Ineta Sokolowski <[email protected]> wrote:
> I wish, there were more details in manual.
Me too. I will make some changes to this manual entry.
Ineta continued with
>
> I need the variance components to calculate the ICC (intra class
> correlation). I tried different methods to calculate ICC, including
> -loneway- and -xtsum-, but it gives very different result.
-xtsum- and -loneway- are producing different summaries of your data.
-loneway- produces estimates of the variance components and the intraclass
correlation. -xtsum- is simply summarizing the within and between
transformed variables.
If you are interested in estimating the ICC, use the results reported by
-loneway-, not -xtsum-.
Ineta also asked for more details. My previous posting provides the details
of what -xtsum- is doing and [R] loneway provides the details of what
-loneway- is doing. Rather than repeat what is available elsewhere, I will
attempt to illustrate what -loneway- is doing by comparing it with another
other estimator of the ICC.
I will use an unbalanced longitudinal dataset on complaints by person over
time. The dependent variable, complain, is binary.
. clear
. set mem 10m
(10240k)
. use http://www.stata-press.com/data/r8/chicken
Now let's use -loneway- to estimate the ICC.
. loneway complain person
One-way Analysis of Variance for complain:
Number of obs = 5952
R-squared = 0.2885
Source SS df MS F Prob > F
-------------------------------------------------------------------------
Between person 239.46604 1075 .2227591 1.84 0.0000
Within person 590.52976 4876 .12110947
-------------------------------------------------------------------------
Total 829.9958 5951 .13947165
Intraclass Asy.
correlation S.E. [95% Conf. Interval]
------------------------------------------------
0.13175 0.01204 0.10815 0.15535
Estimated SD of person effect .1355647
Estimated SD within person .3480079
Est. reliability of a person mean 0.45632
(evaluated at n=5.53)
-loneway- estimates the ICC without any controls. Thus, another way of
estimating the ICC would be to estimate the parameters of random-effects
model without any covariates.
Recall that a random-effects model on a constant only is
y_it = cons + u_i + e_it
where
y_it are the observations on the dependent variable;
cons is a fixed constant to be estimated;
u_i are the unobserved individual level effects,
the u_i are assumed to be identically and independently distributed
(i.i.d.) over the individuals in the sample,
E[u_i e_it] = 0; and,
e_it are the unobserved idiosyncratic errors which are assumed to be
i.i.d. over the entire sample.
With unbalanced data, -xtreg- with the -sa- option will produce an estimate
of the ICC that is very similar to the one produced by -loneway- but not
exactly the same. With balanced data, the estimates will be the same.
Until an update in the near future, -xtreg ,sa- does not run with a constant
only model. However, we can fit the model by including a manually generated
constant, as in the output below.
. gen one = 1
. xtreg complain one , i(person) sa
Random-effects GLS regression Number of obs = 5952
Group variable (i): person Number of groups = 1076
R-sq: within = 0.0000 Obs per group: min = 3
between = 0.0000 avg = 5.5
overall = 0.0000 max = 8
Random effects u_i ~ Gaussian Wald chi2(0) = 738.70
corr(u_i, X) = 0 (assumed) Prob > chi2 = .
------------------------------------------------------------------------------
complain | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
one | .1685169 .0062002 27.18 0.000 .1563646 .1806691
_cons | (dropped)
-------------+----------------------------------------------------------------
sigma_u | .13560089
sigma_e | .34800786
rho | .13181353 (fraction of variance due to u_i)
------------------------------------------------------------------------------
In -xt- terms, the SD of the person effect is the standard deviation of the
individual level effect and the SD within person is the standard deviation
of the idiosyncratic error. -loneway- and -xtreg, sa- each have a
consistent estimator of the standard deviation of the individual level
effect, to use the -xt- terminology. In fact, these estimators produce
exactly the same estimates from balanced data, but, since they use distinct
adjustments for unbalanced data, they produce slightly different estimates
from unbalanced datasets. -loneway- and -xtreg , sa- are using the same
estimator of the standard deviation of idiosyncratic error.
Neither of these estimators explicitly takes account of the binary nature of
the dependent variable.
I hope that this helps.
David
[email protected]
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/
