msd {msd}

Method of Successive Dichotomizations

Description

Estimates item measures, person measures, rating category thresholds and their standard errors using the method of successive dichotomizations. Option provided for anchoring certain items and persons while estimating the rest. Option also provided for estimating infit and outfit statistics.

Usage

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

Arguments

data

a numeric matrix of ordinal rating scale data whose entries are integers with missing data set to NA. Rows are persons and columns are items. The ordinal rating scale is assumed to go from the smallest integer to the largest integer in data in integer steps.

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 are "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

thresholds

a vector of average rating category thresholds used by the persons when rating the items

item_std_errors

a vector of standard errors for the items

person_std_errors

a vector of standard errors for the persons

threshold_std_errors

a vector of standard errors for the thresholds

item_reliability

reliability of the item measures

person_reliability

reliability of the person measures

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 only the highest rating category, or with only the lowest rating category, to all items, that person's person measure cannot be estimated).

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

Author(s)

Chris Bradley ([e-mail])

References

Bradley, C. and Massof, R. W. (2018) Method of successive dichotomizations: An improved method for estimating measures of latent variables from rating scale data. PLoS One, 13(10) doi:10.1371/journal.pone.0206106

See Also

simdata

Examples

# Simple example using a randomly generated ratings matrix
d <- as.numeric(sample(0:5, 200, replace = TRUE))
dm <- matrix(d, nrow = 20, ncol = 10)
m1 <- msd(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 <- msd(dm, items = im, persons = pm)

# To test the accuracy of msd using simdata, set the mean item measure to zero
# (axis origin in msd is the mean item measure) and the mean threshold to
# zero (any non-zero mean threshold is reflected in the person measures).
im <- runif(100, -2, 2)
im <- im - mean(im)
pm <- runif(100, -2, 2)
th <- sort(runif(5, -2, 2))
th <- th - mean(th)
d <- simdata(im, pm, th, missingProb = 0.15, minRating = 0)
m <- msd(d)

# Compare msd 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)
lm(m$thresholds ~ th)