st: 'between' coefficient in xtreg

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

Dear All,

I am querying the interpretation of the 'between' coefficient b1 in the 
following

Y_ij = a + (Xbar_i) b1 + (x_ij - Xbar_i) b2 + v_i + e_ij       (1)

According to the references below, except Begg et al, this is interpreted 
as the effect of xbar_i when xbar_i changes between clusters. However, Begg 
et al argue that the estimate of b1 is not estimating the direct effect of 
the cluster-level mean.

The equation
Y_ij = a + (Xbar_i) b11 + v_i + e_ij                  (2)

estimates b11 as the same value as b1 in equation (1)
Therefore, b1 in equation 1 does not seem to be adjusting for anything, 
especially the change in Xij that can occur with the change in Xbar_i .

Y_ij = a + (Xbar_i) b12 + (x_ij) b22 + v_i + e_ij     (3)

The coefficient b12 seems to give the true effect of a change in cluster 
mean, in that
b12 = b1 - b2

- xtreg y x_ij,i(cluster) be -
gives a coefficient that is equal to b1 and b11.

Any comments or clarifications would be much appreciated.

The above has cited
1. Stata reference manual xtreg,
2. http://www.stata.com/support/faqs/stat/xt.html
3. Neuhaus JM and Kalbfleisch DD (1998) Between- and within-cluster 
covariate effects in the analysis of clustered data. Biometrics 54:638-645
4. Begg MD and Parides MK (2003) Separation of individual-level and 
cluster-level covariate effects in regression analysis of correlated data

Kind regards, Garry


Garry Anderson
School of Veterinary Science
University of Melbourne
250 Princes Highway           Ph  03 9731 2221
WERRIBEE    3030             Fax  03 9731 2388
Email:  g.anderson@unimelb.edu.au 
*
*   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/