st: Design Effect via -loneway- and -svymean-

[Garry Anderson <g.anderson@unimelb.edu.au>]

Hi,

I am trying to figure out why there is a slight discrepancy between the 
value of the design effect (deff) as reported by -svymean- and that 
calculated from using the intraclass correlation coefficient from -loneway- 
and the adjusted mean cluster size.

I have an example where the discrepancy is larger than the following 
example, but I have chosen the following for demonstration because of the 
availability of a data file via Stata

use http://www.stata-press.com/data/r8/auto7.dta

-svyset,psu(manufacturer_grp)-
-svymean mpg-
reports the  deff as   1.836013

Using   -loneway mpg manufacturer_grp-
reports the intraclass correlation as  0.36827

A formula to obtain the intraclass correlation coefficient from loneway is

rho  = (MSB-MSW) / (MSB + (n_o - 1) MSW)  =  0.36827

where n_o = 1/(k-1) [N - sum_i (n_i^2/N]  =  3.1584767
k = number of groups = 23
N = total sample size = 74

Variance Inflation Factor = 1 + (n_o - 1) rho
 = 1 + (3.1584767 - 1) * 0.36827
=  1.7949

The 1.7949 derived from -loneway- does not equal the value of 1.836013 that 
is reported for Deff from -svymean-.

Any clues would be much appreciated.

Kind regards, Garry 
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