#### Abstract

We propose a new parameter for measuring the influence of a random effect in a mixed linear model. This is the probability of preponderance of the random effect under study over the other random effects. In a one-way random effects model, this is simply the probability the group random effect is larger in absolute size than the individual random effect (or error). We discuss the meaning of the parameter and relate it to the more familiar intraclass correlation coefficient. The new parameter has the appealing property that it is applicable for any distribution, whereas the intraclass correlation has its origins in normally distributed random effects. Furthermore, the new parameter directly measures the random effect's impact on the observations whereas the intraclass correlation relies on the variances (second moments) of the random effects. We suggest parametric and nonparametric estimators of the parameter, and demonstrate the applicability of the results using real data. We also indicate how to extend the ideas to models with more than two sources of variation.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

#### Recommended Citation

Harris, Ian R. and Burch, Brent D.
(2003).
"THE PROBABILITY OF PREPONDERANCY: AN ALTERNATIVE TO THE INTRACLASS CORRELATION,"
*Conference on Applied Statistics in Agriculture*.
http://newprairiepress.org/agstatconference/2003/proceedings/11

THE PROBABILITY OF PREPONDERANCY: AN ALTERNATIVE TO THE INTRACLASS CORRELATION

We propose a new parameter for measuring the influence of a random effect in a mixed linear model. This is the probability of preponderance of the random effect under study over the other random effects. In a one-way random effects model, this is simply the probability the group random effect is larger in absolute size than the individual random effect (or error). We discuss the meaning of the parameter and relate it to the more familiar intraclass correlation coefficient. The new parameter has the appealing property that it is applicable for any distribution, whereas the intraclass correlation has its origins in normally distributed random effects. Furthermore, the new parameter directly measures the random effect's impact on the observations whereas the intraclass correlation relies on the variances (second moments) of the random effects. We suggest parametric and nonparametric estimators of the parameter, and demonstrate the applicability of the results using real data. We also indicate how to extend the ideas to models with more than two sources of variation.