## Stata 15 help for icc

```
[R] icc -- Intraclass correlation coefficients

Syntax

Calculate intraclass correlations for one-way random-effects model

icc depvar target [if] [in] [, oneway_options]

Calculate intraclass correlations for two-way random-effects model

icc depvar target rater [if] [in] [, twoway_re_options]

Calculate intraclass correlations for two-way mixed-effects model

icc depvar target rater [if] [in], mixed [twoway_me_options]

oneway_options          Description
-------------------------------------------------------------------------
Main
absolute              estimate absolute agreement; the default
testvalue(#)          test whether intraclass correlations equal #;
default is testvalue(0)

Reporting
level(#)              set confidence level; default is level(95)
format(%fmt)          display format for statistics and confidence
intervals; default is format(%9.0g)
-------------------------------------------------------------------------

twoway_re_options       Description
-------------------------------------------------------------------------
Main
absolute              estimate absolute agreement; the default
consistency           estimate consistency of agreement
testvalue(#)          test whether intraclass correlations equal #;
default is testvalue(0)

Reporting
level(#)              set confidence level; default is level(95)
format(%fmt)          display format for statistics and confidence
intervals; default is format(%9.0g)
-------------------------------------------------------------------------

twoway_me_options       Description
-------------------------------------------------------------------------
Main
* mixed                 estimate intraclass correlations for a
mixed-effects model
consistency           estimate consistency of agreement; the default
absolute              estimate absolute agreement
testvalue(#)          test whether intraclass correlations equal #;
default is testvalue(0)

Reporting
level(#)              set confidence level; default is level(95)
format(%fmt)          display format for statistics and confidence
intervals; default is format(%9.0g)
-------------------------------------------------------------------------
* mixed is required.

bootstrap, by, jackknife, and statsby are allowed; see prefix.

Statistics > Summaries, tables, and tests > Summary and descriptive
statistics > Intraclass correlations

Description

icc estimates intraclass correlations for one-way random-effects models,
two-way random-effects models, or two-way mixed-effects models for both
individual and average measurements.  Intraclass correlations measuring
consistency of agreement or absolute agreement of the measurements may be
estimated.

Options for one-way RE model

+------+
----+ Main +-------------------------------------------------------------

absolute specifies that intraclass correlations measuring absolute
agreement of the measurements be estimated.  This is the default for
random-effects models.

testvalue(#) tests whether intraclass correlations equal #.  The default
is testvalue(0).

+-----------+
----+ Reporting +--------------------------------------------------------

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.

format(%fmt) specifies how the intraclass correlation estimates and
confidence intervals are to be formatted.  The default is
format(%9.0g).

Options for two-way RE and ME models

+------+
----+ Main +-------------------------------------------------------------

mixed is required to calculate two-way mixed-effects models.  mixed
specifies that intraclass correlations for a mixed-effects model be
estimated.

absolute specifies that intraclass correlations measuring absolute
agreement of the measurements be estimated.  This is the default for
random-effects models.  Only one of absolute or consistency may be
specified.

consistency specifies that intraclass correlations measuring consistency
of agreement of the measurements be estimated.  This is the default
for mixed-effects models.  Only one of absolute or consistency may be
specified.

testvalue(#) tests whether intraclass correlations equal #.  The default
is testvalue(0).

+-----------+
----+ Reporting +--------------------------------------------------------

level(#) specifies the confidence level, as a percentage, for confidence
intervals.  The default is level(95) or as set by set level.

format(%fmt) specifies how the intraclass correlation estimates and
confidence intervals are to be formatted.  The default is
format(%9.0g).

Examples

Setup
. webuse judges

Calculate ICCs for one-way random-effects model
. icc rating target

Same as above but test whether ICCs equal 0.5
. icc rating target, testvalue(.5)

Calculate ICCs for two-way random-effects model
. icc rating target judge

Same as above but estimate consistency of agreement
. icc rating target judge, consistency

Calculate ICCs for two-way mixed-effects model
. icc rating target judge, mixed

Same as above but estimate absolute agreement
. icc rating target judge, mixed absolute

Stored results

icc stores the following in r():

Scalars
r(N_target)    number of targets
r(N_rater)     number of raters
r(icc_i)       intraclass correlation for individual measurements
r(icc_i_F)     F test statistic for individual ICC
r(icc_i_df1)   numerator degrees of freedom for r(icc_i_F)
r(icc_i_df2)   denominator degrees of freedom for r(icc_i_F)
r(icc_i_p)     p-value for F test of individual ICC
r(icc_i_lb)    lower endpoint for confidence intervals of individual
ICC
r(icc_i_ub)    upper endpoint for confidence intervals of individual
ICC
r(icc_avg)     intraclass correlation for average measurements
r(icc_avg_F)   F test statistic for average ICC
r(icc_avg_df1) numerator degrees of freedom for r(icc_avg_F)
r(icc_avg_df2) denominator degrees of freedom for r(icc_avg_F)
r(icc_avg_p)   p-value for F test of average ICC
r(icc_avg_lb)  lower endpoint for confidence intervals of average ICC
r(icc_avg_ub)  upper endpoint for confidence intervals of average ICC
r(testvalue)   null hypothesis value
r(level)       confidence level

Macros
r(model)       analysis-of-variance model
r(depvar)      name of dependent variable
r(target)      target variable
r(rater)       rater variable
r(type)        type of ICC estimated (absolute or consistency)

```