lc.2raters: Latent Class Model for Two Exchangeable Raters and One Item

In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

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 \pi_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 \pi_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

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 <- sirt::lc.2raters( data.si05$Ex1)
summary(mod1)

#*** Model 2: one item with five categories
mod2 <- sirt::lc.2raters( data.si05$Ex2)
summary(mod2)

#*** Model 3: one item with eight categories
mod3 <- sirt::lc.2raters( data.si05$Ex3)
summary(mod3)

alexanderrobitzsch/sirt documentation built on Dec. 1, 2024, 2:18 a.m.