WrightMap: Multifaceted models

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We received an email from a user who was interested in displaying results from a multifaceted model in WrightMap. In the WrightMap manual, we show how to use multifaceted results from ConQuest:

fpath <- system.file("extdata", package = "WrightMap")

model4 <- CQmodel(file.path(fpath, "ex4a.mle"), file.path(fpath, "ex4a.shw"))
wrightMap(model4, item.table = "rater", interactions = "rater*topic", step.table = "topic")

(See this tutorial for more details.)

But if your results aren’t from ConQuest, this example won’t be as useful to you. However, the basic WrightMap function is program-independent. If you can put your results into a matrix, WrightMap can graph it. The most important thing to remember is that WrightMap treats rows as “items” and columns as “steps”. So if you would like to make a graph like the one above with your data, each rater (Amy, Beverley, etc.) should be associated with a column, and each topic (School, Family) with a row.

For this example, we will be using results from the R package TAM (created by Thomas Kiefer, Alexander Robitzsch, and Margaret Wu). We discussed using TAM results in WrightMap in this post and this follow-up, using a simple dichotomous model. For this tutorial, we’ll use a item * rater model.

The setup and comments here are taken from the TAM manual:

dat <- data.ex10

facets <- dat[, "rater", drop = FALSE]  # define facet (rater)
pid <- dat$pid  # define person identifier (a person occurs multiple times)
resp <- dat[, -c(1:2)]  # item response data
formulaA <- ~item * rater  # formula

mod <- tam.mml.mfr(resp = resp, facets = facets, formulaA = formulaA, pid = dat$pid)

persons.mod <- tam.wle(mod)
theta <- persons.mod$theta

The tam.thresholds command provides us with the estimated difficulty for each item-by-rater (item + rater + item * rater).

thr <- tam.threshold(mod)
item.labs <- c("I0001", "I0002", "I0003", "I0004", "I0005")
rater.labs <- c("rater1", "rater2", "rater3")

Now we need to turn it into a matrix formatted the way WrightMap expects. We could organize it by item:

thr1 <- matrix(thr, nrow = 5, byrow = TRUE)
wrightMap(theta, thr1, label.items = item.labs, thr.lab.text = rep(rater.labs, each = 5))

Or by rater:

thr2 <- matrix(thr, nrow = 3)
wrightMap(theta, thr2, label.items = rater.labs, thr.lab.text = rep(item.labs,  each = 3), axis.items = "Raters")

Another option is to show the item, rater, and item * rater parameters separately. We can get these from the xsi.facets table.

pars <- mod$xsi.facets$xsi
facet <- mod$xsi.facets$facet

item.par <- pars[facet == "item"]
rater.par <- pars[facet == "rater"]
item_rat <- pars[facet == "item:rater"]

We could put them in separate bands, adding NA to make them all the same length.

len <- length(item_rat)
item.long <- c(item.par, rep(NA, len - length(item.par)))
rater.long <- c(rater.par, rep(NA, len - length(rater.par)))
ir.labs <- mod$xsi.facets$parameter[facet == "item:rater"]

wrightMap(theta, rbind(item.long, rater.long, item_rat), label.items = c("Items",  "Raters", "Item*Raters"), thr.lab.text = rbind(item.labs, rater.labs, ir.labs), axis.items = "")

But the item*rater band is a little crowded. So let’s separate it by rater:

ir_rater<- matrix(item_rat, nrow = 3, byrow = TRUE)

wrightMap(theta, rbind(item.par, c(rater.par, NA, NA), ir_rater), label.items = c("Items", "Raters", "Item*Raters (R1)", "Item*Raters (R2)", "Item*Raters (R3)"), axis.items = "", thr.lab.text = rbind(item.labs, rater.labs, matrix(item.labs, nrow = 3, ncol = 5, byrow = TRUE)))

Or by item:

ir_item <- matrix(item_rat, nrow = 5)

wrightMap(theta, rbind(item.par, c(rater.par, NA, NA), cbind(ir_item, NA, NA)), label.items = c("Items", "Raters", "Item*Raters (I1)", "Item*Raters (I2)", "Item*Raters (I3)", "Item*Raters (I4)", "Item*Raters (I5)"), axis.items = "", thr.lab.text = rbind(item.labs, matrix(c(rater.labs, NA, NA), nrow = 6, ncol = 5, byrow = TRUE)))

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