Make a map of objects (based on difficulty)
I have a set of items that correspond to items in a questionnaire that looks like this:
## item difficulty
## 1 ITEM_01_A 2.31179818
## 2 ITEM_02_B 1.95215238
## 3 ITEM_03_C 1.93479536
## 4 ITEM_04_D 1.62610855
## 5 ITEM_05_E 1.62188759
## 6 ITEM_06_F 1.45137544
## 7 ITEM_07_G 0.94255210
## 8 ITEM_08_H 0.89941812
## 9 ITEM_09_I 0.72752197
## 10 ITEM_10_J 0.61792597
## 11 ITEM_11_K 0.61288399
## 12 ITEM_12_L 0.39947791
## 13 ITEM_13_M 0.32209970
## 14 ITEM_14_N 0.31707701
## 15 ITEM_15_O 0.20902108
## 16 ITEM_16_P 0.19923607
## 17 ITEM_17_Q 0.06023317
## 18 ITEM_18_R -0.31155481
## 19 ITEM_19_S -0.67777282
## 20 ITEM_20_T -1.15013758
I want to create an item map from these items that is similar (not quite) to this (I created this in word, but I am missing true scaling as I just looked at the scale). This is not traditional statistical graphics and so I really don't know how to approach this. I don't care what graphics system this is done on, but I'm more familiar with ggplot2 and the base.
I would really appreciate a method for building such an unusual plot.
Here's the dataset (I'm including it as I'm having difficulty using it read.table
in the data area above):
DF <- structure(list(item = c("ITEM_01_A", "ITEM_02_B", "ITEM_03_C",
"ITEM_04_D", "ITEM_05_E", "ITEM_06_F", "ITEM_07_G", "ITEM_08_H",
"ITEM_09_I", "ITEM_10_J", "ITEM_11_K", "ITEM_12_L", "ITEM_13_M",
"ITEM_14_N", "ITEM_15_O", "ITEM_16_P", "ITEM_17_Q", "ITEM_18_R",
"ITEM_19_S", "ITEM_20_T"), difficulty = c(2.31179818110545, 1.95215237740899,
1.93479536058926, 1.62610855327073, 1.62188759115818, 1.45137543733965,
0.942552101641177, 0.899418119889782, 0.7275219669431, 0.617925967008653,
0.612883990709181, 0.399477905189577, 0.322099696946661, 0.31707700560997,
0.209021078266059, 0.199236065264793, 0.0602331732900628, -0.311554806052955,
-0.677772822413495, -1.15013757942119)), .Names = c("item", "difficulty"
), row.names = c(NA, -20L), class = "data.frame")
Thanks in advance.
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3 answers
Here's a solution with basic graphics.
# Compute the position of the labels to limit overlaps:
# move them as little as possible, but keep them
# at least .1 units apart.
library(quadprog)
spread <- function(b, eps=.1) {
stopifnot(b == sort(b))
n <- length(b)
Dmat <- diag(n)
dvec <- b
Amat <- matrix(0,nr=n,nc=n-1)
Amat[cbind(1:(n-1), 1:(n-1))] <- -1
Amat[cbind(2:n, 1:(n-1))] <- 1
bvec <- rep(eps,n-1)
r <- solve.QP(Dmat, dvec, Amat, bvec)
r$solution
}
DF <- DF[ order(DF$difficulty), ]
DF$position <- spread(DF$difficulty, .1)
ylim <- range(DF$difficulty)
plot( NA,
xlim = c(.5,2),
ylim = ylim + .1*c(-1,1)*diff(ylim),
axes=FALSE, xlab="", ylab=""
)
text(.9, DF$position, labels=round(DF$difficulty,3), adj=c(1,0))
text(1.1, DF$position, labels=DF$item, adj=c(0,0))
arrows(1,min(DF$position),1,max(DF$position),code=3)
text(1,min(DF$position),labels="Easier",adj=c(.5,2))
text(1,max(DF$position),labels="More difficult",adj=c(.5,-1))
text(.9, max(DF$position),labels="Difficulty",adj=c(1,-2))
text(1.1,max(DF$position),labels="Item", adj=c(0,-2))
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Here's a quick example:
ggplot(DF, aes(x=1, y=difficulty, label = item)) +
geom_text(size = 3) +
scale_y_continuous(breaks = DF$difficulty, minor_breaks = NULL, labels = sprintf("%.02f", DF$difficulty)) +
scale_x_continuous(breaks = NULL) +
opts(panel.grid.major = theme_blank())
but sometimes the two elements are too narrow, so they overlap. You can do the following:
m <- 0.1
nd <- diff(rev(DF$difficulty))
nd <- c(0, cumsum(ifelse(nd < m, m, nd)))
DF$nd <- rev(rev(DF$difficulty)[1] + nd)
ggplot(DF, aes(x=1, y=nd, label = item)) +
geom_text(size = 3) +
scale_y_continuous(breaks = DF$nd, labels = sprintf("%.02f", DF$difficulty), DF$difficulty, minor_breaks = NULL) +
scale_x_continuous(breaks = NULL) +
opts(panel.grid.major = theme_blank())
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My own attempt, but I think I will like Vincent's solution much better as it is similar to my original spec.
DF <- DF[order(DF$difficulty), ]
par(mar=c(1, 1, 3, 0)+.4)
plot(rep(1:2, each=10), DF$difficulty, main = "Item Map ",
ylim = c(max(DF$difficulty)+1, min(DF$difficulty)-.2),
type = "n", xlab="", ylab="", axes=F, xaxs="i")
text(rep(1.55, 20), rev(DF$difficulty[c(T, F)]),
DF$item[c(F, T)], cex=.5, pos = 4)
text(rep(1, 20), rev(DF$difficulty[c(F, T)]),
DF$item[c(T, F)], cex=.5, pos = 4)
par(mar=c(0, 0, 0,0))
arrows(1.45, 2.45, 1.45, -1.29, .1, code=3)
text(rep(1.52, 20), DF$difficulty[c(T, F)],
rev(round(DF$difficulty, 2))[c(T, F)], cex=.5, pos = 2)
text(rep(1.44, 20), DF$difficulty[c(F, T)],
rev(round(DF$difficulty, 2))[c(F, T)], cex=.5, pos = 2)
text(1.455, .5, "DIFFICULTY", cex=1, srt = -90)
text(1.45, -1.375, "More Difficult", cex=.6)
text(1.45, 2.5, "Easier", cex=.6)
par(mar=c(0, 0, 0,0))
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