)

#### Documented in interactionModelplot.imprim

```#' Interaction model
#'
#' Estimates the parameters of the interaction model. The plots can be produced with the
#' appropriate plotting method.
#'
#'
#' @param x A matrix of responses: persons as rows, items as columns,
#' entries are either 0 or 1, no missing data
#' @param eps Convergence criterion, default is 1e-1
#' @param rasch if TRUE, the Rasch model will be estimated instead.
#' @return A matrix
#' @author Ivailo Partchev, using C code and theory by Gunter Maris
#' @references Shelby Haberman. The interaction model. Chapter in:
#' Mathias von Davier & Claus H. Carstensen (Eds.) (2007).
#' Multivariate and Mixture Distribution Rasch Models. New York:Springer
#' @keywords models
#'
interactionModel = function(x, eps=1e-1, rasch=FALSE) {
# not sure if I can handle NAs -- remove until I find out
x[is.na(x)] = 0
# do the sufficient statistics
sumsc = rowSums(x)
bsuf = colSums(x)
csuf = crossprod(sumsc-1, x)
b = runif(length(bsuf))
c = rep(0,length(bsuf))
score=sapply(0:length(bsuf),function(p)sum(sumsc==p))
r = IM_update(b,c,bsuf,csuf,score,rasch)
itr = 1
while (r\$conv > eps)
{
# cat("Iteration ", itr, "    Criterion ", r[[3]], "\n")
r = IM_update(r[[1]],r[[2]],bsuf,csuf,score,rasch)
itr = itr + 1
}
result = r
result\$scores=score
class(result) = "imp"
return(result)
}

#' A plot method for the interaction model
#'
#' Plot the item-total regressions fit by the interaction (or Rasch) model
#'
#'
#' @param x An object produced by function \code{interactionModel}
#' @param items The items to plot (column numbers). If NULL, all items will be plotted
#' @param shade The part of the probability mass for the sum scores to shade out,
#' shown as percentage. Default is 10: shade the most extreme 10% of the distribution.
#' @param highlight Cutpoint for the interaction parameter below which a regression
#' line will be highlighted in red. Default is -Inf (do not highlight).
#' plot is started. Default is FALSE.
#' @param main The main title of the plot, given that \code{add=FALSE}.
#' @param label When \code{label=TRUE}, individual curves will be labeled with the
#' item number.
#' @param ... Any additional plotting parameters
#' @author Ivailo Partchev, using theory and C code by Gunter Maris
#' @keywords models
#' @method plot imp
#'
#' @examples
#'
#' plot(interactionModel(Scored), highlight=-.3)
#'
plot.imp = function(x, items=NULL, shade=10, highlight=-Inf,
add=FALSE, main="Item-total regression", label=FALSE, ...) {
p = curv(x)
n = ncol(p)
if (!is.null(items)) items=sort(items) else items=1:n
p = p[, items, drop=FALSE]
k = ncol(p)
scores = rep(0:n, x\$scores)
plot(c(0,n), c(0,1), ty="n", xlab="Sum score", ylab="Probability", main=main, ...)
tmp = par('usr')
# par(new=TRUE)
rect(tmp[1], tmp[3], q[1], tmp[2], col="#DDDDDD", border=NA)
rect(q[2], tmp[3], tmp[2], tmp[4], col="#DDDDDD", border=NA)
}
couleur = 1 + (x\$c[items] < highlight)
for (i in 1:k) lines(0:n, p[,i], col=couleur[i], ...)
if (label) {
lx = sample(0:n, k, replace = FALSE)
for (i in 1:k) {
points(lx[i], p[lx[i]+1,i], co="white", cex=1.6, pch=19)
text(lx[i], p[lx[i]+1,i], items[i], co=1, cex=.6)
}
}
box()
}

#void Update(double *b, double *c, int *n, int *m, int *bsuf, int *csuf, double *converged);
# make a wrapper around .C
IM_update=function(b,c,bsuf,csuf,score,rasch=FALSE)
{
n=length(b)
converged=-1
tmp<-.C("Update",
b=as.double(b),
c=as.double(c),
n=as.integer(n),
score=as.integer(score),
bsuf=as.integer(bsuf),
csuf=as.integer(csuf),
converged=as.double(converged),
rasch=as.integer(rasch))
return(list(b=tmp\$b,c=tmp\$c,conv=tmp\$converged))
}

curv = function(x) {
#void ItTotal(double *b, double *c, int *n, double* prob, int *i)
n = length(x\$b) # nItems
b = x\$b
c = x\$c
o = matrix(0, n+1, n)
for (i in 1:n) {
prob = double(n+1)
tmp <- .C("ItTotal",
as.double(b),
as.double(c),
as.integer(n),
as.double(prob),
as.integer(i-1))
prob = tmp[[4]]
o[,i] = prob
}
o
}

clik<-function(x,b,c)
{
n=ncol(x)
score=rowSums(x)
l=rep(0,nrow(x))
for (s in 1:(n-1))
{
who=which(score==s)
g=elsym(exp(b+(s-1)*c))
l[who]=x[who,]%*%(b+(s-1)*c)-log(g[s+1])
}
return(l)
}

elsym = function(b) {
n = length(b)
g = rep(0, n)
j = -1L
tmp = .C("ElSym",
b=as.double(b),
n = as.integer(n),
g = as.double(g),
j = as.integer(j))
return(tmp\$g)
}

#' Item-total regressions for the Rasch vs. the interaction model
#'
#' Compare the item-total regressions fit by the Rasch model and
#' the interaction model, for one, several, or all items in the test.
#'
#'
#' @param x A matrix of scored responses (persons in rows, items in columns)
#' @param items The items to plot (column numbers). If NULL, all items will be plotted
#' @param showData If TRUE, the observed proportion correct at each sum score will
#' be shown on the plot. Default is FALSE (show only the regressions)
#' @param shade The part of the probability mass for the sum scores to shade out,
#' shown as percentage. Default is 10: shade the most extreme 10% of the distribution.
#' @param ncol When plotting  multiple items, the user can suggest the number of
#' columns in the matrix of plots (up to 3, will be adjusted if necessary)
#' @param ... Any additional plotting parameters
#' @author Ivailo Partchev, using theory and C code by Gunter Maris
#' @keywords models
#'
#' @examples
#'
#' rim(Scored, items=2)
#'
rim = function(x, items=NULL, showData=FALSE, shade=10, ncol=3, ...) {
ncol = min(ncol,3)
ss = rowSums(x)
xx = sort(unique(ss))
rm = interactionModel(x, rasch=TRUE)
im = interactionModel(x)
rmp = curv(rm)
imp = curv(im)
n = ncol(rmp)
if (!is.null(items)) items=sort(items) else items=1:n
npic = length(items)
ncol = min(ncol, npic)
nrow = npic %/% ncol + npic %% ncol
nrow = min(3, nrow)
mxs = nrow*ncol
layout(matrix(1:mxs, byrow=TRUE, ncol=ncol))
sumScores = rep(0:n, rm\$scores)
for (i in items) {
plot(c(0,n), c(0,1), ty="n", xlab="Sum score", ylab="Probability",
main=paste("Item",i), ...)
tmp = par('usr')
# par(new=TRUE)
rect(tmp[1], tmp[3], q[1], tmp[2], col="#DDDDDD", border=NA)
rect(q[2], tmp[3], tmp[2], tmp[4], col="#DDDDDD", border=NA)
if (showData) {
yy = tapply(x[,i], ss, mean)
points(xx, yy)
}
lines(0:n, rmp[,i], col=1)
lines(0:n, imp[,i], col=2)
box()
}
layout(1)
return(NULL)
}
```

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irtoys documentation built on May 2, 2019, 3:03 a.m.