waba: Covariance Theoreom Decomposition of Bivariate Two-Level...

In multilevel: Multilevel Functions

Covariance Theoreom Decomposition of Bivariate Two-Level Correlation

Description

Performs the covariance theorem decomposition of a raw correlation in situations where lower-level entities (individuals) are nested in higher-level groups (see Robinson, 1950). Dansereau, Alutto and Yammarino (1984) refer to the variance decomposition as "Within-And-Between-Analysis II" or "WABA II". The waba function decomposes a raw correlation from a two-level nested design into 6 components. These components are (1) eta-between value for X, (2) eta-between value for Y, (3) the group-size weighted group-mean correlation, (4) the within-eta value for X, (5) the within-eta value for Y, and (6) the within-group correlation between X and Y. The last value represents the correlation between X and Y after each variable has been group-mean centered (demeaned).

The program is designed to automatically perform listwise deletion on missing values; consequently, users should pay attention to the diagnostic information (Number of Groups and Number of Observations) provided as part of the output.

Note that Within-And-Between-Analysis proposed by Dansereau et al. involves more than covariance theorem decomposition of correlations. Specifically, WABA involves decision rules based on eta-values. These are not replicated in the R multilevel library because the eta based decision rules have been shown to be highly related to group size (Bliese, 2000; Bliese & Halverson, 1998), a factor not accounted for in the complete Within-And-Between-Analysis methodology.

Usage

waba(x, y, grpid)

Arguments

x	A vector representing one variable in the correlation.
y	A vector representing the other variable in the correlation.
grpid	A vector identifying the groups from which x and y originated.

Value

Returns a list with three elements.

Cov.Theorem	A 1 row dataframe with all of the elements of the covariance theorem.
n.obs	The number of observations used to calculate the covariance theorem.
n.grps	The number of groups in the data set.

Author(s)

Paul Bliese [e-mail]

References

Bliese, P. D. (2000). Within-group agreement, non-independence, and reliability: Implications for data aggregation and Analysis. In K. J. Klein & S. W. Kozlowski (Eds.), Multilevel Theory, Research, and Methods in Organizations (pp. 349-381). San Francisco, CA: Jossey-Bass, Inc.

Bliese, P. D., & Halverson, R. R. (1998). Group size and measures of group-level properties: An examination of eta-squared and ICC values. Journal of Management, 24, 157-172.

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

rgr.waba

Examples

data(bh1996)
waba(bh1996$HRS,bh1996$WBEING,bh1996$GRP)

multilevel documentation built on March 18, 2022, 5:47 p.m.