# Plot method for fitted IRT models Produces the Item Characteristic or Item Information Curves for fitted IRT models. ```r ## S3 method for class '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 class '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 class '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 class '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 class '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()`. ## 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). ## Returns 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. ## 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. ## Author(s) Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl ## See Also `information`, `gpcm`, `grm`, `ltm`, `rasch`, `tpm` ## Examples ```r # 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") ```

plot function