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

Description Usage Arguments Value Author(s) References See Also Examples


This routine performs the covariance theorem decomposition discussed by Robinson (1950) and Dansereau, Alutto and Yammarino (1984). Dansereau et al. have labeled the variance decomposition Within-And-Between-Analysis II or WABA II. The program 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.

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.


waba(x, y, grpid)



A vector representing one variable in the correlation.


A vector representing the other variable in the correlation.


A vector identifying the groups from which x and y originated.


Returns a list with three elements.


A 1 row dataframe with all of the elements of the covariance theorem.


The number of observations used to calculate the covariance theorem.


The number of groups in the data set.


Paul Bliese paul.bliese@moore.sc.edu


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.

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