mcm-methods {plink}R Documentation

Multiple-Choice Model Response Probabilities

Description

This function computes the probability of responding in a specific category for one or more items for a given set of theta values using the multiple-choice model.

Usage

mcm(x, cat, theta = seq(-4,4,0.05), ...)

## S4 method for signature 'matrix', 'numeric'
mcm(x, cat, theta, ...)

## S4 method for signature 'data.frame', 'numeric'
mcm(x, cat, theta, ...)

## S4 method for signature 'list', 'numeric'
mcm(x, cat, theta, ...)

## S4 method for signature 'irt.pars', 'ANY'
mcm(x, cat, theta, ...)

## S4 method for signature 'sep.pars', 'ANY'
mcm(x, cat, theta, ...)

Arguments

x an R object containing item parameters
cat vector identifying the number of response categories plus one for each item (the additional category is for 'do not know')
theta vector of theta values for which probabilities will be computed. If theta is not specified, an equal interval range of values from -4 to 4 is used with an increment of 0.05
... further arguments passed to or from other methods

Value

Returns an object of class irt.prob

Methods

x = "matrix", cat = "numeric"
This method allows one to specify an n x k matrix for n items and k equal to three times the maximum number of response categories (including the 'do not know' category) across items minus one (e.g. if some items have four response categories and others have five categories, k will equal 14).

Discrimination Parameters:
The first (k+1)/3 columns are for category discrimination parameters. The first column should contain the parameters for the 'do not know' category. For any items with fewer categories than the maximum, the remaining cells in the (k+1)/3 row should be NA.
Category Difficulty Parameters:
The second set of (k+1)/3 columns are for category difficulty parameters. The first column of this subset of columns should contain the category difficulties for the 'do not know' category. Similar to the discrimination columns, items with fewer response categories than the maximum should have NAs in the remaining cells of the (k+1)/3 subset of columns.

Guessing Probabilities:
The remaining ((k+1)/3)-1 columns are for the guessing probabilities. As with the discrimination and category difficulties, the remaining cells for items with fewer categories than the maximum should be filled with NAs.

For example, for one four category and one five category item, the first column includes the discrimination parameters for the 'do not know' categories. Columns 2-5 contain the discrimination parameters for the other categories. The fifth column for the four response item should be NA. The sixth column includes the category difficulties for the 'do not know' category. Columns 7-10 contain the difficulty parameters for the other categories. The tenth column for the four response item should be NA. The remaining four columns include the guessing probabilities, although the last column for the four response item should be NA.

x = "data.frame", cat = "numeric"
See the method for x = "matrix"
x = "list", cat = "numeric"
This method is for a list with three elements. The first list element is for discimination parametes, the second is for category difficulty parameters, and the third is for alternative response probability parameters.
Discrimination Parameters:
The first list element should conatain an n x k matrix of category discrimination values for n items and k equal to the maximum number of response categories (including the 'do not know' category) across all items. The first column of this matrix should include the parameters for the 'do not know' category. For any items with fewer categories than the maximum, the remaining cells in the row should be NA.
Category Difficulty Parameters:
The second list element is an n x k matrix of category difficulty parameters. The first element of this matrix should include the category difficulties for the 'do not know' category. Similar to the discrimination list element, items with fewer response categories than the maximum should have NAs in the remaining cells.

Guessing Probabilities:
The third list element is an n x (k-1) matrix of guessing probabilities (i.e. there is no column for the 'do not know' category). As with the discrimination and category difficulties, the remaining cells for items with fewer categories than the maximum should be filled with NAs.

For example, for one four category and one five category item, the first four columns for the four response item in the first list element would include the discrimination parameters. The fifth column for this item would be NA. The first four columns for the four response item in the second list element would include the category difficulty parameters. The fifth column for this item would be NA. The first three columns for the four response item in the third list element would include the guessing probabilities. The fourth column for this item would be NA.

x = "irt.pars", cat = "ANY"
This method can be used to compute probabilities for the mcm items in an object of class "irt.pars". If x contains dichotomous items or items associated with another polytomous model, a warning will be displayed stating that probabilities will be computed for the mcm items only. If x contains parameters for multiple groups, a list of "irt.prob" objects will be returned.
x = "sep.pars", cat = "ANY"
This method can be used to compute probabilities for the mcm items in an object of class sep.pars. If x contains dichotomous items or items associated with another polytomous model, a warning will be displayed stating that probabilities will be computed for the mcm items only.

Author(s)

Jonathan P. Weeks weeksjp@gmail.com

References

Thissen, D., & Steinberg, L. (1984). A response model for multiple choice items. Psychometrika, 49(4), 501-519.

Thissen, D., & Steinberg, L. (1996) A response model for multiple choice items. In W.J. van der Linden & Hambleton, R. K. (Eds.) Handbook of Modern Item Response Theory. New York: Springer-Verlag

See Also

mixed: compute probabilities for mixed-format items
plot: plot item characteristic/category curves
irt.prob, irt.pars, sep.pars: classes

Examples

## Item parameters from Thissen & Steinberg (1984, p. 510)
## Items R,S,T,U for the whole test
a <- matrix(c(-1.7, -1, 1.1, .3, 1.9, -2.1, -.6, 1.2, 2.3, -.8, -1.3, -.9, -.2, 1.9, .5, 
  -1.9, -.5, 0, -.6, 1.9),4,5,byrow=TRUE)
c <- matrix(c(.3, -2.3, 2.4, -2.5, 2.1, 2.1, .05, -3, -.6, 1, -.9, -2.5, -.1, 1.8, 1.6, 
  -.1, -2, .5, .8, .8),4,5,byrow=TRUE)
d <- matrix(c(.25, .25, .25, .25, .2, .2, .4, .2, .2, .2, .4, .2, .25, .25, .25, .25),
  4,4,byrow=TRUE)
pars <- cbind(a,c,d)
x <- mcm(pars, rep(5,4))
plot(x,item.names=paste("Item",c("R","S","T","U")), auto.key=list(space="right"))

## Item parameters from Thissen & Steinberg (1984, p. 511)
## Items W,X,Y,Z for the 
pars <- vector("list",3)
pars[[1]] <- matrix(c(-2.3, -.2, 2, .9, -.3, -.8, .6, -.5, 1.1, -.4, -.5, -.2, 2, -1.2, 0, 
  -1.5, -.7, -.2, .1, 2.3),4,5,byrow=TRUE)
pars[[2]] <- matrix(c(.5, .7, -.5, -1.9, 1.1, 1.6, -2.8, 1.5, 0, -.3, -.3, .7, -1, .7, 0, 
  .4, .4, -.5, .5, -.8),4,5,byrow=TRUE)
pars[[3]] <- matrix(c(.2, .4, .2, .2, .2, .2, .4, .2, .2, .4, .2, .2, .2, .2, .2, .4),
  4,4,byrow=TRUE)
x <- mcm(pars, rep(5,4))
plot(x,item.names=paste("Item",c("W","X","Y","Z")), auto.key=list(space="right"))

[Package plink version 0.1-1 Index]