mcm-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 multiple-choice model or multidimensional multiple-choice model.
mcm(x, cat, theta, dimensions = 1, ...) ## S4 method for signature 'matrix', 'numeric' mcm(x, cat, theta, dimensions, ...) ## S4 method for signature 'data.frame', 'numeric' mcm(x, cat, theta, dimensions, ...) ## S4 method for signature 'list', 'numeric' mcm(x, cat, theta, dimensions, ...) ## S4 method for signature 'irt.pars', 'ANY' mcm(x, cat, theta, dimensions, ...) ## S4 method for signature 'sep.pars', 'ANY' mcm(x, cat, theta, dimensions, ...)
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, 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 six columns (7-12) are for category difficulty
parameters. The first column of this subset of columns (column 7) should contain the
category difficulties for the 'do not know' category. Similar to the block of columns
containing the slopes, the last column in this subset of columns (column 12) for the
four category item should be NA
. The remaining five columns are for the lower
asymptote (guessing) parameters. The last column for the four category item would
be NA
. NA
. Columns
13-17 would include the category difficulties associated with the first dimension (again
the parameters for the 'do not know' category should be in the first column of this
block of columns) and columns 23-24 would be NA
. The remaining five columns are
for the lower asymptote (guessing) parameters. The last column for the four category
item 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 mcm items only. If x
contains parameters for multiple groups, a list of "irt.prob"
objects will be
returned. The argument dimensions
does not need to be included for this method.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. The argument
dimensions
does not need to be included for this method.No multidimensional extension of the multiple-choice model has officially been presented in the literature; however, this model is consistent with how the 3PL and nominal response model were extended to the multidimensional context.
Jonathan P. Weeks weeksjp@gmail.com
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.
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
mixed:
compute probabilities for mixed-format items
plot:
plot item characteristic/category curves
irt.prob
, irt.pars
, sep.pars:
classes
###### Unidimensional 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")) ###### Multidimensional Example ###### ## Discrimination and category parameters 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, 0.01, 0.09, 0.09, 0.28, 0.22, 0.31),1,27) x <- mcm(pars, cat=7, dimensions=2) # Plot separated surfaces plot(x,separate=TRUE,drape=TRUE)