6. Three-Level Model


Model Data

Stata

use "_data/ess50prep.dta", clear

xtmixed stfdem || cntry: || region: 
estat icc

. use "_data/ess50prep.dta", clear

. 
. xtmixed stfdem || cntry: || region: 

Performing EM optimization: 

Performing gradient-based optimization: 

Iteration 0:   log likelihood = -24464.864  
Iteration 1:   log likelihood = -24464.864  

Computing standard errors:

Mixed-effects ML regression                     Number of obs     =     11,022

-------------------------------------------------------------
                |     No. of       Observations per Group
 Group Variable |     Groups    Minimum    Average    Maximum
----------------+--------------------------------------------
          cntry |         22         46      501.0      1,547
         region |        248          5       44.4         50
-------------------------------------------------------------

                                                Wald chi2(0)      =          .
Log likelihood = -24464.864                     Prob > chi2       =          .

------------------------------------------------------------------------------
      stfdem |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _cons |   5.450264   .1661121    32.81   0.000      5.12469    5.775837
------------------------------------------------------------------------------

------------------------------------------------------------------------------
  Random-effects Parameters  |   Estimate   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
cntry: Identity              |
                   sd(_cons) |   .7574878   .1209403      .5539531    1.035806
-----------------------------+------------------------------------------------
region: Identity             |
                   sd(_cons) |   .3520568    .031297      .2957624    .4190661
-----------------------------+------------------------------------------------
                sd(Residual) |   2.201376    .014992      2.172188    2.230957
------------------------------------------------------------------------------
LR test vs. linear model: chi2(2) = 1240.96               Prob > chi2 = 0.0000

Note: LR test is conservative and provided only for reference.

. estat icc

Intraclass correlation

------------------------------------------------------------------------------
                       Level |        ICC   Std. Err.     [95% Conf. Interval]
-----------------------------+------------------------------------------------
                       cntry |    .103501   .0296641      .0581124    .1776538
                region|cntry |   .1258583   .0290843      .0789848    .1946692
------------------------------------------------------------------------------

R

multi6 <- lmer(stfdem ~ (1|cntry/region), data = ess, REML = FALSE)
tidy(multi6)
glance(multi6)
icc(multi6)
## 
## Linear mixed model
##  Family: gaussian (identity)
## Formula: stfdem ~ (1 | cntry/region)
## 
##   ICC (region:cntry): 0.022357
##          ICC (cntry): 0.103499

ICC values need to be summed to equal stata’s

0.022357 + 0.103499 
## [1] 0.125856