Re: st: minor queries about new official Stata commands -icc- & -estat icc-

[clindsey@stata.com (Charles Lindsey, StataCorp)]

Tom Palmer had several questions about the new commands -icc- and -estat icc-:

> I see StataCorp released two new commands for calculating the intraclass
> correlation coefficient (ICC) and confidence intervals in the 23 May update. I
> wonder if they could provide some more detail before the manual entries are
> available.

The -estat icc- command is documented in the [XT] xtmixed postestimation and
[XT] xtmelogit postestimation entries.  The updated entries can be accessed
through the links provided in the corresponding PDF documentation.  The
documentation for -icc- is forthcoming.

> I think:
>
> 1.a. -icc- reports CIs using an F distribution like a user-written command 
> called -iccconf- (-ssc describe iccconf-).

The confidence intervals reported by -icc- do use the F distribution.  The
-icc- command implements methodology described in Shrout and Fleiss (1979) and
McGraw and Wong (1996).


>  b. by default -estat icc- reports CI limits back-transformed from a logit 
>  transformation; presumably because this has similar properties to
>  Fisher's z as per Nick Cox's Stata Journal article (SJ 2008, 8-3, 413-439).

Using the Fisher's z transformation as suggested in Cox (2008) provides a
confidence interval for a correlation coefficient limited to be in the range
(-1,1).  Similarly, back-transforming from the logit transformation in -estat
icc- provides a confidence interval for an intraclass correlation coefficient
limited to be in the range (0,1).


> c. -estat icc- has an undocumented -normal- option which reports a 
> delta-method SE and CI limits as obtained from -nlcom-.

This is correct.  This option is intended primarily for internal testing
purposes.


> 2. -estat icc- works after -xtmixed- and -xtmelogit-, but not after 
> -xtmepoisson-. Is there a specific reason for this?

The command -estat icc- is only allowed after -xtmixed- and -xtmelogit-.  The
use of -estat icc- after -xtmepoisson- is not supported.  

The -estat icc- command employs the definition of ICC with respect to
continuous responses.  For binary variables, the definition of ICC is based on
the latent-response formulation of a binary multilevel model.  No such
formulation exists for Poisson multilevel models so -estat icc- is not
supported after -xtmepoisson-.


References:

Cox, Nicholas J.  Speaking Stata: Correlation with confidence, or Fisher's z
revisited.  The Stata Journal 8: 413-439.

McGraw, K. O., and S. P. Wong. 1996a.  Forming inferences about some
intraclass correlation coefficients.  Psychological Methods 1: 30-46.

Shrout, P. E., and J. L. Fleiss.  1979.  Intraclass correlations: Uses in
assessing rater reliability.  Psychological Bulletin 86: 420-428.


-- Charles
clindsey@stata.com
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