st: 'between' coefficient in xtreg with completed ref #4

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

Dear All,

(My previous email did not have the complete reference for reference #4. I 
apologize for this omission)

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. 
Statistics in Medicine 22(16) : 2591-2602

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  
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