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

From   Garry Anderson <>
Subject   st: 'between' coefficient in xtreg with completed ref #4
Date   Wed, 12 Nov 2003 11:23:06 +1100

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,
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
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