ad.m.sim {multilevel}R Documentation

Simulate significance of average deviation around mean or median

Description

This function uses procedures detailed in Dunlap, Burke & Smith-Crowe (2003) and Cohen, Doveh & Nahum-Shani (2006) to estimate the significance of the average deviation around the mean or median (AD.M). Dunlap et al. proposed a strategy to use Monte Carlo techniques to estimate the significane of single item AD.M measures. Cohen et al., (2006) expanded these ideas to cover multiple item scales, ADM(J) and account for correlations among items. The ad.m.sim function is flexible and covers single item or multiple item measures. In the case of multiple item measures, correlations among items can be included (preferred method) or excluded. If item correlations are provided, the mvrnorm function in the MASS library is needed. In the Monte Carlo simulations conducted by both Dunlap et al. (2003) and Cohen et al., (2006), 100,000 repetitions were used. In practice, it will require considerable time to perform 100,000 repititions in the ad.m.sim function and in most cases 10,000 will most likely suffice. The examples use 1,000 repetitions simply for speed purposes.

Usage

ad.m.sim(gsize, nitems=1, nresp, itemcors=NULL, type="mean",nrep)

Arguments

gsize Simulated group size.
nitems Number of items to simulate. The default is 1 for single item measures. If itemcors are provided, this is an optional argument as nitems will be calculated from the correlation matrix, thus it is only necessary for multiple item scales where no correlation matrix is provided.
nresp The number of response options on the items. For instance, nresp would equal 5 for a 5-point response option ranging from strongly disagree, disagree, neither, agree strongly agree.
itemcors An optional matrix providing correlations among items.
type A character string with either "mean" or "median".
nrep The number of simulation repetitions. In published sources 100,000 simulations were used. In practice 10,000 repetitions probably suffices. In the examples, 1,000 are used simply to make the examples fast.

Value

ad.m Simulated estimates of AD.M values for each of the nrep runs.
gsize Simulated group size.
nresp Simulated number of response options.
nitems Number of items. Either provided in the call (default of 1) or calculated from the correlation matrix, if given.
ad.m.05 Estimated p=.05 value. Observed values equal to or smaller than this value should be considered significant.
pract.sig Estimate of practical significance calculated as nresp/6 (see ad.m).

Author(s)

Paul Bliese paul.bliese@us.army.mil

References

Cohen, A., Doveh, E. & Nahum-Shani, I. (2006). Testing agreement for multi-item scales with the indices rwg(j) and adm(j). Israel Institute of Technology, Haifa.

Dunlap, W. P., Burke, M. J., & Smith-Crowe, K. (2003). Accurate tests of statistical significance for rwg and average deviation interrater agreement indices. Journal of Applied Psychology, 88, 356-362.

See Also

ad.m rgr.agree rwg.sim rwg.j.sim

Examples

#Example from Dunlap et al. (2003), Table 3.  The listed significance value (p=.05)
#for a group of size 5 with a 7-item response format is 0.64 or less 
SIMOUT<-ad.m.sim(gsize=5, nitems=1, nresp=7, itemcors=NULL, type="mean", nrep=1000) 
summary(SIMOUT)

#Example with a multiple item scale basing item correlations on observed correlations
#among 11 leadership items in the lq2002 data set.  Estimate in Cohen et al., (2006)
#is 0.99
library(MASS)
data(lq2002)
SIMOUT<-ad.m.sim(gsize=10, nresp=5, itemcors=cor(lq2002[,3:13]), type="mean", nrep=1000) 
summary(SIMOUT)
quantile(SIMOUT,c(.05,.10))

[Package multilevel version 2.2 Index]