multilevel (version 2.6)

rwg.j.sim: Simulate rwg(j) values from a random null distribution

Description

This function is based on the work of Cohen, Doveh and Eick (2001) and Cohen, Doveh and Nahum-Shani (2009). The function draws data from a random uniform null distribution, and calculates the James, Demaree and Wolf (1984) within group agreement measure rwg(j) for multiple item scales. By repeatedly drawing random samples, a distribution of the rwg(j) is generated. The sampling distribution can be used to calculate confidence intervals for different combinations of group sizes and number of items (J). Users provide the number of scale response options (A) and the number of random samples. By default, items (J) drawn in the simulation are independent (non-correlated); however, an optional argument (itemcors) allows the user to specify a correlation matrix with relationships among items. Cohen et al. (2001) show that values of rwg(j) are primarily a function of the number of items and the group size and are not strongly influenced by correlations among items; nonetheless, assuming correlations among items is more realistic and thereby is a preferred model (see Cohen et al., 2009). If item correlations are provided, the MASS library also needs to be attached.

Usage

rwg.j.sim(gsize, nitems, nresp, itemcors=NULL, nrep)

Arguments

gsize

Group size used in the rwg(j) simulation.

nitems

The number of items (J) in the multi-item scale on which to base the simulation. If itemcors are provided, this is an optional argument as nitems will be calculated from the correlation matrix.

nresp

The number of response options for the J items in the simulation (e.g., there would be 5 response options if using Strongly Disagree, Disagree, Neither, Agree, Strongly Agree).

itemcors

An optional argument containing a correlation matrix with the item correlations.

nrep

The number of rwg(j) values to simulate. This will generally be 10,000 or more, but only 1,000 are used in the examples to increase the speed.

Value

rwg.j

rwg(j) value from each of the nrep simulations.

gsize

Simulation group size.

nresp

Simulated number of response options.

nitems

Number of items in the multiple item scale. Either provided in the call or calculated from the correlation matrix, if given.

rwg.j.95

95 percent confidence interval estimate associated with a p-value of .05. Values greater than or equal to the rwg.j.95 value are considered significant.

References

Cohen, A., Doveh, E., & Nahum-Shani, I. (2009). Testing agreement for multi-item scales with the indices rwg(j) and adm(j). Organizational Research Methods, 12, 148-164.

Cohen, A., Doveh, E., & Eick, U. (2001). Statistical properties of the rwg(j) index of agreement. Psychological Methods, 6, 297-310.

James, L.R., Demaree, R.G., & Wolf, G. (1984). Estimating within-group interrater reliability with and without response bias. Journal of Applied Psychology, 69, 85-98.

See Also

rwg.j rwg rwg.sim rwg.j.lindell rgr.agree

Examples

# NOT RUN {
#An example assuming independent items
RWG.J.OUT<-rwg.j.sim(gsize=10,nitems=6,nresp=5,nrep=1000)
summary(RWG.J.OUT)
quantile(RWG.J.OUT, c(.95,.99))

#A more realistic example assuming correlated items.  The 
#estimate in Cohen et al. (2006) is .61.

data(lq2002)
library(MASS)
RWG.J.OUT<-rwg.j.sim(gsize=10,nresp=5,
  itemcors=cor(lq2002[,c("TSIG01","TSIG02","TSIG03")]),
  nrep=1000)
summary(RWG.J.OUT)
quantile(RWG.J.OUT,c(.95,.99))
# }