nrm-methods {plink}R Documentation

Nominal Response Model 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 nominal response model.

Usage

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

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

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

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

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

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

Arguments

x Object containing item parameters. See below for more details.
cat vector identifying the number of response categories for each item
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 two times the maximum number of response categories across items (e.g. if some items have four response categories and others have five categories, k will equal 10). The first k/2 columns are for category discrimination parameters. For any items with fewer categories than the maximum, the remaining cells in the k/2 row should be NA. The remaining columns are for the category difficulty parameters. Similarly, items with fewer response categories than the maximum should have NAs in the remaining cells. For example, for one four category and one five category item, the first four columns for the four response item would include the discrimination parameters. The fifth column for this item would be NA. The next four columns would include the category difficulty values, and the last column would be NA.
x = "data.frame", cat = "numeric"
See the method for x = "matrix"
x = "list", cat = "numeric"
This method is for a list with two elements. The first element is and n x k matrix of category discrimination values for n items and k equal to the maximum number of response categories across items. The second list element is an n x k matrix of category difficulty parameters. For either element, for items with fewer categories than the maximum, the remaining cells in the rows should be NA. 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.
x = "irt.pars", cat = "ANY"
This method can be used to compute probabilities for the nrm 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 nrm 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 nrm items only.

Author(s)

Jonathan P. Weeks weeksjp@gmail.com

References

Bock, R.D. (1972) Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51.

Bock, R.D. (1996) The nominal categories model. In W.J. van der Linden & Hambleton, R. K. (Eds.) Handbook of Modern Item Response Theory. New York: Springer-Verlag

Kolen, M. J., & Brennan, R. L. (2004) Test Equating, Scaling, and Linking. New York: Springer

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 Bock (1972, p. 46,47)
a <- matrix(c(.905, .522, -.469, -.959, NA, .828, .375, -.357, -.079, -.817),
  2,5,byrow=TRUE)
c <- matrix(c(.126, -.206, -.257, .336, NA, .565, .865, -1.186, -1.199, .993),
  2,5,byrow=TRUE)
pars <- cbind(a,c)
x <- nrm(pars, c(4,5))
plot(x,auto.key=list(space="right"))


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