R: Latent Class Model for Two Exchangeable Raters and One Item
lc.2raters
R Documentation
Latent Class Model for Two Exchangeable Raters and One Item
Description
This function computes a latent class model for ratings on an item
based on exchangeable raters (Uebersax & Grove, 1990). Additionally,
several measures of rater agreement are computed (see e.g. Gwet, 2010).
Usage
lc.2raters(data, conv = 0.001, maxiter = 1000, progress = TRUE)
## S3 method for class 'lc.2raters'
summary(object,...)
Arguments
data
Data frame with item responses (must be ordered from 0 to K) and two
columns which correspond to ratings of two (exchangeable) raters.
conv
Convergence criterion
maxiter
Maximum number of iterations
progress
An optional logical indicating whether iteration progress should be displayed.
object
Object of class lc.2raters
...
Further arguments to be passed
Details
For two exchangeable raters which provide ratings on an item, a latent
class model with K+1 classes (if there are K+1 item categories
0,...,K) is defined. Where P(X = x, Y=y | c) denotes
the probability that the first rating is x and the second rating is
y given the true but unknown item category (class) c. Ratings are
assumed to be locally independent, i.e.
P(X=x , Y=y | c ) = P( X =x | c) cdot P(Y=y | c ) = p_{x|c} cdot p_{y|c}
Note that P(X=x|c)=P(Y=x|c)=p_{x|c} holds due to the exchangeability of raters.
The latent class model estimates true class proportions π_c and
conditional item probabilities p_{x|c}.
Value
A list with following entries
classprob.1rater.like
Classification probability P(c|x) of latent
category c given a manifest rating x (estimated by maximum likelihood)
classprob.1rater.post
Classification probability P(c|x) of latent
category c given a manifest rating x (estimated by the posterior
distribution)
classprob.2rater.like
Classification probability P(c|(x,y))
of latent category c given two manifest ratings x and y
(estimated by maximum likelihood)
classprob.2rater.post
Classification probability P(c|(x,y))
of latent category c given two manifest ratings x and y
(estimated by posterior distribution)
f.yi.qk
Likelihood of each pair of ratings
f.qk.yi
Posterior of each pair of ratings
probs
Item response probabilities p_{x|c}
pi.k
Estimated class proportions π_c
pi.k.obs
Observed manifest class proportions
freq.long
Frequency table of ratings in long format
freq.table
Symmetrized frequency table of ratings
agree.stats
Measures of rater agreement. These measures include
percentage agreement (agree0, agree1), Cohen's kappa and weighted
Cohen's kappa (kappa, wtd.kappa.linear),
Gwet's AC1 agreement measures (AC1; Gwet, 2008, 2010) and
Aickin's alpha (alpha.aickin; Aickin, 1990).
data
Used dataset
N.categ
Number of categories
Author(s)
Alexander Robitzsch
References
Aickin, M. (1990). Maximum likelihood estimation of agreement in the constant
predictive probability model, and its relation to Cohen's kappa.
Biometrics, 46, 293-302.
Gwet, K. L. (2008). Computing inter-rater reliability and its variance
in the presence of high agreement.
British Journal of Mathematical and Statistical Psychology,
61, 29-48.
Gwet, K. L. (2010). Handbook of Inter-Rater Reliability.
Advanced Analytics, Gaithersburg. http://www.agreestat.com/
Uebersax, J. S., & Grove, W. M. (1990). Latent class analysis of diagnostic
agreement. Statistics in Medicine, 9, 559-572.
See Also
See also rm.facets and rm.sdt for
specifying rater models.
See also the irr package for measures of rater agreement.
Examples
#############################################################################
# EXAMPLE 1: Latent class models for rating datasets data.si05
#############################################################################
data(data.si05)
#*** Model 1: one item with two categories
mod1 <- lc.2raters( data.si05$Ex1)
summary(mod1)
#*** Model 2: one item with five categories
mod2 <- lc.2raters( data.si05$Ex2)
summary(mod2)
#*** Model 3: one item with eight categories
mod3 <- lc.2raters( data.si05$Ex3)
summary(mod3)