irt (version 0.2.9)

kappa_coef: Calculate Cohen's Kappa Coefficient

Description

This function calculates weighted or unweighted Kappa coefficient for two sets of ratings. Kappa coefficient quantifies the agreement between two sets of ratings (like two raters) beyond what is expected by chance. It can be used as a measure of inter-rater reliability.

If the ratings are ordinal (for example Likert scale), weighted kappa coefficient can be used. Weighted Kappa penalizes the larger discrepancies between raters. More emphasis is put to large differences between rating and small emphasis will be put on smaller differences. The available weighting options are "linear" and "quadratic". By default the function calculates "unweighted" Kappa coefficient.

Usage

kappa_coef(x, weights = "unweighted")

Value

A Kappa coefficient which is a number between -1 and 1. 1 means perfect agreement between ratings. 0 means agreement between rating is no better than agreement one would get merely by chance. Negative values means the agreement is even worse than one would get by chance.

Arguments

x

A matrix/data.frame with two columns where each column contains a set of ratings. When weights = "linear" or weights = "quadratic", each row should be an ordered factor or numbers. The rows with missing values (i.e. NA) will be removed from the analysis.

weights

Either a string representing the weighting method. Or, a square matrix of weights that will be applied to the cross table (assuming the ratings are ordered factors or numeric). There are three possible weighting methods (aside from the custom weights method):

'unweighted'

This is the original Kappa coefficient where no weighting applied. This is the default method. This method is appropriate for both nominal (i.e. unordered) data or ordinal (i.e. ordered) data.

'linear'

Linear weights applied.

'quadratic'

Quadratic weights applied.

Author

Emre Gonulates

References

Cohen, Jacob (1960). "A coefficient of agreement for nominal scales". Educational and Psychological Measurement. 20 (1): 37–46.

Sim, J., & Wright, C. C. (2005). The kappa statistic in reliability studies: use, interpretation, and sample size requirements. Physical therapy, 85(3), 257-268.

Examples

#########  Example 1  #########
# Hypothetical data from Sim and Wright (2005), Table 1
# "Diagnostic Assessments of Relevance of Lateral Shift by 2 Clinicians"
dtf <- data.frame(c1 = c(rep("Relevant", 22), rep("Relevant", 2),
                         rep("Not Relevant", 4), rep("Not Relevant", 11)),
                  c2 = c(rep("Relevant", 22), rep("Not Relevant", 2),
                         rep("Relevant", 4), rep("Not Relevant", 11)))
kappa_coef(dtf)

#########  Example 2  #########
# Hypothetical data from Sim and Wright (2005), p.260, Table 2
pain_raw <- data.frame(t1 = c(rep("No Pain", 15 + 3 + 1 + 1),
                              rep("Mild Pain", 4 + 18 + 3 + 2),
                              rep("Moderate Pain", 4 + 5 + 16 + 4),
                              rep("Severe Pain", 1 + 2 + 4 + 17)),
                       t2 = c(rep("No Pain", 15), rep("Mild Pain", 3),
                              rep("Moderate Pain", 1), rep("Severe Pain", 1),
                              rep("No Pain", 4), rep("Mild Pain", 18),
                              rep("Moderate Pain", 3), rep("Severe Pain", 2),
                              rep("No Pain", 4), rep("Mild Pain", 5),
                              rep("Moderate Pain", 16), rep("Severe Pain", 4),
                              rep("No Pain", 1), rep("Mild Pain", 2),
                              rep("Moderate Pain", 4), rep("Severe Pain", 17))
  )
# Since data is ordinal, convert columns to ordinal factors:
ordered_levels <- c("No Pain", "Mild Pain", "Moderate Pain", "Severe Pain")
pain_ordered <- data.frame(
  t1 = factor(pain_raw$t1, levels = ordered_levels, ordered = TRUE),
  t2 = factor(pain_raw$t2, levels = ordered_levels, ordered = TRUE))
table(pain_ordered)

# Unweighted Kappa Coefficient
kappa_coef(pain_ordered)
# Kappa Coefficient with linear weights
kappa_coef(pain_ordered, weights = "linear")
# Kappa Coefficient with quadratic weights
kappa_coef(pain_ordered, weights = "quadratic")