nrm-methods {plink} | R Documentation |
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 or multidimensional nominal response model.
nrm(x, cat, theta, dimensions = 1, ...) ## S4 method for signature 'matrix', 'numeric' nrm(x, cat, theta, dimensions, ...) ## S4 method for signature 'data.frame', 'numeric' nrm(x, cat, theta, dimensions, ...) ## S4 method for signature 'list', 'numeric' nrm(x, cat, theta, dimensions, ...) ## S4 method for signature 'irt.pars', 'ANY' nrm(x, cat, theta, dimensions, ...) ## S4 method for signature 'sep.pars', 'ANY' nrm(x, cat, theta, dimensions, ...)
x |
Object containing item parameters. See below for more details. |
cat |
vector identifying the number of response categories for each item |
theta |
vector, matrix, or list 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 0.5. See details below for more information. |
dimensions |
number of modeled dimensions |
... |
further arguments passed to or from other methods |
theta
can be specified as a vector, matrix, or list. For the unidimensional case, theta
should be a vector. If a matrix or list of values is supplied, they will be converted to a single vector
of theta values. For the multidimensional case, if a vector of values is supplied it will be assumed
that this same set of values should be used for each dimension. Probabilities will be computed for each
combination of theta values. Similarly, if a list is supplied, probabilities will be computed for each
combination of theta values. In instances where probabilities are desired for specific combinations of
theta values, a j x m matrix should be specified for j ability points and m dimensions where the columns
are ordered from dimension 1 to m.
Returns an object of class irt.prob
NA
.
NA
. The next
four columns would include the category difficulty values, and the last column would
be NA
. NA
. Columns 11-14 would include the
category difficulties associated with the first dimension and columns 19-20 would
be NA
. NA
(see the examples for method x = "matrix" for
specification details). "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.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.Jonathan P. Weeks weeksjp@gmail.com
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
Bolt, D. M. & Johnson, T. J. (in press) Applications of a MIRT model to self-report measures: Addressing score bias and DIF due to individual differences in response style. Applied Psychological Measurement.
Kolen, M. J., & Brennan, R. L. (2004) Test Equating, Scaling, and Linking. New York: Springer
Takane, Y., & De Leeuw, J. (1987) On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52(3), 393-408.
mixed:
compute probabilities for mixed-format items
plot:
plot item characteristic/category curves
irt.prob
, irt.pars
, sep.pars:
classes
###### Unidimensional Example ###### ## 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")) ###### Multidimensional Example ###### # From Bolt & Johnson (in press) pars <- matrix(c(-1.28, -1.029, -0.537, 0.015, 0.519, 0.969, 1.343, 1.473, -0.585, -0.561, -0.445, -0.741, -0.584, 1.444, 0.29, 0.01, 0.04, 0.34, 0, -0.04, -0.63), 1,21) x <- nrm(pars, cat=7, dimensions=2) # Plot separated surfaces plot(x,separate=TRUE,drape=TRUE)