rasch {msd}

Dichotomous Rasch Model

Description

Estimates item measures, person measures and their standard errors using the dichotomous Rasch model. A special case of the function msd when the rating scale consists of only two rating categories: 0 and 1. Option provided for anchoring certain items and persons while estimating the rest. Option also provided for estimating infit and outfit statistics.

Usage

rasch(data, items = NULL, persons = NULL, misfit = FALSE)

Arguments

data

a numeric matrix of 0's and 1's with missing data set to NA. Rows are persons and columns are items.

items

a numeric vector of anchored item measures. Item measures to be estimated are set to NA. Default is NULL (see Details).

persons

a numeric vector of anchored person measures. Person measures to be estimated are set to NA. Default is NULL (see Details).

misfit

logical for calculating infit and outfit statistics. Default is FALSE.

Details

items and persons are optional numeric vectors that specify item and person measures that should be "anchored" and not estimated. The length of items must equal the number of columns in data and the length of persons must equal the number of rows in data. Only entries set to NA in items and persons are estimated. Default for both items and persons is NULL, which is equivalent to a vector of NA so that all items and persons are estimated.

Value

A list whose elements are:

item_measures

a vector of item measures for each item

person_measures

a vector of person measures for each person

item_std_errors

a vector of standard errors for the items

person_std_errors

a vector of standard errors for the persons

item_reliability

reliability value for the items

person_reliability

reliability value for the persons

infit_items

if misfit = TRUE, a vector of infit statistics for the items

outfit_items

if misfit = TRUE, a vector of outfit statistics for the items

infit_persons

if misfit = TRUE, a vector of infit statistics for the persons

outfit_persons

if misfit = TRUE, a vector of outfit statistics for the persons

Note

The axis origin is set by convention at the mean item measure. All item measures and person measures that cannot be estimated will return as NA (e.g., if a person responds with a single rating category to all items, that person's person measure cannot be estimated).

rasch is the basis for the "successive dichotomizations" in msd and is repeatedly called by msd when there are three or more rating categories.

The accuracy of rasch can be tested using the simdata function (see Examples).

Author(s)

Chris Bradley ([e-mail])

See Also

msd simdata

Examples

# Simple example using a randomly generated ratings matrix
d <- as.numeric(sample(0:1, 200, replace = TRUE))
dm <- matrix(d, nrow = 20, ncol = 10)
m1 <- rasch(dm, misfit = TRUE)

# Anchor first 5 item measures and first 10 person measures
im <- m1$item_measures
im[6:length(im)] <- NA
pm <- m1$person_measures
pm[11:length(pm)] <- NA
m2 <- rasch(dm, items = im, persons = pm)

# To test the accuracy of rasch using simdata, set the true mean item measure to
# zero (axis origin in rasch is the mean item measure).  Note that the threshold for
# dichotomous data is at 0.
im <- runif(100, -2, 2)
im <- im - mean(im)
pm <- runif(100, -2, 2)
th <- 0
d <- simdata(im, pm, th, missingProb = 0.15, minRating = 0)
m <- rasch(d)

# Compare rasch parameters to true values.  Linear regression should
# yield a slope very close to 1 and an intercept very close to 0.
lm(m$item_measures ~ im)
lm(m$person_measures ~ pm)