# Random Group Resampling of Covariance Theorem Decomposition

### Description

This routine performs the covariance theorem decomposition discussed by Robinson (1950) and Dansereau, Alutto and Yammarino (1984), but builds upon this work by incorporating Random Group Resampling or RGR. RGR is used to randomly assign individuals to pseudo groups. This creates sampling distributions of the covariance theorem components, and allows one to contrast actual group covariance components to pseudo group covariance components.

Note that rgr.waba is a labor intensive routine.

### Usage

1 | ```
rgr.waba(x, y, grpid, nrep)
``` |

### Arguments

`x` |
A vector representing one variable for the correlation. |

`y` |
A vector representing the other variable for the correlation. |

`grpid` |
A vector identifying the groups from which X and Y originated. |

`nrep` |
The number of times that the entire data set is reassigned to pseudo groups |

### Value

Returns an object of class rgr.waba. The object is a list containing each random run for each component of the covariance theorem.

### Author(s)

Paul Bliese paul.bliese@moore.sc.edu

### References

Bliese, P. D. & Halverson, R. R. (1996). Individual and nomothetic models of job stress: An examination of work hours, cohesion, and well- being. Journal of Applied Social Psychology, 26, 1171-1189.

Bliese, P. D., & Halverson, R. R. (2002). Using random group resampling in multilevel research. Leadership Quarterly, 13, 53-68.

Dansereau, F., Alutto, J. A., & Yammarino, F. J. (1984). Theory testing in organizational behavior: The varient approach. Englewood Cliffs, NJ: Prentice-Hall.

Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. American Sociological Review, 15, 351-357.

### See Also

`waba`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
# This example is from Bliese & Halverson (1996). Notice that all of the
# values from the RGR analysis differ from the values based on actual
# group membership. Confidence intervals for individual components can
# be estimated using the quantile command.
data(bh1996)
#estimate the actual group model
waba(bh1996$HRS,bh1996$WBEING,bh1996$GRP)
#create 100 pseudo group runs and summarize the model
RWABA<-rgr.waba(bh1996$HRS,bh1996$WBEING,bh1996$GRP,100)
summary(RWABA)
#Estimate 95th percentile confidence intervals (p=.05)
quantile(RWABA,c(.025,.975))
``` |