lc.2raters.Rd
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).
lc.2raters(data, conv=0.001, maxiter=1000, progress=TRUE) # S3 method for lc.2raters summary(object,...)
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 |
... | Further arguments to be passed |
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 \(p_{x|c}\).
A list with following entries
Classification probability \(P(c|x)\) of latent category \(c\) given a manifest rating \(x\) (estimated by maximum likelihood)
Classification probability \(P(c|x)\) of latent category \(c\) given a manifest rating \(x\) (estimated by the posterior distribution)
Classification probability \(P(c|(x,y))\) of latent category \(c\) given two manifest ratings \(x\) and \(y\) (estimated by maximum likelihood)
Classification probability \(P(c|(x,y))\) of latent category \(c\) given two manifest ratings \(x\) and \(y\) (estimated by posterior distribution)
Likelihood of each pair of ratings
Posterior of each pair of ratings
Item response probabilities \(p_{x|c}\)
Estimated class proportions \(\pi_c\)
Observed manifest class proportions
Frequency table of ratings in long format
Symmetrized frequency table of ratings
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).
Used dataset
Number of categories
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 rm.facets
and rm.sdt
for
specifying rater models.
See also the irr package for measures of rater agreement.
############################################################################# # 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)