ltm (version 1.2-0)

plot IRT: Plot method for fitted IRT models

Description

Produces the Item Characteristic or Item Information Curves for fitted IRT models.

Usage

# S3 method for gpcm
plot(x, type = c("ICC", "IIC", "OCCu", "OCCl"), 
    items = NULL, category = NULL, zrange = c(-3.8, 3.8), 
    z = seq(zrange[1], zrange[2], length = 100), annot,
    labels = NULL, legend = FALSE, cx = "top", cy = NULL, ncol = 1, 
    bty = "n", col = palette(), lty = 1, pch, xlab, ylab, main, sub = NULL, 
    cex = par("cex"), cex.lab = par("cex.lab"), cex.main = par("cex.main"), 
    cex.sub = par("cex.sub"), cex.axis = par("cex.axis"), ask = TRUE,
    plot = TRUE, …)
# S3 method for grm
plot(x, type = c("ICC", "IIC", "OCCu", "OCCl"), 
    items = NULL, category = NULL, zrange = c(-3.8, 3.8), 
    z = seq(zrange[1], zrange[2], length = 100), annot,
    labels = NULL, legend = FALSE,
    cx = "top", cy = NULL, ncol = 1, bty = "n", col = palette(), lty = 1, pch,
    xlab, ylab, main, sub = NULL, cex = par("cex"), cex.lab = par("cex.lab"),
    cex.main = par("cex.main"), cex.sub = par("cex.sub"), 
    cex.axis = par("cex.axis"), ask = TRUE, plot = TRUE, …)
# S3 method for ltm
plot(x, type = c("ICC", "IIC", "loadings"), 
    items = NULL, zrange = c(-3.8, 3.8),
    z = seq(zrange[1], zrange[2], length = 100), annot,
    labels = NULL, legend = FALSE, cx = "topleft", cy = NULL, 
    ncol = 1, bty = "n", col = palette(), lty = 1, pch, xlab, 
    ylab, zlab, main, sub = NULL, cex = par("cex"),
    cex.lab = par("cex.lab"), cex.main = par("cex.main"), 
    cex.sub = par("cex.sub"), ask = TRUE,
    cex.axis = par("cex.axis"), plot = TRUE, …)
# S3 method for rasch
plot(x, type = c("ICC", "IIC"), items = NULL, 
    zrange = c(-3.8, 3.8), z = seq(zrange[1], zrange[2], length = 100), 
    annot, labels = NULL, legend = FALSE, cx = "topleft", cy = NULL, 
    ncol = 1, bty = "n", col = palette(), lty = 1, pch, xlab, ylab, 
    main, sub = NULL, cex = par("cex"), cex.lab = par("cex.lab"),
    cex.main = par("cex.main"), cex.sub = par("cex.sub"), 
    cex.axis = par("cex.axis"), plot = TRUE, …)
# S3 method for tpm
plot(x, type = c("ICC", "IIC"), items = NULL, 
    zrange = c(-3.8, 3.8), z = seq(zrange[1], zrange[2], length = 100), 
    annot, labels = NULL, legend = FALSE, cx = "topleft", cy = NULL, 
    ncol = 1, bty = "n", col = palette(), lty = 1, 
    pch, xlab, ylab, main, sub = NULL, cex = par("cex"), 
    cex.lab = par("cex.lab"), cex.main = par("cex.main"), 
    cex.sub = par("cex.sub"), cex.axis = par("cex.axis"), 
    plot = TRUE, …)

Arguments

x

an object inheriting either from class gpcm, class grm, class ltm, class rasch or class tpm.

type

the type of plot; "ICC" refers to Item Response Category Characteristic Curves whereas "IIC" to Item Information Curves. For ltm objects the option "loadings" is also available that produces the scatter plot of the standardized loadings. For grm objects the options "OCCu" and "OCCl" are also available that produces the item operation characteristic curves.

items

a numeric vector denoting which items to plot; if NULL all items are plotted; if 0 and type = "IIC" the Test Information Curve is plotted.

category

a scalar indicating the response category for which the curves should be plotted; if NULL all categories are considered. This argument is only relevant for grm objects.

zrange

a numeric vector of length 2 indicating the range for the latent variable values.

z

a numeric vector denoting the values for the latent variable(s) values to be used in the plots.

annot

logical; if TRUE the plotted lines are annotated.

labels

character vector; the labels to use in either the annotation or legend. If NULL adequate labels are produced.

legend

logical; if TRUE a legend is printed.

cx, cy, ncol, bty

arguments of legend; cx and cy correspond to the x and y arguments of legend.

col, lty, pch

control values, see par; recycling is used if necessary.

xlab, ylab, zlab, main, sub

character string or an expression; see title.

cex, cex.lab, cex.main, cex.sub, cex.axis, ask

the cex family of argument; see par.

plot

logical; if TRUE the plot(s) is(are) produced otherwise only the values used to create the plot(s) are returned.

…

extra graphical parameters to be passed to plot(), lines(), legend() and text().

Value

The values used to create the plot, i.e., the x-, y-coordinates. This is either a matrix or a list in which the first column or element provides the latent variable values used, and the remaining columns or elements correspond to either probabilities or information or loadings, depending on the value of the type argument.

Details

Item response category characteristic curves show how the probability of responding in the \(k\)th category, in each item, changes with the values of the latent variable (ability).

The item information curves indicate the relative ability of an item to discriminate among contiguous trait scores at various locations along the trait continuum. The test information curve, which is the sum of item information curves, provides a visual depiction of where along the trait continuum a test is most discriminating (Reise and Waller, 2002).

References

Reise, S. and Waller, N. (2002) Item response theory for dichotomous assessment data. In Drasgow, F. and Schmitt, N., editors, Measuring and Analyzing Behavior in Organizations. San Francisco: Jossey-Bass.

See Also

information, gpcm, grm, ltm, rasch, tpm

Examples

# NOT RUN {
# Examples for plot.grm()

fit <- grm(Science[c(1,3,4,7)])

## Item Response Category Characteristic Curves for 
## the Science data
op <- par(mfrow = c(2, 2))
plot(fit, lwd = 2, legend = TRUE, ncol = 2)
# re-set par()
par(op)

## Item Characteristic Curves for the 2nd category,
## and items 1 and 3
plot(fit, category = 2, items = c(1, 3), lwd = 2, legend = TRUE, cx = "right")

## Item Information Curves for the Science data;
plot(fit, type = "IIC", legend = TRUE, cx = "topright", lwd = 2, cex = 1.4)

## Test Information Function for the Science data;
plot(fit, type = "IIC", items = 0, lwd = 2)


###################################################


# Examples for plot.ltm()

## Item Characteristic Curves for the two-parameter logistic
## model; plot only items 1, 2, 4 and 6; take the range of the
## latent ability to be (-2.5, 2.5):
fit <- ltm(WIRS ~ z1)
plot(fit, items = c(1, 2, 4, 6), zrange = c(-2.5, 2.5), lwd = 3, cex = 1.4)

## Test Information Function under the two-parameter logistic
## model for the Lsat data
fit <- ltm(LSAT ~ z1)
plot(fit, type = "IIC", items = 0, lwd = 2, cex.lab = 1.2, cex.main = 1.3)
info <- information(fit, c(-3, 0))
text(x = 2, y = 0.5, labels = paste("Total Information:", round(info$InfoTotal, 3), 
    "\n\nInformation in (-3, 0):", round(info$InfoRange, 3), 
    paste("(", round(100 * info$PropRange, 2), "%)", sep = "")), cex = 1.2)

## Item Characteristic Surfaces for the interaction model:
fit <- ltm(WIRS ~ z1 * z2)
plot(fit, ticktype = "detailed", theta = 30, phi = 30, expand = 0.5, d = 2, 
     cex = 0.7, col = "lightblue")

###################################################


# Examples for plot.rasch()

## Item Characteristic Curves for the WIRS data;
## plot only items 1, 3 and 5:
fit <- rasch(WIRS)
plot(fit, items = c(1, 3, 5), lwd = 3, cex = 1.4)
abline(v = -4:4, h = seq(0, 1, 0.2), col = "lightgray", lty = "dotted")

fit <- rasch(LSAT)

## Item Characteristic Curves for the LSAT data;
## plot all items plus a legend and use only black:
plot(fit, legend = TRUE, cx = "right", lwd = 3, cex = 1.4, 
     cex.lab = 1.6, cex.main = 2, col = 1, lty = c(1, 1, 1, 2, 2),
     pch = c(16, 15, 17, 0, 1))
abline(v = -4:4, h = seq(0, 1, 0.2), col = "lightgray", lty = "dotted")

## Item Information Curves, for the first 3 items; include a legend
plot(fit, type = "IIC", items = 1:3, legend = TRUE, lwd = 2, cx = "topright")

## Test Information Function
plot(fit, type = "IIC", items = 0, lwd = 2, cex.lab = 1.1, 
     sub = paste("Call: ", deparse(fit$call)))

## Total information in (-2, 0) based on all the items
info.Tot <- information(fit, c(-2, 0))$InfoRange
## Information in (-2, 0) based on items 2 and 4
info.24 <- information(fit, c(-2, 0), items = c(2, 4))$InfoRange
text(x = 2, y = 0.5, labels = paste("Total Information in (-2, 0):", 
    round(info.Tot, 3), 
    "\n\nInformation in (-2, 0) based on\n Items 2 and 4:", round(info.24, 3), 
    paste("(", round(100 * info.24 / info.Tot, 2), "%)", sep = "")), 
    cex = 1.2)

## The Standard Error of Measurement can be plotted by
vals <- plot(fit, type = "IIC", items = 0, plot = FALSE)
plot(vals[, "z"], 1 / sqrt(vals[, "info"]), type = "l", lwd = 2,
     xlab = "Ability", ylab = "Standard Error", 
     main = "Standard Error of Measurement")

###################################################


# Examples for plot.tpm()

## Compare the Item Characteristic Curves for the LSAT data,
## under the constraint Rasch model, the unconstraint Rasch model,
## and the three parameter model assuming equal discrimination
## across items
par(mfrow = c(2, 2))
pl1 <- plot(rasch(LSAT, constr = cbind(length(LSAT) + 1, 1)))
text(2, 0.35, "Rasch model\nDiscrimination = 1")
pl2 <- plot(rasch(LSAT))
text(2, 0.35, "Rasch model")
pl3 <- plot(tpm(LSAT, type = "rasch", max.guessing = 1))
text(2, 0.35, "Rasch model\nwith Guessing parameter")

## Compare the Item Characteristic Curves for Item 4
## (you have to run the above first)
plot(range(pl1[, "z"]), c(0, 1), type = "n", xlab = "Ability", 
     ylab = "Probability", main = "Item Characteristic Curves - Item 4")
lines(pl1[, c("z", "Item 4")], lwd = 2, col = "black")
lines(pl2[, c("z", "Item 4")], lwd = 2, col = "red")
lines(pl3[, c("z", "Item 4")], lwd = 2, col = "blue")
legend("right", c("Rasch model Discrimination = 1", "Rasch model", 
       "Rasch model with\nGuessing parameter"), lwd = 2, col = c("black", 
       "red", "blue"), bty = "n")

# }