## Concept Description

Last Updated: 2009-02-03

### Introduction

The intraclass (sometimes called intracluster) correlation coefficient (ICC) tells us how similar elements in the same cluster (group) are. It provides a measure of homogeneity within the clusters (Lohr, Sharon L. (1999)). It ranges from 0 to 1 with values closer to 1 indicating greater homogeneity.

The information in this concept is attributable to Phongsack Manivong, who worked with Dr. L. Roos at MCHP in 2008/2009.

### Applicability to MCHP Research

• The ICC is used to determine how similar values of some variable are within the same class/group. Essentially, it is a measure of the WITHIN subject (group) variability. Within each group, the mean of a value can be computed, and if values are similar then the difference between the mean and a single value will be small. With this being said, the ICC is thus, not necessarily a correlation between two outcomes.

• The ICC is particularly relevant for work with families and siblings because of the possibility of having more than two siblings within a family (group).

• In MCHP research using the ICC, the variable investigated was the Language Arts Achievement Index test scores. For more information on the Language Arts Achievement Index, see the Education Indices concept.

### SAS Programming

There are two main SAS procedures that can be used to compute an ICC:

### 1. PROC NLMIXED

• can compute an ICC for a continuous or binary outcome.
• can be used to compute an ICC when there are families with three kids without looking at individual pairs.
• can handle varying sample family sizes. For example, it can compute an ICC using families with two kids, or three kids, or more at the same time.

### 2. PROC MIXED

• can compute an ICC only for continuous outcomes.
• an ICC has to be computed manually or by manipulating the covariance parameter output dataset. Refer to section 3 containing the ODS statement in the SAS code examples below.
• if there are many clusters (levels or groups in the RANDOM variable), this can be problematic as SAS can run out of memory.
See the SAS code and formats section below for more information on different methods of computing the ICC and for an example of each method.

## References

• Lohr SL. Sampling: Design and Analysis. Pacific Grove, CA: Duxbury Press; 1999.(View)