schouten: Schouten estimators for multiobserver agreement.

Description

Use the Schouten estimator of agreement for nominal or ordinal data. This includes a range of statistics on agreement.

Usage

schouten(X, weights=c("unweighted","linear","quadratic","user"), w=NULL,
score=NULL)

Value

N: Number of subjects
M: Number of observers
L: Number of categories
data: Re-formatted X
w: Weight matrix
kab: Kappas between each pair of observers
ka: Average kappas for each observer
kappa: Average kappa
pab,pa,p,ma,qab,qa,q,oab,eab,oa,ea,o,e,wa,wab: Working fields
varkab: Variances for kab
varka: Variances for ka
vark: Variance for the kappa
covkka: Covariance term between the overall average kappa and the average kappas for each observer
chi: Chi-squared statistics comparing the overall average kappa and the average kappa for each observer (df=1 under the null hypothesis)
pchi: P-values that the overall average kappa equals the average kappa for each observer
var0kab: Variance for kab under the null hypothesis
var0ka: Variance for ka under the null hypothesis
var0k: Variance for the overall average kappa under the null hypothesis
p0: P-value for kappa=0
p0a: P-values that the average kappa for a observer equals zero (i.e. ka=0)
weights: As input
X: As input
call: As per sys.call(), to allow for using update

Arguments

X

A matrix or data-frame with subjects as rows and observers as columns.

weights

"unweighted": For nominal categories - only perfect agreement is counted.

"linear"

For ordinal categories where disagreement is proportional to the distance between the categories. This is analogous to the agreement weights \(w_{i,j}=1-|i-j|/(c-1)\).

"quadratic"

For ordinal categories where disagreement is proportional to the square of the distance between the categories. This is analogous to the agreement weights \(w_{i,j}=1-(i-j)^2/(c-1)^2\).

"user"

An indicator for a user-defined weight matrix. The weights argument will be defined as "user" if the w argument is specified.

A user-defined weights matrix. This argument takes precedence over weights and score if it is specified and the weight argument will be defined as "user".

score

A user-defined set of scores for each category. If this is not specified, it is assumed that score=1:L, where L is the number of categories. This is used with the weights argument to define the w matrix.

Details

Fortran code was written by Mark Clements based on the algorithms in Schouten (1982).

The output object is closely related to the Fortan code. Not all of the variance terms are currently used in the print, summary and plot methods.

Examples

Run this code


## Weights matrix used by Schouten (1982)
w <- outer(1:5,1:5,function(x,y) ((x<=2 & y<=2) | (x>=3 & y>=3))+0)
fit <- schouten(landis,w=w) # user-defined weights

summary(fit) # Schouten (1982), Tables 2 and 5

## we can fit the same model with oconnell() or magree() using the score argument
magree(landis,score=c(1,1,2,2,2))

## plot of the average kappas by observer
plot(fit, type="kappa by observer")