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From |
Garry Anderson <g.anderson@unimelb.edu.au> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: 'between' coefficient in xtreg |

Date |
Tue, 11 Nov 2003 17:48:14 +1100 |

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

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