ad.m.sim {multilevel}

Simulate significance of average deviation around mean or median

Description

Uses procedures detailed in Dunlap, Burke, and Smith-Crowe (2003) and Cohen, Doveh, and Nahum-Shani (2009) to estimate the significance of the average deviation of 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., (2009) 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. In the Monte Carlo simulations conducted by both Dunlap et al. (2003) and Cohen et al., (2009), 100,000 repetitions were used. In practice, it will require considerable time to perform 100,000 repetitions and 10,000 should suffice. The examples use 500 repetitions simply to speed up the process.

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, the nitems option will be ignored, so the nitems option 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 of 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.

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 itemcors correlation matrix.

ad.m.05

Estimated p=.05 value. Observed values equal to or smaller than this value are considered significant.

pract.sig

Estimate of practical significance calculated as nresp/6 (see ad.m).

Author(s)

Paul Bliese [e-mail]

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.

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. Use more than 500 iterations in practice.
 
SIMOUT<-ad.m.sim(gsize=5, nitems=1, nresp=7, itemcors=NULL,
        type="mean", nrep=500) 
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., (2009) is 0.99

data(lq2002)
SIMOUT<-ad.m.sim(gsize=10, nresp=5, itemcors=cor(lq2002[,3:13]), 
        type="mean", nrep=500) 
summary(SIMOUT)
quantile(SIMOUT,c(.05,.10))